In this paper we introduce a two-level modular neuro fuzzy network based on incentive games where the modules are organized as autonomous local optimizers in a leader-follower game hierarchy. Incentive-reaction pairs are used as a measure for the capacity and responsiveness assessment of each follower module. Learning within the follower modules is performed in a traditional error-based manner (e.g., backpropagation) The allocation of targets and incentives to each follower module , on the other hand is independent of connection weights; incentive games are used for that purpose. Two important advantages of the new architecture are its physically significant follower module outputs and the context-based enhancement it makes to backpropagation.
Keywords: neural fuzzy systems, incentive games, system identification
One of the desirable properties of generalized modus ponens in fuzzy
X is A----> Y is B
X is not A
Y is unknown
From a truth-value viewpoint, unknown can be represented as the interval [0,1]. However, most existing fuzzy reasoning mechanisms use the truth value 1 to represent ``unknown''. In this paper, we propose a new approach to fuzzy reasoning based on a possible world approach. We show that our approach obtains the desired interval truth value [0, 1] when the known proposition is the negation of the antecedent. We also compare our approach to Baldwin's and Godo's approaches and discuss the impact of the proposed approach to other desired properties of generalized modus ponens and generalized modus tollens.
Department of Mathematics,Physical Science and Engineering Technology
West Texes A&U University
WT Box 787
Traditional fuzzy logic inference and control algorithm can not be used effectively in phaserelated mechanical velocity control since fuzzy logic is essentially a trail strategy which is based upon observation from the next system response.Experimental results and process applications show that this algorithm is not suitable for fast-reaction system.This report will discuss a modified fuzzy inference/control algorithm - lead and lag fuzzy logic compensation algorithm,which uses lead and lag algorithm to compensate phase error.This algorithm was used on multiple-function food-packing lines successfully.It can trace the phase correctly and reduce phase accumulate-error within an accpetable degree.
Department of Industrial Engineering
Texas Tech University
This report systematically reviewed the historical development,theoretical research and practical application of the fuzzy logic inference-control modeling (FLM) for the complex systems- multiple-input-multiple-output (MIMO) system and nonlinear system.The most common and important issues related with fuzzy models: self- organizing FLM,adaptive flm,general purpose FLM,Mamdani-FLM and Tagagi-Sugeno-Kang FLM,fuzzy vector-spaces,hierarchical structured FLM,and fuzzy phase-plane,were exhibited,analyzed,or compared.The survey reveal that the design of inference and control system,especial for MIMO systems and nonlinear systems with uncertainty,can be considered through multiple scenarios,not just thrir rigid dynamic mathematical models but also fuzzy logic models.
The Life Cycle Analysis in Systems Engineering and Environmental Engineering is associated with large uncertainties, being of a forecasting, or predictive nature. Various approaches are used to estimate trends in the Life Cycle, either by probabilistic nature or by fuzzy variables. Regardless approach, the models are used for decision support and need to be assured and controlled for their quality in describing the real situation. The paper draws attention to this problem, and suggests methods for cross-checking simulation models, by various methods based on underlying fundamental principles, asymptotic conditions, average properties, submodel interrelations, etc. A generic Systems Engineering Principles approach is used in developing the model of the Life Cycle. This approach is based on analyses and justifications of needs and a definition of requirements to the model and its simulation result.
To develop quality systems, both engineering and management require fundamental principles and methodologies to guide design decision making and advanced planning. This paper presents a systematic approach to support the need for developing better system designs in the face of uncertainties. This approach is developed by integrating statistical decision theory, elements of the systems engineering process, and Taguchi's philosophy of robust design. The result is a structured, systematic methodology for evaluating system design alternatives.
Keywords: Design Evaluation, Robust Design, Systems Analysis, Decision Analysis, Uncertainty Analysis, Design Optimization
The emergence of semantic structure as a self-organizing process is studied in Semiotic Cognitive Information Processing Systems on the basis of word usage regularities in natural language discourse whose linearly agglomerative (syntagmatic) and whose selectively interchangeable (paradigmatic) constraints are exploited by text analysing algorithms. They accept natural language discourse as input and produce a vector space structure as output which may be interpreted as an internal (endo) representation of the SCIP system's states of adaptation to the external (exo) structures of its environment as mediated by the discourse processed. In order to evaluate the sytem's endo-representation against the exo-view of its environment as described by the natural language discourse processed, a corpus of texts -- composed of correct and true sentences with well-defined referential meanings -- was generated according to a (very simple) phrase structure grammar and a fuzzy referential semantics which interpret simple composite predicates of cores (like: on the left, in front, etc.) and hedges (like: extremely nearby, very faraway, etc.). Processed during the system's training phase, the corpus reveals structural constraints which the system's hidden structures or internal meaning representations apparently reflect. The system's architecture is a two-level consecutive mapping of distributed representations of systems of (fuzzy) linguistic entities whose states acquire symbolic functions that can be equaled to (basal) referencial predicates. Test results from an experimental setting with varying fuzzy interpretations of hedges are produced to illustrate the SCIP system's miniature (cognitive) language understanding and meaning acquisition capacity without any initial explicit syntactic and semantic knowledge.
Institute of Computer Science and Information Engineering
National Chung-Cheng University, Chiayi, Taiwan, R.O.C.
(email@example.com) and (firstname.lastname@example.org)
A new fuzzy filter, called Weighted Fuzzy Mean (WFM) filter is proposed and analyzed in this paper. The WFM filter is powerful for removing heavy additive impulse noises from images. By the filtering of each WFM filter, the filtered output signal is the mean value of the corrupted signals in a sample matrix, and these signals are weighted respectively by a membership grade of an associated fuzzy number stored in a knowledge base. The knowledge base contains a set of fuzzy numbers decided by experts or derived from the histogram of referred image. When the probability of occurrence of mixed impulse noises is over 0.3, the WFM filter can recover the noise- corrupted image quite well in contrast with the conventional filters, for examples, the median filters, RCRS, WOS, CWM, an stack filters, based on the Mean Absolute Error (MAE) and Mean Square Error (MSE) criteria. Besides, on the subjective evaluation of filtered images, the WFM filter also results in a higher quality of global restoration.
