Showing papers on "Fuzzy logic published in 1986"

Fuzzy cognitive maps

Abstract: Fuzzy cognitive maps (FCMs) are fuzzy-graph structures for representing causal reasoning. Their fuzziness allows hazy degrees of causality between hazy causal objects (concepts). Their graph structure allows systematic causal propagation, in particular forward and backward chaining, and it allows knowledge bases to be grown by connecting different FCMs. FCMs are especially applicable to soft knowledge domains and several example FCMs are given. Causality is represented as a fuzzy relation on causal concepts. A fuzzy causal algebra for governing causal propagation on FCMs is developed. FCM matrix representation and matrix operations are presented in the Appendix.

Efficient Implementation of the Fuzzy c-Means Clustering Algorithms

Abstract: This paper reports the results of a numerical comparison of two versions of the fuzzy c-means (FCM) clustering algorithms. In particular, we propose and exemplify an approximate fuzzy c-means (AFCM) implementation based upon replacing the necessary ``exact'' variates in the FCM equation with integer-valued or real-valued estimates. This approximation enables AFCM to exploit a lookup table approach for computing Euclidean distances and for exponentiation. The net effect of the proposed implementation is that CPU time during each iteration is reduced to approximately one sixth of the time required for a literal implementation of the algorithm, while apparently preserving the overall quality of terminal clusters produced. The two implementations are tested numerically on a nine-band digital image, and a pseudocode subroutine is given for the convenience of applications-oriented readers. Our results suggest that AFCM may be used to accelerate FCM processing whenever the feature space is comprised of tuples having a finite number of integer-valued coordinates.

Fuzzy Mathematical Approach to Pattern Recognition

Abstract: This book aims to present results of investigations, both experimental and theoretical, into the effectiveness of fuzzy algorithms as classification tools in some problems concerned with the field of pattern recognition and image processing. Compares results to those obtained with statistical classification techniques.

Fuzzy Set Theory in Medical Diagnosis

Abstract: Fuzzy set theory has a number of properties that make it suitable for formalizing the uncertain information upon which medical diagnosis and treatment is usually based. Firstly, it defines inexact medical entities as fuzzy sets. Secondly, it provides a linguistic approach with an excellent approximation to texts. Finally, fuzzy logic offers reasoning methods capable of drawing approximate inferences. These facts suggest that fuzzy set theory might be a suitable basis for the development of a computerized diagnosis system. This is verified by trials performed with the medical expert system CADIAG-2, which uses fuzzy set theory to formalize medical relationships and fuzzy logic to model the diagnostic process.

Expert System on a Chip: An Engine for Real-Time Approximate Reasoning

Abstract: The role of inferencing with uncertainty is becoming more important in rule-based expert systems (ES), since knowledge given by a human expert is often uncertain or imprecise. We have succeeded in designing a VLSI chip which can perform an entire inference process based on fuzzy logic. The design of the VLSI fuzzy inference engine emphasizes simplicity, extensibility, and efficiency (operational speed and layout area). It is fabricated in 2.5 mm CMOS technology. The inference engine consists of three major components; a rule set memory, an inference processor, and a controller. In this implementation, a rule set memory is realized by a read only memory (ROM). The controller consists of two counters. In the inference processor, one data path is laid out for each rule. The number of the inference rule can be increased adding more data paths to the inference processor. All rules are executed in parallel, but each rule is processed serially. The logical structure of fuzzy inference proposed in the current paper maps nicely onto the VLSI structure.A two-phase nonoverlapping clocking scheme is used. Timing tests indicate that the inference engine can operate at approximately 20.8 MHz. This translates to an execution speed of approximately 80,000 Fuzzy Logical Inferences Per Second (FLIPS), and indicates that the inference engine is suitable for a demanding real-time application. The potential applications include decision-making in the area of command and control for intelligent robot systems, process control, missile and aircraft guidance, and other high performance machines.

