Showing papers on "Fuzzy number published in 1975"
TL;DR: Fuzzy set theory is applied to fuzzy linear programming problems and it is shown how fuzzylinear programming problems can be solved without increasing the computational effort.
Abstract: The concept of fuzzy sets is presented as a new tool for the formulation and solution of systems and decision problems which contain fuzzy components or fuzzy relationships. After a brief description of the basic theory of fuzzy sets, implications to systems theory and decision making are indicated. Fuzzy set theory is then applied to fuzzy linear programming problems and it is shown how fuzzy linear programming problems can be solved without increasing the computational effort. Some critical remarks concerning the presently existing axioms and necessary future research efforts conclude this introductionary paper.
899 citations
TL;DR: The McCulloch-Pitts model of a neuron is extended to a more general model which allows the activity of a neurons to be a “fuzzy” rather than an “all-or-none” process, called a fuzzy neuron.
Abstract: In this paper, the McCulloch-Pitts model of a neuron is extended to a more general model which allows the activity of a neuron to be a “fuzzy” rather than an “all-or-none” process. The generalized model is called a fuzzy neuron. Some basic properties of fuzzy neural networks as well as their applications to the synthesis of fuzzy automata are investigated. It is shown that any n-state minimal fuzzy automatan can be realized by a network of m fuzzy neurons, where ⌈log2n⌉
214 citations
TL;DR: This paper considers how a topology for a set 3 may give rise to an “induced fuzzy topology” for S, thus characterizing the fuzzy subsets of % which may naturally be considered “open” and furnishing a concrete class of examples of the “fuzzy topologies” defined by C. L. Chang.
176 citations
01 Jan 1975
TL;DR: In this article, the concept of similarity relation introduced by L. A. Zadeh is derivable in much the same way as equivalence relation, and the resolution identity is brought out quite naturally.
Abstract: Publisher Summary This chapter discusses the basic terminologies and notations regarding fuzzy relations and fuzzy graphs. The the concept of similarity relation introduced by L. A. Zadeh is derivable in much the same way as equivalence relation. Moreover, through this derivation, the resolution identity is brought out quite naturally. The chapter analyzes fuzzy graphs from the connectedness viewpoint and the presents the application of results to clustering analysis and modeling of information networks. The usual graph-theoretical approaches to clustering analysis involve first obtaining a threshold graph from a fuzzy graph and then applying various techniques to obtain clusters as maximal components under different connectivity considerations. These methods have a common weakness, namely, the weight of edges are not treated fairly because any weight greater (less) than the threshold is treated as 1(0).
170 citations
TL;DR: In this paper the methodology of Zadeh's fuzzy set theory is summarized and applied to fuzzy decision making.
Abstract: When goals and constraints are stated imprecisely, decision problems grow in importance, particularly in the investigation of complex and social systems. In this paper the methodology of Zadeh's fuzzy set theory is summarized and applied to fuzzy decision making.
74 citations
01 Jan 1975
TL;DR: This chapter introduces a set function, that is, conditional fuzzy measure and a relation between a priori and a posteriori fuzzy measures, very useful for describing any kind of transition of fuzzy phenomena such as communication of rumors, the reprint of color photograph, and the development of human abilities by education.
Abstract: Publisher Summary This chapter introduces a set function, that is, conditional fuzzy measure and a relation between a priori and a posteriori fuzzy measures. These are very useful for describing any kind of transition of fuzzy phenomena such as communication of rumors, the reprint of color photograph, and the development of human abilities by education. The common characteristics of these phenomena are that the measures describing their status are very vague and that their transitions are influenced greatly by the subjectivity of the people who are involved in such fuzzy phenomena. It is well known that the uncertainty of human behavior is sometimes conveniently expressed by the subjective probability (judgmental probability) in Bayesian statistics. But one cannot say that this is the best way of expressing the fuzziness unless the problem is directly related to decision making.
42 citations
IBM1
TL;DR: In this paper, a fuzzy program is defined through a flowchart where each arc is associated with a fuzzy relation (called a fuzzy branching condition) and a fuzzy assignment and the execution of the fuzzyprogram is equivalent to searching a solution path in the tree, i.e., tree searching.
Abstract: In this paper, a fuzzy program is defined through a flowchart where each arc is associated with a fuzzy relation (called a fuzzy branching condition) and a fuzzy assignment. Input, program and output variables occurring in a fuzzy program represent fuzzy subsets. A fuzzy program is interpreted as implicitly defining a tree; and the execution of the fuzzy program is equivalent to searching a solution path in the tree, i.e., tree searching. Examples of fuzzy programs and their executions are given.