Keywords: Weighted Fuzzy Mean Filter, Impulse Noise, Fuzzy Number, Knowledge Base, Histogram, Fuzzy Estimator
V. B. Kats
Department of Industrial Engineering
Ben Gurion University of the Negev
Beer Sheva, ISRAEL 84105
L. K. Meyzin
Department of Computer Systems
Holon Center for Technological Education
Holon, ISRAEL 58102
A problem of scheduling a transportation robot in a production line with uncertain input data is considered. The data are presented by fuzzy numbers. A heuristic algorithm based on operations over the fuzzy numbers is developed. In the case of exact input data the algorithm produces an exact solution, its complexity being qubic in the number of workstations in the line. The fuzzy algorithm has been tested on real-life problems, and turned out to work better than the random search and FIFO-type heuristics.
Keywords: Scheduling, Heuristics, Fuzzy Algorithms
The US Army Corps of Engineers (USACE) has designed pile-founded navigation structures to provide a consistently high level of safety and serviceability. This has been achieved by utilizing allowable values for pile stresses, pile load capacity, and deflections in their design. The reliability assessment of older in-service pile-founded navigation structures can be developed using the same limit states used in the design of new pile-founded structures. This paper will be to examine the reliability assessment of timber pile-founded navigation structures without the loss of support. The techniques developed to perform the reliability assessment employ a capacity/demand relationship for limit states of axial capacity, lateral deflections, axial deflections, and combined bending. Monte Carlo Simulations and First Order Second Moment techniques were utilized to calibrate the limit states to an instrumented pile load test data from field tests. An example of a river dam monolith subjected to impact loading will also be discussed.
Keywords: Reliability assessment, pile foundations, navigation structures, timber piles, dams
In microprocessor system diagnosis, temporal reasoning of event changes occurring at imprecisely known time instants is an important issue. The time range approach was proposed to capture the notion of time imprecision in event occurrence. According to this concept, efficient time range constraint reasoning techniques were developed for embedding domain knowledge in a deep-level constraint model. The imprecision in these events contributes to a certain degree of uncertainty in the correctness of a microprocessor system operation. A knowledge-based diagnostic system for microprocessor systems design was designed and developed. The system performs worst-case timing analysis. In particular, for the asynchronous bus operation of the MC68000 microprocessor, the sequence of events during a read cycle was traced through an inference process to determine if any constraint in the model was violated. Although satisfactory results were obtained, the possibility measures implicitly embedded within time ranges were not properly quantified for effective temporal reasoning. To overcome this shortcoming, the fuzzy time point model is proposed. The original time-range representation, specified by two crisp interval end-points, is replaced by the fuzzy time point representation that is specified by a single fuzzy value. The degree of fuzziness of a fuzzy time point has dependency on the functional specification of the corresponding timing parameter. The use of simplistic assumptions on the fuzzy time point model has been shown to enhance the deductive capability of the existing time-range models. The implementation of this system extension has shown promising results in fuzzy time point reasoning.
Keywords: Temporal uncertainty modeling, fuzzy time point reasoning, microprocessor systems diagnosis, knowledge-based systems
We deal with a multi-stage decision process with fuzzy transitions, which is termed fuzzy decision process. We consider the fuzzy decision process, where both state and action are assumed to be fuzzy, from a point of view of a dynamic fuzzy system which has been developed by the authors. The discounted total reward is described by a fuzzy number on a closed bounded interval, and a partial order of convex fuzzy numbers, which is called a fuzzy max order, is used to discuss the optimization problem. We characterize the discounted total reward associated with an admissible stationary policy by a unique fixed point of the contractive mapping. Further, we estimate the fuzzy rewards, by introducing a fuzzy expectation generated by a fuzzy goal.
Classical two-valued logic has been thought to be inadequate as a logic of fuzzy predicates, because the interpretation of a predicate in classical two-valued logic is just a set of objects, and a set is a precise mathematical entity with nothing fuzzy about it. The aim of this paper is to show that fuzziness may, after all, be successfully modelled in classical two-valued logic via (i) the introduction of a notion of weak negation, where natural language occurrences of `not' are not necessarily translated into logic as `\neg', and (ii) giving fuzzy predicates recursively enumerable but not recursive interpretations. The model developed here is computer-implementable and well-motivated.
Keywords: Fuzzy, vague, classical logic, two-valued logic
This paper deals with the control of battlefield radio communications. The particular properties of battlefield communications in modern warfare make a distributed access control highly desirable. Inputs for such a control are approximate descriptions of the status of the network.The control rules are heuristic because the controlled process does not have a set point.On the other hand, the network nodes have ample computing power that can be used to analyze the input and exercise access control algorithms. These circumstances suggest the use of fuzzy-logic control procedures.The author has developed such control procedures and tested their behavior on a computer model of battlefield communications.
Keywords: radio communications; battlefield communications; distributed control; fuzzy-logic control
Municipal Solid Waste (MSW) or refuse incineration plant is designated to reduce the volume of the refuse and recover the energy from it. The steam generated from a boiler heated by burning refuse is sent to a turbine to generate the electricity. Batch-feeding style and the uncertainty of refuse composites result in periodical and uncertain fluctuation of refuse combustion and then the steam flow rate. The fluctuation could lead to the unsteady generation of the electricity. Moreover, the incomplete combustion of the refuse is often observed. This leads to the poor efficiency of the refuse volume reduction and the energy recovery. Therefore, the proper controlled combustion of the refuse will be of both environmental and commercial significance. In this paper, we explore the problems of refuse combustion control and discuss how rule-base fuzzy logic control algorithms can be used to damp the fluctuation of the steam flow rate and achieve more complete combustion of the refuse by properly adjusting the grate rotating rates. The extensive simulations based on the data and information from the Ulu Pandan refuse incineration plant, Singapore, show the effectiveness of the rule-base fuzzy logic controller and indicate that the proposed control algorithm has potential of about 10% of increase on the capacity of refuse processing and electricity generation.