Ordination on the basis of fuzzy set theory

Abstract: Fuzzy set theory is an extension of classical set theory where elements of a set have grades of membership ranging from zero for non-membership to one for full membership. Exactly as for classical sets, there exist operators, relations, and mappings appropriate for these fuzzy sets. This paper presents the concepts of fuzzy sets, operations, relations, and mappings in an ecological context. Fuzzy set theory is then established as a theoretical basis for ordination, and is employed in a sequence of examples in an analysis of forest vegetation of western Montana, U.S.A. The example ordinations show how site characteristics can be analyzed for their effect on vegetation composition, and how different site factors can be synthesized into complex environmental factors using the calculus of fuzzy set theory. In contrast to current ordination methods, ordinations based on fuzzy set theory require the investigator to hypothesize an ecological relationship between vegetation and environment, or between different vegatation compositions, before constructing the ordination. The plotted ordination is then viewed as evidence to corroborate or discredit the hypothesis. I am grateful to Dr R. D. Pfister (formerly USDA Forest Service) for kind permission to publish data from a Forest Service study. I would like to gratefully acknowledge the helpful comments and criticisms of Drs. G. Cottam, J. D. Aber, T. F. H. Allen, E. W. Beals, I. C. Prentice, C. G. Lorimer, and two anonymous reviewers.

Low-Level Segmentation of Aerial Images with Fuzzy Clustering

Abstract: A low-level segmentation methodology based upon fuzzy clustering principles is developed. The approach utilizes region growing concepts and a pyramid data structure for the hierarchical analysis of aerial images. It is assumed that measurement vectors corresponding to perceptually homogeneous regions cluster together in the measurement space. The fuzzy c-means (FCM) clustering algorithm is used in the formulation. Utilization of the fuzzy partitioning allows one to derive a correspondence between the cluster membership function values and (the proportions of) the classes constituting a region. Thus cluster membership values can be used to split mixture regions into smaller regions at a higher resolution level. The feasibility of the methodology is evaluated using a three-channel Landsat image. The results show that the FCM clustering can be used in the single-level segmentation; and that cluster membership function values derived using this algorithm can be utilized effectively as indicators of region homogeneity.

Fuzzy sets theory and applications

Abstract: 1: Some theoretical Aspects.- 1.1 Mathematics and fuzziness.- 1.2 Radon-Nikodym Theorem for fuzzy set-valued measures.- 1.3 Construction of a probability distribution from a fuzzy information.- 1.4 Convolution of fuzzyness and probability.- 1.5 Fuzzy sets and subobjects.- 2: From theory to applications.- 2.1 Outline of a theory of usuality based on fuzzy logic.- 2.2 Fuzzy sets theory and mathematical programming.- 2.3 Decisions with usual values.- 2.4 Support logic programming.- 2.5 Hybrid data - various associations between fuzzy subsets and random variables.- 2.6 Fuzzy relation equations : methodology and applications.- 3: Various particular applications.- 3.1 Multi criteria decision making in crisp and fuzzy environments.- 3.2 Fuzzy subsets applications in O.R. and management.- 3.3 Character recognition by means of fuzzy set reasoning.- 3.4 Computerized electrocardiography and fuzzy sets.- 3.5 Medical applications with fuzzy sets.- 3.6 Fuzzy subsets in didactic processes.

The Current Mode Fuzzy Logic Integrated Circuits Fabricated by the Standard CMOS Process

Abstract: Nine basic fuzzy logic circuits employing p-ch and n-ch current mirrors are presented, and the fuzzy information processing hardware system design at a low cost with only one kind of master slice (semicustom fuzzy logic IC) is described. The fuzzy logic circuits presented here will be indispensable for a "fuzzy computer" in the near future.

Multivariable Structure of Fuzzy Control Systems

Abstract: In the analysis and design of expert control systems, when linguistic types of control algorithms are used, it is important to model a physical system using fuzzy theoretic approach. The modeling, analysis, and synthesis of multivariable structures of fuzzy control systems is discussed. First, a multivariable open-loop fuzzy system is described by a set of fuzzy equations. Then a block diagram of the system consisting of functional blocks and intersectional blocks is presented. Series, parallel, and series-parallel connections of multivariable open-loop systems are also analyzed. Multivariable feedback structures are depicted by a set of fuzzy equations and block diagrams. Then the theory of multivariable-multilevel structures is presented. An example of two interconnected tank liquid-level system is given.

Semisimple algebras of infinite valued logic and bold fuzzy set theory

Abstract: In classical two-valued logic there is a three way relationship among formal systems, Boolean algebras and set theory. In the case of infinite-valued logic we have a similar relationship among formal systems, MV-algebras and what is called Bold fuzzy set theory. The relationship, in the latter case, between formal systems and MV-algebras has been known for many years while the relationship between MV-algebras and fuzzy set theory has hardly been studied. This is not surprising. MV-algebras were invented by C. C. Chang [1] in order to provide an algebraic proof of the completeness theorem of the infinitevalued logic of Lukasiewicz and Tarski. Having served this purpose (see [2]), the study of these algebras has been minimal, see for example [6], [7]. Fuzzy set theory was also being born around the same time and only in recent years has its connection with infinite-valued logic been made, see e.g. [3], [4], [5]. It seems appropriate then, to take a further look at the structure of MV-algebras and their relation to fuzzy set theory.

