Showing papers on "Membership function published in 1974"

Fuzzy Relations in Group Decision Theory

Abstract: This paper develops the notion of fuzzy preference orderings for individuals and groups, on the basis of the theory of fuzzy (binary) relations as developed by L. A. Zadeh [4]. This concept is illustrated with well known methods of group decision-making and some of its formal properties are investigated. Finally an algorithm to map fuzzy orderings on non-fuzzy ones is proposed to guide the decision-maker in reaching decisions which reflect the fuzziness of the preferences over the available options.

Concept representation in natural and artificial languages: Axioms, extensions and applications for fuzzy sets

Abstract: This paper reports research related to mathematics, philosophy, computer science and linguistics. It gives a system of axioms for a relatively simple form of fuzzy set theory, and uses these axioms to consider the accuracy of representing concepts in various ways by fuzzy sets. By-products of this approach include a number of new operations and laws for fuzzy sets, parallel to those for ordinary sets, and a demonstration that all the basic operations are intrinsically determined. In addition, the paper explores both hierarchical and algorithmic extensions of fuzzy sets, and then applications to problems in natural language semantics and combinatorics. Finally, the paper returns to the problem of representing concepts, and discusses some implications for artificial intelligence.

Clinical Pure Types as a Fuzzy Partition

Abstract: This paper discusses the applicability of the ideas of fuzzy sets and grades of membership to problems encountered in the quantification of clinical (i.e., diagnostic and prognostic) judgment. The methods of constrained maximum likelihood are used to derive consensus estimates of grades of membership given a set of categorical data and an a priori set of specified pure types. A numerical example is given.

Entropy of L-fuzzy sets*

Abstract: The notion of “entropy” of a fuzzy set, introduced in a previous paper in the case of generalized characteristic functions whose range is the interval [0, 1] of the real line, is extended to the case of maps whose range is a poset L (or, in particular, a lattice). Some of the reasons giving rise to the non-comparability of the truth values and then the necessity of considering poset structures as range of the maps are discussed. The interpretative problems of the given mathematical definitions regarding the connections with decision theory are briefly analyzed.

Fuzzy Sets and Neural Networks

Abstract: It is possible that a better model for the behavior of a nerve cell may be provided by what might be called a fuzzy neuron, which is a generalization of the McCulloch-Pitts model. The concept of a fuzzy neuron employs some of the concepts and techniques of the theory of fuzzy sets which was introduced by Zadeh [2, 3] and applied to the theory of automaton by Wee and Fu [6], Tanaka et al. [7], Santo [8] and others. In effect, the introduction of fuzziness into the model of a neuron makes it better adapted to the study of the behavior of systems which are imprecisely defined by virtue of their high degree of complexity. Many of the biological systems, economic systems, urban systems and more generally, large-scale systems fall into this category. In the nearly three decades since its publication, the pioneering work of McCulloch and Pitts [1], has had a profound influence on the development of the theory of neural nets, in addition to stimulating much of the early work in automata theory and regula...

On the Precision of Adjectives Which Denote Fuzzy Sets

Abstract: The characteristic function of a fuzzy set denoted by a phrase “much larger than 5,” or “heavy,” is investigated experimentally. The S-shaped curve for the characteristic function is derived from some plausible assumptions involving a differential equation, and its parameters are estimated statistically. It was found that the precision of the fuzzy set–measured by the maximum slope of the characteristic function–denoted by “much greater than 5” is less than that denoted by “very much greater than 5.” When the subject is allowed to be fuzzy in his response about grade of membership, there is greater consistency in the response. Anchoring was also found to make an adjective denoting fuzzy set more precise.

Fuzzy sets in the theory of measurement of incompatible observables

Abstract: The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state.

On the Properties of Fuzzy Switching Functions

Abstract: A strictly binary approach to the treatment of switching circuits today is not always adequate to describe systems in the real world. This approach is partly due, to the relative simplicity of designing binary switching systems, and to the fact that basic switching modules in common use are two-positional. Consequently, every variable in Boolean logic is assumed to be two-valued. However, because of real-world constraints, the attributes of system variables are often ambiguously defined. In other words, quite often variables might have values other than falsehood and truth. Cases with such attributes arise, for example in artifical intelligence and related subjects. Ever since Zadeh introduced the idea of fuzzy set theory [11 by utilizing the concept of membership grade, a number of authors have been concerned with the analysis and applications of fuzzy models. Especially, the relation of fuzzy to switching systems have been discussed in [2]–[12] and by other researchers in relation to other topi...

Application of fuzzy logic to the detection of static hazards in combinational switching systems

Abstract: In this paper the fuzzy set as discussed by Zadeh is viewed as a multivalued logic with a continuum of truth values in the interval [0,1]. The concept of static hazard in combinational switching systems is related to fuzzy logic and various properties of this relation are established. The paper derives the necessary and sufficient conditions for a fuzzy function to adequately describe the steady-state and static hazard behavior of a combinational system, by extending the ternary method discussed by Yoeli and Rinon and using the resolution principle of mechanical theorem-proving.

Evaluation Model of Humanistic Systems by Fuzzy Multiple Integral and Fuzzy Correlation

Abstract: We have proposed a mathematical model of subjective evaluation on the basis of fuzzy integral. In particular, we have developed the evaluating method of complex systems composed of several subsystems by virtue of fuzzy multiple integral. Furthermore, for the sake of identifying the preference measure, that is fuzzy measure , effectively, we have introduced the fuzzy correlation.