Keywords:Waste Treatment, Fuzzy Logic Control, Combustion
This paper provides a novel Chinese Chess model which is based on fuzzy cognitive map (FCM) and rule-based system for reasoning a best legal move. A 10*9 guard matrix is generated by FCM to show the status of each intersection. Each entry in the matrix is called a guard value which indicates how an intersection is guarded by the player's side or attacked by the opponent's. Based on the proposed model, not only the legitimacy of the next move can be improved but also the decision time is much shorter than the game tree searching method of alpha-beta model. An example is given to verify the effectiveness of the proposed methodology.
Keywords: Guard heuristic, fuzzy reasoning, fuzzy cognitive map, guard matrix, Chinese chess
In this paper we are concerned with the problem of defining a fuzzy dependency in the framework of a fuzzy relational database. Of primary interest is the development of a fuzzy algebra operator called RULE which extracts the information included in the data of an original relation r. This is a kind of projection which allows us to store that information in a separated relation RULE(r), with fewer tuples.
This process will be done whenever it is possible to detect a 'rules based fuzzy functional dependency'. In order to define it we will need to extend a resemblance relation defined for crisp data to the fuzzy case. It will lead us to define a weak resemblance used to compare antecedent values and a strong resemblance for consequent values. We show how can we detect such dependency through two equivalent approaches: once constructing first relation RULE(r), and another one, working directly with the tuples appearing in r.
Keywords: Fuzzy Databases, Fuzzy Dependencies, Fuzzy Rules.
Recent studies of DSS have raised serious questions regarding the conflict between the ideal of DSS as aids to ill-structured problem-solving and the reality of DSS implementations which tend to focus on moderately- to well-structured problems. Lack of tools to aid certain types of cognitive effort relates directly to this concern. An additional worry is that incorporating inappropriate cognitive tools may do more harm than good. The potential for distortion or miscarriage of the decision process is great in the area of strategic planning. Supporting symbolic representation and reasoning for this area with tools involving fuzzy sets technology has worked very well for Carlssen and Walden with the Finish forest products industry. Augmenting the decision support toolkit with fuzzy-set-theoretic tools as needed can open the door to more successful design and implementation of DSS.
Keywords: fuzzy decision aids, fuzzy DSS, cognitive processing, strategic planning
In this paper, I will derive an exact solution for the membership function of the output of a fuzzy system consisting of n Mamdani-type rules. The consequents of the rules are triangular fuzzy sets that are evenly spaced on a univariate universe of discourse. All the consequents have the same support width, d, which determines the degree to which the consequents overlap. The derivation makes no assumptions about the rule antecedents, since the fuzzy output is expressed as a function of the degree to which each rule is satisfied. Using this function, I derive an exact solution for the defuzzified output of the system using the centroid defuzzification procedure. Finally, a numerical example involving four rules with two input variables illustrates a preliminary investigation into the effect of varying the support width of the consequent fuzzy sets.
Institute for Simulation and Training
University of Central Florida
The Fidelity Measurement question in Distributed Interactive Simulation (DIS) needs to be answered. It's resolution is crucial to defining and resolving the interoperability issue of "How to compare and contrast simulations of varying fidelities on a quantifiable basis"?" Once such a measure of fidelity is modeled, it would allow high-fidelity simulators to play fairly with low fidelity simulations. The Fidelity Subgroup of the DIS Standards Development Project has developed a Draft Fidelity Description Requirement (FDR) Document, in an hierarchical taxonomy format. This framework provides an object-oriented, modular referent to model. The input and output descriptors are defined verbally, linguistically. Recent research would suggest this linguistic base can easily be transformed into quantifiable measures, indices. This paper provides a methodology for providing quantifiable Fidelity Indices; through the application of Fuzzy Logic.
In this paper, a logical approach to the fuzzification of binary mathematical morphology is presented. Fuzzy dilation and fuzzy erosion are introduced independently, using the logical operators `conjunctor' and `implicator'. In this way, duality relationships are not forced from the very beginning. It is shown that by choosing suitable logical operators, all classical duality and other relationships can be preserved. Following a similar line of reasoning, it is possible to obtain the idempotence of the fuzzy closing and fuzzy opening. This important result leads to the introduction of the concepts of B-open and B-closed fuzzy objects. Fundamental classical theorems are generalized for the minimum operator and its residual implicator, and for the Lukasiewicz t-norm and its residual implicator.
The paper discusses the general feeling of uneasiness engineers and scientists experience when they assume probability models for basic uncertainties governing a risk or reliability analysis. Specifically, the aspect of tail behavior is addressed. It is well known that quantitative risk estimation is critically dependent on the tail behavior. The present paper focuses on tail heaviness and the effect of tail heaviness of basic uncertainties on the overall risk or failure probability. This is of interest to a model-based risk analysis as well as a structural reliability analysis. Two examples are included to illustrate some of the concepts introduced in this paper.
Information Technology Research Laboratory, Sharp Corporation
2613-1, Ichinomoto-cho, Tenri, Nara 632 Japan
For automatic rule extraction from a set of input-output data examples, decision tree generating methods such as ID3 and Fuzzy ID3 play a mejor role. These methods, however, are difficult to apply when there is a tendency for the examples to change dynamically. This paper presents a new method for adaptive rule extraction with the Fuzzy Self-Organizing Map and the results of simulations to present the effectiveness by a comparison with other methods such as RBF and GA. We got the result that our methodd is superior to other methods for automatic and adaptive rule extraction.