Fuzzy Set Analysis for Behavioral and Social Sciences

Abstract: Introduction: Why Fuzzy Sets?.- 1. Fuzzy Set Theory: The Basics.- 2. Is Fuzzy Set Theory Realistic?.- 3. Fuzzy Scales and Measurement.- 4. Fuzziness and Internal Category Structure.- 5. Intercategory Relations and Taxonomic Analysis.- 6. Fuzzy Set Theory and Nonlinear Models.- 7. Prediction and Fuzzy Logic.- Epilogue: From Words to Numbers and Back Again.- Technical Glossary.- References.- Author Index.

Is Probability Theory Sufficient for Dealing with Uncertainty in AI: A Negative View

Abstract: An issue which has become a focus of controversy in recent years is whether or not classical probability theory is sufficient for dealing with uncertainty in AI. The topicality of this issue has grown as a result of the emergence of expert systems as one of the principal areas of activity in AI and the development of methods for evidential reasoning based on the Dempster-Shafer theory and fuzzy logic which extend beyond the current boundaries of probability theory. A point of view which is articulated in this paper is that the inadequacy of probability theory stems from its lack of expressiveness as a language of uncertainty, especially for describing fuzzy events and fuzzy probabilities. For example, how would one represent the meaning of the proposition p: it is very likely that Mary is young, in which likely is a fuzzy probability and young is a fuzzy predicate? Furthermore, how can one infer from this proposition an answer to the question: What is the likelihood that Mary is not very young? We show through examples that problems of this type – problems which do not lend themselves to solution by conventional probability-based methods – can be dealt with effectively through the use of fuzzy logic.

Probabilistic versus Fuzzy Reasoning

Abstract: This paper shows how to solve problems using probability theory that the fuzzy approaches claim probability cannot solve. By using the view that probabilities are a measure of belief in a proposition in a particular context, limitations imposed by the frequncy interpretations of probability are avoided. The various fuzzy approaches (fuzzy sets, fuzzy logic, possibility theory and higher order generalizations) seem to fill the gap caused by the restricted frequency interpretation. Close examination shows that the fuzzy approaches have exactly the same representation as the corresponding probabilistc approach and include similar calculi. The probabilistic approach assumes less information when the calculi differ.

Fuzzy knowledge combination

Abstract: A general answer is given to what one should conclude from disagreeing experts. the answer is generalized further to incorporate the experts' credibility weights. the answer rests on a wide range of intuitively based epistemic axioms, scientific and philosophical conjectures, and formal mathematical relationships. A recurring theme is the making of Bellman - Zadeh fuzzy decisions, wherein a decision is the intersection of fuzzy goal and fuzzy constraint subsets of some space of alternatives. Another result is that measures of central tendency, such as the arithmetic mean, make poor knowledge combination operators. Formally, fuzzy knowledge combination operators are sought. the function space of knowledge combination operators o: K″ K is shrunk by imposing successive axioms. the final shrunken set is said to consist of admissible knowledge combination operators. Some of its mathematical properties are explored and a simple admissible operator is finally chosen. Knowledge sources Xi: S K are mappings from epistemic stimuli or questions into a knowledge response set K. the uncertainty of the underlying epistemic situations is captured by the cardinality of K and by the fuzziness of its partial ordering. Admissible knowledge combination operators Aggregate knowledge responses in some desirable way. the arithmetic mean is not admissible. Nor in general is a probabilistic framework even definable in the abstract poset setting employed by this theory. the fuzzy knowledge combination theory is extended by associating general credibility weights with the knowledge sources. A new set of weighting axioms is required to satisfy certain intuitions and to satisfy the admissibility axioms. General weighting functions are obtained and thereby weighted admissible operators are obtained. the weighted mean still proves inadmissible. Appendix I contains a technical glossary and summary of the proposed fuzzy knowledge combination theory. Appendix II contains proofs of the probabilistic uncertainty theorems required for the uncertainty testbed used in the theory.