32 citations
01 Jan 1975
TL;DR: The chapter presents a computer simulation of the process of human learning by making use of the concept of fuzzy program and learning algorithm.
Abstract: Publisher Summary This chapter discusses several methods that translate a given sequence of fuzzy instructions into another sequence of precise instructions called a machine program. A finite-state automaton is taken up as a fuzzy machine model that executes a fuzzy program. The chapter presents the formulation of an extended fuzzy machine based on a generalized automaton and a few procedures for execution of fuzzy programs. An L-fuzzy automaton with the weight space defined in the lattice ordered semigroup is considered as a general machine. Several machines are also derived from L-fuzzy automata as their specific examples. The chapter discusses a more general way of executing fuzzy programs by making use of the generalized fuzzy machine. The chapter presents a computer simulation of the process of human learning by making use of the concept of fuzzy program and learning algorithm.
29 citations
01 Jan 1975
TL;DR: A multistage decision process is a fuzzy mapping from X × UN → X where X and U are the state and policy spaces and risk and optimum decisions are defined in terms of the inclusive properties.
Abstract: A multistage decision process is a fuzzy mapping from X × UN → X where X and U are the state and policy spaces. Given the initial fuzzy set Si on X, the set of final fuzzy sets Sf on X has certain inclusive properties. Risk and optimum decisions are defined in terms of the inclusive properties.
23 citations
01 Jan 1975
TL;DR: A fuzzy system that generates fuzzy sets of trees as an extension of dendrolanguage generating system is introduced, and the fuzzy tree transducer is shown to be able to describe the fuzzy meanings of fuzzy context-free languages at the level of syntax structure.
Abstract: Publisher Summary This chapter discusses three systems to manipulate fuzzy sets of trees, generators, acceptors, and transducers It introduces a fuzzy system that generates fuzzy sets of trees as an extension of dendrolanguage generating system Two context-free dendrolanguage generating system (F-CFDS) is said to be equivalent if they generate the same fuzzy dendrolanguage For any F-CFDS, an equivalent F-CFDS of order can be constructed The set of derivation trees of any fuzzy context-free grammar is shown to be a fuzzy set of trees generated by a fuzzy context-free dendrolanguage generating system and also to be a fuzzy set of trees recognizable by a fuzzy tree automaton The fuzzy tree transducer is shown to be able to describe the fuzzy meanings of fuzzy context-free languages at the level of syntax structure In the sense that it can fuzzily associate each fuzzy derivation tree of the fuzzy language with a tree representation of the computation process of its fuzzy meaning
20 citations
TL;DR: By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point at some instant.
Abstract: The measurement of one or more observables can be considered to yield sample points which are in general fuzzy sets. Operationally these fuzzy sample points are the outcomes of calibration procedures undertaken to ensure the internal consistency of a scheme of measurement. By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point at some instant. These sample points are the possible outcomes of any infinitely rapid succession of measurements at that instant of any sequence of observables of the system.
01 Jan 1975
TL;DR: A classification algorithm of multicategory classifiers which is based on fuzzy logic and can be used even if statistical independency of pattern vectors is violated and requires an unusually short time for learning is discussed.
Abstract: The present paper discusses a classification algorithm of multicategory classifiers which is based on fuzzy logic and can be used even if statistical independency of pattern vectors is violated. The algorithm is comparatively simple and requires an unusually short time for learning. We also consider the memory systems that recall entities stored in an associative manner. Entities are stored in the form of fuzzy matrix and are recalled by fuzzy logic according to the conditional probability of each category. A computer simulation is made in English character reading and its results are presented.
Posted Content•
TL;DR: This paper attempts to present the state equation for linear systems in a fuzzy form, illustrating in a simple way how to generalize classical results.
Abstract: This paper attempts to present the state equation for linear systems in a fuzzy form A “categorical” approach is given, illustrating in a simple way how to generalize classical results
Posted Content•
01 Jan 1975
TL;DR: The objective of this chapter will be to show how much of fuzzy systems theory goes through in this context and then to see how finiteness is reflected in the dynamics.
Abstract: In this chapter we introduce the concept of a fuzzy automaton in such a way as to make it clear that every finite relational fuzzy system is a fuzzy automaton. Our objective will then be to show how much of fuzzy systems theory goes through in this context and then to see how is finiteness reflected in the dynamics. Because of their finiteness, most of the problems concerning fuzzy automata are better understood. Turning this insinuation into formal theorems requires the use of matrix theory.