Selection of an appropriate hand shape and orientation for grasp preshaping depends on the geometry and physical properties of the target object, along with information on the goal of the task. Features of the target object and the task are mapped onto various grasp attributes. Preshaping of the robot hand is done according to the results of this mapping. A fuzzy logic grasp preshaping methodology is presented in this paper.
Electrical and Computer Eng.
Syracuse, NY 13244-1240
In this paper we overview various knowledge-based defuzzification functions from a system modeling and controls perspective, and introduce a new variant which is useful in applications where fuzzy variables are related to deviations from a norm, such as feedback control. We also summarize results of simulation experiments.
Keywords: fuzzy sets, defuzzification, fuzzy control
Les M. Sztandera
Philadelphia College of Textiles and Science
Decision making is a process of selecting an optimal course of action from the available alternatives. Ordering fuzzy subsets is an important event in dealing with fuzzy decision problems in many areas. This issue has been of concern for many researchers over the years. This is obvious due to the extensive number of papers published in the last fifteen years dealing with ordering. Some twenty eight methods have been proposed in the publications for ranking fuzzy subsets.
Also, in the last several years, there has been a large and energetic upswing in neuroengineering research efforts aimed at synthesizing fuzzy logic with computational neural networks. The two technologies often complement each other: neural networks supply the brute force necessary to accommodate and interpret large amounts of sensor data and fuzzy logic provides a structural framework that utilizes and exploits these low level results. We have the ways to use either technology as a "tool" within the framework of a model based on the other. As a neural network is well known for its ability to represent functions, and the basis of every fuzzy model is the membership function, so the natural application of neural networks in fuzzy models has emerged to provide good approximations to the membership functions that are essential to the success of the fuzzyapproach. It is the purpose of this paper to evaluate and analyze the performance of available methods of ranking fuzzy subsets on a set of selected examples that cover possible situations we might encounter as defining fuzzy subsets at each node of a neural network. Through this analysis, suggestions as to which methods have better performance for utilization in neural network architectures, as well as criteria for choosing an appropriate method for ranking will be made.
This paper discuses systems of difference equations with fuzzy parameters and presents some solution procedures with the purpose to study the dynamic behaviour of economic systems in case of uncertainty. The trajectories of the endogenous variables are evaluated firstly at contiguous moments of time, and then, simultaneously. The relations between different solutions are shown. We also provide a more informative crisp solution (than the ordinary one) for each level of uncertainty, in case the economic system authorities have no enough time to consider all possibilities. Finally, the author consider essential to provide an algorithm for computing the exact (-cuts of the obtained fuzzy solutions.
Keywords: Econometrics; dynamics; systems of difference equations; nonlinear programming
A Common problem in the design of fuzzy systems, is the selection of the shape and the number of fuzzy sets. Unlike the iterative and computationaly intensive Neuro-Fuzzy optimization methods, we propose the use of a one pass, suboptimal method. The idea is based on the wavelet packet decomposition method, in which a function is expanded into basis functions in a recursive way. An information cost tree is built which tracks the various expansion possibilities. A cost norm is used to prune the tree as a tradeoff between complexity and accuracy. The result is a suboptimal fuzzy system. the algorithm is O(MlogM).
Keywords: Fuzzy systems, Spline wavelets, wavelet transform
This paper presents a genetic algorithm based approach to redundancy resolution of robot manipulators using self-motion topology knowledge. The genetic algorithm presented can work under joint limits and produces end-effector positions with negligible error. Any solution determined by the genetic algorithm is physically realizable, as demonstrated on a PUMA 700 robot manipulator which is configured as a redundant positional manipulator.
Univeristy of Delaware
Understanding the way vehicles interact with one another within a traffic stream is an important topic in transportation engineering. By developing accurate representations of these interactions we can improve highway safety, control measures and efficiency of operations. Further understanding of vehicle interaction is important for the development of advanced vehicle control mechanism. The specific situation studied is when a driver is following another vehicle because his/her speed is constrained by the vehicle ahead, (traveling at a speed less than what the driver wish), and roadway or traffic conditions that do not allow passing. This is termed a car-following situation.
Car-following phenomena have traditionally been modeled as a stability problem using deterministic methods. Such approach does not take the inherent vagueness and uncertainty of the driver's decision process into account. When a human is controlling a vehicle in a congested traffic stream, he/she does not perceive and react to the situation in the exact manner assumed by traditional methods. Instead, the conditions at any point in time are perceived in terms of linguistic variables (the headway is a bit long, or the relative speed is about zero). Then, the driver processes that information through an approximate set of rules (e.g., if the vehicle ahead is closing too quickly, slow down) and finally performs some vague action (decelerate somewhat, accelerate hard). In all parts of the perception, decision and reaction process, the relevant variables contain a degree of uncertainty and a model of this process should include. Fuzzy inference based control systems can explicitly model this uncertainty.
This paper examines the potential of fuzzy set theory for representing the car-following phenomena and its application to platoon operation. The proposed model has simplified the model developed first time by Chakroborty by using 36 rules (as compared to 396 used by Chakroborty). The proposed model directly addresses the fact that the distance headway maintained between vehicles is a function of speed by utilizing empirical speed-headway data. This allows the model to maintain an accurate headway at any speed. An additional advantage of using this speed-headway data is that drivers with different personalities may be simulated (i.e., aggressive, moderate, or conservative).
The major focus of the proposed model is to simulate the propagation of vehicle-to-vehicle interaction along a platoon of vehicles. The model results are compared the actual driver behavior observed on the highway using a test vehicle. The model allows analysis of the asymptotic stability of the platoon under various conditions, such as different types of drivers are in the platoon )aggressive and conservative). The proposed model also performed well in the examination of emergency conditions and traffic signal release and stopping situations.
In testing a sharp point hypothesis there is a difference between frequentist and Bayesian results. Even for sample sizes increasing to infinity, Bayesian methods accept the point null hypothesis for values where the frequentist method leads to rejection. This is called the Lindley paradox. Here it is attempted to explain this. The reason appears to be not a specific feature of Bayesian methods, but a misuse of the theorem of Bayes.
Structural reliability analysis requires characterizing uncertainties in strength and loads for selected failure modes. The objective of this paper is to study the uncertainties associated with the vertical wave-induced bending moment on ship hull girders. Also uncertainties in whipping effects are investigated. Spectral analysis was used to calculate the maximum life time wave loads on a ship with and without whipping. This type of analysis requires knowing a set of basic random variables. The uncertainties in wave-induced and whipping bending moments were investigated using Monte Carlo simulation by randomly generating these basic random variables and calculating wave and whipping loads on a ship. A parameteric study was performed to investigate the effect of variability in these basic random variables on the uncertainties of wave loads
Keywords: Reliability, Loads, Waves, Bending, Whipping, Uncertainty, Spectral
The analysis of existing structures requires engineers to model two types of uncertainty, cognitive and non-cognitive types. The objective of this paper is to reexamine structural analysis methods by considering the cognitive type of uncertainty. Two approaches based on the displacement method for structural analysis are proposed: (1) fuzzy arithmetic approach, and (2) permutations approach. The first approach only obtains approximate solutions. The second approach produces the exact solution but requires more computing time. The behavior of fundamental structural systems was investigated, and the results based on the second approach showed that if the modulus of elasticity is a triangular fuzzy number, the member forces can be either fuzzy numbers or crisp values depending on the structural system type. Modified fuzzy division and subtraction were also proposed for solving simultaneous equations with fuzzy coefficients using fuzzy arithmetic. Keyword: cognitive, fuzzy arithmetic, permutation, structural analysis, triangular fuzzy number, uncertainty
Keywords: cognitive, fuzzy, random, marginal density function, normalized membership function, probability density function, uncertainty
Previous empirical studies indicate that differences exist between self-reported measures of post-decision confidence and Yager's predicted measures of decision tranquility. The purpose of this article is to demonstrate that some systematic differences are a result of attractors, round numbers that appear reasonable at or near special cases although they depart from a broader pattern. The results indicate that the strength of the attractors varies as a function of the decision structure. The research is a preliminary attempt to apply fuzzy mathematics to cognitive psychology. Subjects reported their confidence in a choice based on alternatives using random sets. Subjects'frequencies of responses were compared by decision type. Three decision structures that appear to increase attractor strength were identified. Univariate t tests of the differences of mean response frequencies between decision structure types were significant at the .05 level.
Keywords: Fuzzy set, decision making, confidence, tranquility, attractor
Inference analysis plays a major role in database security and knowledge discovery. Common sense knowledge, typically expressed in imprecise or fuzzy terms, can be introduced as catalytic relations to existing databases. Analyzing the augmented databases materializes new rules and latent compromising inference channels based on common knowledge and existing database data. This paper shows how fuzzy relations can be used to catalyze new inferences in database systems. A knowledge discovery tool for analyzing catalytic inference in Oracle databases is described.
Keywords: Database inference, knowledge discovery, database security, fuzzy relational databases
The main objective of structural design is to insure safety, function, and performance of an engineering system for target reliability levels and for specified time period. As this must be accomplished under conditions of uncertainty, probabilistic analyses are necessary in the development of such probability-based design of unstiffened panels for ship structures. The load and resistance factor design (LRFD) format was developed in this paper for unstiffened panels. Partial safety factors were determined to account for the uncertainties in strength and load effect. In developing these factors, Monte Carlo simulation was utilized to assess the probabilistic characteristics of strength models by generating the basic random variables that define the strength and substituting in these models; while the First-Order Reliability Method (FORM) was used to determine the partial safety factors based on prescribed probabilistic characteristics of load effects.
Keywords: Reliability, Panels, Plates, Steel, Ship, Probability, Design, Load Factors, Strength Factors, Safety Factors
Prior works by the author have introduced the system QUAL (herein Q) of qualified syllogisms. An example of such a syllogism is ``Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly''. Q provides a formal language for expressing such syllogisms, together with a semantics which validates them. Also introduced in the prior works is the notion of a path logic. Reformulating Q as a path logic allows for the expression of modifier combination rules, such as ``From likely P and unlikely P, infer uncertain P''. The present work builds on this, showing how to incorporate Q into a system for default reasoning. Here is introduced the notion of a dynamic reasoning system (DRS), consisting of a path logic, together with a semantic net, or more exactly, a taxonomic hierarchy that allows for multiple inheritance.
The taxonomic hierarchy enables definition of a specificity relation, which can then be used in default reasoning (more specific information takes priority over less specific). Modifier combination rules prescribe what to do when defaults are applied in the context of multiple inheritance. Propositions derived in this manner all bear qualitative likelihood modifiers, representing the extent to which the proposition is believed.
Keywords: default reasoning, fuzzy quantifiers, fuzzy likelihood, usuality, qualified syllogisms, dynamic reasoning systems
The process relating to qualitative chemical analyses is based on sample analyses of minerals. Several considerations are performed by chemists, involving features such as hardness, luster, etc. Besides, solubility tests have a problem - how to determine suitable solvents to specific samples (based on color recognition). The process demands an expert knowledge and involves pon- derations and cognitive inferences, peculiar to human reasoning. This kind of uncertainty is difficult to be modeled with traditional models. The color recog- nition is a complex process, because it is variable from observer to observer. This work proposes an Expert System, based on fuzzy logic, which has a knowledge base structured using a classification tree with a membership function. To solve the color problem, the HSI method is used, because of its similarity with the way human observers colors.
Keywords: qualitative chemical analyses, fuzzy expert system, fuzzy classification tree, HSI method
The paper presents an autonomous approach for the clustering algorithm based on a mountain function proposed by Yager and Filev. It intends to answer the parameter selection problem and attenuate the effects of the granularity of the griding in algorithm's performance using a cluster realocation procedure. The solving of those problems has greatly enhanced the possibility of achieving an autonomous clustering process. The proposed clustering approach is explained in detail and examples of its performance are analyzed.
Keywords: Clustering, mountain method, data structure
A nonlinear 5-layer artificial neural autoencoder network for image data compression is constructed and trained using the back propagation algorithm and medical CT-images. The influence of linear and nonlinear pre/postprocessing operations is studied as well as an alternative compression scheme. Important implementational issues of neural networks are addressed as well as autoencoder issues. One of the results of this work is a compression/decompression tool that provides maximum flexibility and can be used independent from the training environment.
Keywords: Autoencoder, Back Propagation, Compression, Neural Networks
The paper presents some steps towards linear statistical inference for fuzzy data. In establishing best linear unbiased estimators (BLUE) it is necessary to consider a suitable notion of expectation and variance for random fuzzy sets. As methodological guide, we use the Frechét-approach which leads for a given metric to an associated expectation and variance. Especially the well known Aumann expectation appears as Frechét-expectation and the associated variance has the advantage, that at least special fuzzy number data can formally be handled like Euclidean vectors. Application to linear regression shows that only in special cases the fuzzified version of classical BLUE keeps their optimality.
Keywords: Best linear unbiased estimation, Expectation and variance of random fuzzy sets
A key step in fuzzy relational modeling is the generation of appropriate reference sets. The membership functions used to define these reference sets are often based on heuristics. However, more attention must be paid to how these reference sets are created if the actual statistical characteristics of the system signals are to be reflected in the shape of the membership functions. A new algorithm which automatically generates reference sets without neglecting important information hidden in the data statistics is described in this paper. The method employs a Scalar Quantization (SQ) algorithm to partition the universe of discourse, and a polyline technique to generate the membership functions on the partitioned universe. The performance of the reference set generator algorithm is analyzed by modeling and simulating a stochastic process.
Keywords: fuzzy relational modeling, fuzzy reference set design, Fuzzy c-Means, scalar quantization, polyline algorithm
Kaufmann's formulation of hybrid numbers, which simultaneously express fuzzy and probabilistic uncertainty, allows addition and subtraction, but offers no obvious way to do multiplication, division or other operations.We describe another, more comprehensive formulation for hybrid numbers that allows the full suite of arithmetic operations, permitting them to be incorporated into complex mathematical calculations.There are two complementary approaches to computing with these hybrid numbers.The first is extremely efficient and yields theoretically optimal results in many circumstances.The second more general approach is based on Monte Carlo simulation using intervals or fuzzy numbers rather than scalar numbers.
Keywords: fuzzy numbers, probability distributions, Kaufmann, multiplication
Three major problems inhibit the routine use of Monte Carlo methods in risk and uncertainty analyses:
Keywords: correlation, dependency, input distributions, mathematical structure
A prototype computational methodology for reliability assessment of continuum structures using finite element analysis with instability failure modes is described in this paper. Examples were used to illustrate and test the methodology. Geometric and material uncertainties were considered in the finite element model. A Computer program was developed to implement this methodology by integrating uncertainty formulations to create a finite element input file, and to conduct the reliability assessment on a machine level. A commercial finite element package was used as a basis for the strength assessment in the presented procedure. A parametric study for a stiffened panel strength was also carried out. The developed method is expected to have significant impact on the reliability assessment of structural components and systems. This impact can extend beyond structural reliability into the generalized field of engineering mechanics.
Keywords: reliability, reliability assessment, uncertainty, structures, finite element method, geometric, simulation, probability, continuum
This paper describes improvements to previous work on the use of genetic algorithms and evolutionary strategies to generate fuzzy partitions of unlabeled data. It was found that genetically guided clustering could be used in some domains to produce fuzzy partitions for which the objective function does not get trapped in local extrema. Gray code representation, two point crossover, tournament selection, and variable crossover and mutation rates combine for improved performance in terms of the final partition and the required population size. Also, methods to allow this approach to scale to problems such as magnetic resonance imaging (22000 pixels in 3 dimensions) are detailed. Initially, using properly chosen subsamples of the full data allows the genetically guided approach to move to good regions in the search space quickly. Examples are given to show how local extrema of an objective function (and thereby poor data partitions) can be avoided in domains with a large number of patterns.
An extension of two key robust statistics to fuzzy sets is presented and applied to the fuzzy c-means clustering algorithm. Examples of a robust statistic are the median and the median absolute deviation from the median or MAD, a robust estimate of dispersion. These extensions are derived, and the fuzzy median is applied to the fuzzy c-means clustering algorithm. The modified clustering algorithm shows improved performance in clustering data sets generated by heavy-tailed distributions like the Cauchy distribution. Approved for public release; distribution unlimited.
Dip. Metodi e Modelli Matematici - Universita' "La Sapienza"
Via Scarpa 16 - 00161 ROMA (Italy)
We apply the theory of (de Finetti) coherent inference to the handling of uncertainty in the process of automatical medical diagnosis. Given some possible diseases (that could explain an initial piece of information) and a tentative probability assessment on them, the data base consists of con- ditional probabilities P(E|K), where each K is a disease and each evidence E comes from a suitable test. The coherence of the whole assessment is checked. The doctor can now update the probability of each disease and check again coherence of the whole assessment, since the diseases do not constitute, in general, a partition (so that the usual Bayes theorem can- not be applied). These steps can be iterated until a degree of belief suf- ficient to make a diagnosis is reached: the coherence condition acts as a control tool on every stage.
Keywords: Coherence, Subjective probability, expert systems, medical diagnosis
Automatic classification and tissue labeling of 2-D magnetic resonance images of the human brain may involve a preliminary clustering stage. Segmenting large multi-dimensional data sets like those from magnetic resonance images is very time consuming. Better performance at the clustering stage is achieved if partial classification of the image can be done before applying clustering. We show the use of fuzzy rules to do this partial classification to be very effective. Fuzzy rules can pre-classify a major portion of the image giving a clustering algorithm a lesser number of pixels to operate upon. Furthermore, as the pre-classification stage is itself fuzzy, it can be directly used to initialize a fuzzy clustering algorithm, giving it a much needed headstart. In this paper we present an approach to using fuzzy rules to pre-classify magnetic resonance images of the normal human brain. Good segmentation of normal brain into tissues of interest is obtained much faster than with clustering alone.
Luis F. Chaparro
Department of Electrical Engineering
University of Pittsburgh
Robert J. Sclabassi
Department of Neurological Surgery
University of Pittsburgh
Estimation of temporal fuzzy sets that model dynamic processes is discussed. It has been found that although poles of attraction can be estimated fairly well with different fuzzy partitioning algorithms, membership function estimates may fail in accurately describing dynamic changes within the observed signals. Two types of fuzzy partitioning algorithms are compared: fuzzy c-means (FCM) and fuzzy maximum likelihood (FMLE). The simulations performed on quasi-stationary Gaussian signals suggest that the membership functions estimated by FMLE fail to follow continuous changes of dynamics, while those estimated by FCM provide a good compromise between precision and physical relevance.
Keywords: temporal fuzzy sets, signal processing, fuzzy clustering, dynamic systems
Reinforced concrete coupled shear wall systems are widely accepted as a rational and economical part of tall buildings. The purpose of the system is to provide lateral resistance against external horizontal loads arising from wind and earthquakes. Much progress has been made in the last decade on the static and dynamic analysis of coupled shear walls.One method of analysis of plane coupled sherar wall is to replace the discrete connecting beam between the piers by an equivalent continuous system of laminae. Dynamic analysis has also been done to determine the fundamental frequency on order to apply the response spectrum. In modern earthquake engineering the response spectrum plays a vital role in the most commonly used method of analysis of coupled shear wall systems. Based on the free vibration analysis of coupled shears and mode superposition method of dynamic analysis of coupled shear walls, a method is established in this paper with the contribution of response spectrum using probability and random cibration concepts.
The modified probabilistic and random vibration concepts uses a new method to determine mean and standard deviation of peak response for a coupled shear wall subjected to earthquake excitation. The main practical application fo this method to determine the response mean frequency of coupled shear wall systems. This frequency determines the average number of cycles over a unit duration of time. The effectivenes and flexibility of this method is that it provides the designer a simple basis for specifying the earthquake loading. The technique results in a considerable reduction in computaionsl effort. The procedure is demonstrated using hypothetical structure subjected to earthquke induced base excitations. Computed results based on this method are close agreement with simulation results obtained from time-hsitory dynamic analysis. None of the existing methods provide any menas for computing the mean and standard deviation of peak repsonse of coupled shear wall systems. This aspect of formulatin is unique and furtherance of state of art.
The paper presents a simple robust algorithm for the recognition of a 2100 Hz tone with periodic phase reversal and the disabling of an echo canceller based on Soft Computing. The authors have used a novel tool that is able to extract fuzzy knowledge using a hybrid technique based on Genetic Algorithms and Neural Networks. The approach proposed, compared with signal detection solutions existing in literature, is certainly more efficient in terms of robustness to channel noise and can therefore be usefully applied in all cases in which signals are to be detected with very low SNRs.
The concept of a fuzzy numerical function is introduced as a special fuzzy multivalued mapping associating to each element of the universe of discourse a fuzzy (real) number. The notion of a truncated fuzzy number is introduced and its properties are studied. It is proven that the direct image of a fuzzy singleton under a fuzzy numerical function always is a truncated fuzzy number. A strict ordering in the set of truncated fuzzy numbers is constructed and it is shown that the class of fuzzy numbers, endowed with this ordering, forms a lattice. Addition, subtraction, multiplication, division, maximum and minimum of fuzzy numerical functions are defined and the distributivity of the direct image of a fuzzy singleton with respect to these operations is obtained. Carefully chosen definitions of lower and upper semi-continuity of fuzzy numerical functions are presented. The behaviour of addition, subtraction, maximum and minimum of lower (resp. upper) semi-continuous fuzzy numerical functions is investigated.
Keywords: fuzzy numerical function, fuzzy multivalued mapping, fuzzy number, truncated fuzzy number, lower and upper semi-continuity
In this paper, we address some aspects of the extension problem for possibility measures: given the values that a (fuzzy) set mapping takes on a family of (fuzzy) sets, is it possible to extend this mapping to a possibility measure? This problem is shown to be equivalent to a special system of relational equations. When the family of sets considered is a (semi)partition, two important solutions are identified. It is shown that these solutions, and their fuzzifications, play a central part in the treatment of the more general extension problem. This role is shown to be even more conspicuous when the family of fuzzy sets considered is a T-(semi)partition, a notion introduced and studied for the first time in this paper.
This paper investigates the effect of the shapes of membership functions on a fuzzy inference system to detect a signal in a noisy waveform. The detector, which uses values of features derived from the waveform, can classify the waveform as signal or noise, or it can be uncertain, that is, it can decide that no conclusion regarding presence or absence of a signal can be drawn. Piece-wise linear membership functions were used, and analytical expressions for the dependence of classification on the membership function parameters were obtained. These results were verified in a simulation, using sensory evoked potential signals and simulated noise. The performance of the system was compared to a Bayesian maximum likelihood detector. By varying membership function parameters, the fuzzy detector can be made comparable to the Bayesian detector or it can almost completely eliminate errors, at the cost of a large number of uncertain classifications.
In this paper, we propose a signal representation based on fuzzy morphology and adaptive structuring functions which is analogous to polynomial transforms. For completeness, we use a set of normalized and ordered structuring functions derived from orthogonal polynomials defined on a window. After windowing the given signal, the geometric decomposition of a windowed signal is achieved by applying fuzzy morphological opening sequentially using each of the structuring functions to fit the signal. The resulting representation is made to resemble an orthogonal expansion by constraining the result of opening to equal the adapted structuring function. Properties of the geometric decomposition permit us to develop an iterative procedure to calculate the adaptation parameters. The analysis and synthesis procedures are illustrated for images.
Keywords: Fuzzy sets, mathematical morphology and data compression
Chandra S. Putcha
California State University
Fullerton, CA 92634, USA
This work is an extension of the earlier research done by the authors in this area (1) wherein these principles were applied to a steel beam with an external moment. The main methods used for estimation of reliability in the previous as well as the present research are: the First Order Second Moment (FOSM) method, the Advanced First Order Second Moment (AFOSM) and the Point Estimate Method (PEM). For each method, the reliability of the tension element is calculated.The safety indices (b) are calculated for the various types of probabilistic combinations of resistance and load. Results obtained by these three methods are compared to one another. Subsequently, relevant conclusions are drawn.
Keywords: safety, reliability, tension, safety index, probability of failure, normal, log-normal
A hybrid fuzzy neural system is used to improve a handwritten word recognition algorithm. The word recognition algorithm matches digital images of handwritten words to strings in a lexicon. This algorithm requires a module to assign character class membership values to images of segments of handwritten words. Many of these images are not characters. It is shown that a hybrid neural system consisting of a cascade of a Kohonen Self Organizing Feature Map (SOFM) followed by Choquet fuzzy integrals can yield improved performance over a multi-layer feedforward network (MLFN). The hybrid method scored a word recognition rate of 85% compared to 77% for the MLFN method.
Keywords: Handwriting Recognition, Self-Organizing Feature Maps, Fuzzy Integrals, Character Recognition, Backpropagation
A hierarchical architecture for fuzzy modeling and inference has been developed to allow adaptation based on system performance feedback. A general adaptive algorithm is presented and its performance examined for three types of adaptive behaviour: continued learning, gradual change, and drastic change. In continued learning, the underlying system does not change and the adaptive algorithm utilizes the real-time data and associated feedback to improve the accuracy of the existing model. Gradual and drastic change represent fundamental alterations to the system being modeled. In each of the three types of behaviour, the adaptive algorithm has been shown to be able to reconfigure the rule bases to either improve the original approximation or adapt to the new system.
Keywords: fuzzy model, adaptivity, rule base completion
The performance and reliability of a system are strongly influenced by its operating conditions. However, existing reliability models are unable to calculate the reliability of a system operating in variable conditions. This paper presents a new approach to this problem and discusses two typical cases: (1) one item operating sequentially under different conditions, where the transition points are deterministic; (2) a system consisting of two parallel sub-systems sharing a load, where the failure rate of each sub-system is dependent on the load it shares. We show that if the underlying failure time distribution of the item (or sub-system) can be represented by the accelerated failure time model (AFTM), the system reliability at any time can be obtained easily by using the formulas derived in this paper.
Department of Mechanical and Industrial Engineering
New Jersey Institute of Technology, Newark, NJ 07102
The Hard and Fuzzy C-Means algorithms are commonly used in many applications. However, they are highly sensitive to noise and outliers. In this paper, we reformulate the Hard and Fuzzy C-Means algorithms and combine them with a robust estimator called the Least Trimmed Squares to produce robust versions of these algorithms. To find the optimum trimming ratio of the data set and to eliminate the noise from the data set, we develop an unsupervised algorithm based on a cluster validity measure. We illustrate the robustness of these algorithm with examples.
Keywords: Fuzzy C-Means, Least Trimmed Squares, Robust Methods, Noisy Data, Clustering
This paper is concerned with the use of fuzzy sets for automatic telephone answering systems for large organisations or organisations providing large amounts of vaguely structured information. Currently available commercial systems are generally based on hierarchical dialogue systems, reflecting a hierarchical information structure. The authors have been investigating alternative approaches where the information structures are less well defined. In these cases, callers often have a degree of vagueness about what information they require. The paper looks at the idea of using fuzzy sets for modelling both the domain of interest and the users emerging goals, as perceived by the system. It then goes on to describe two algorithms for traversing the information structures. Conclusions and further work are then discussed.
Effective inference under uncertainty in Artificial Intelligence depends on context.InferencesbasedonBayesianconditional probabilities use context effectively.However,the concept of context is not sufficiently developed for reasoning based upon the variousothertheoriesofuncertainty,suchasfuzzy set theory, Dempster-Shafer theory ,or rough set theory.Inthis paper,wedevelopaconceptof "context space" forfuzzy systems theory. Such a description of context spaceallowsone to usefully construct fuzzy setsforspecificapplications,and thus improves the foundation for fuzzysystemstheory.In addition,theproblemofestablishingmembershipfunctions (MFs) for context spaces is considered. It is shown that Hisdal's operational procedures and modal logic are preferable when used jointly with a complete and exactly defined context space as introduced in the paper. Finally, the theory of fuzzy sets is compared with probability theory in connection with the problem of MF acquisition.