Showing papers on "Fuzzy number published in 1983"
TL;DR: A fuzzy version of Saaty's pairwise comparison method (1980) extended by de Graan and Lootsma (1981), adapted in such a way, that decision-makers are asked to express their opinions in fuzzy numbers with triangular membership functions.
2,631 citations
TL;DR: The computational approach to fuzzy quantifiers which is described in this paper may be viewed as a derivative of fuzzy logic and test-score semantics.
Abstract: The generic term fuzzy quantifier is employed in this paper to denote the collection of quantifiers in natural languages whose representative elements are: several, most, much, not many, very many, not very many, few, quite a few, large number, small number, close to five, approximately ten, frequently, etc. In our approach, such quantifiers are treated as fuzzy numbers which may be manipulated through the use of fuzzy arithmetic and, more generally, fuzzy logic.
A concept which plays an essential role in the treatment of fuzzy quantifiers is that of the cardinality of a fuzzy set. Through the use of this concept, the meaning of a proposition containing one or more fuzzy quantifiers may be represented as a system of elastic constraints whose domain is a collection of fuzzy relations in a relational database. This representation, then, provides a basis for inference from premises which contain fuzzy quantifiers. For example, from the propositions “Most U's are A's” and “Most A's are B's,” it follows that “Most2 U's are B's,” where most2 is the fuzzy product of the fuzzy proportion most with itself.
The computational approach to fuzzy quantifiers which is described in this paper may be viewed as a derivative of fuzzy logic and test-score semantics. In this semantics, the meaning of a semantic entity is represented as a procedure which tests, scores and aggregates the elastic constraints which are induced by the entity in question.
1,736 citations
TL;DR: F fuzzy logic is suggested, which is the logic underlying approximate or, equivalently, fuzzy reasoning, which leads to various basic syllogisms which may be used as rules of combination of evidence in expert systems.
1,278 citations
TL;DR: A complete set of comparison indices is proposed in the framework of Zadeh's possibility theory and it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers.
938 citations
TL;DR: A realistic fuzzy reasoning algorithm and a method to identify control rules from human operators actual control actions and the performance of the proposed algorithm is examined by applying it to water cleaning process control.
821 citations
TL;DR: Fuzzy linear programming belongs to goal programming in the sense that implicitly or explicitly aspiration levels have to be defined at which the membership functions of the fuzzy sets reach their maximum or minimum.
574 citations
Book•
01 Dec 1983
TL;DR: A new approach to analyze the risks a computer system may be subject to and a non-numeric method that allows natural language expression is presented.
Abstract: A new approach to analyze the risks a computer system may be subject to. A non-numeric method that allows natural language expression is presented. A tutorial for implementation of the ideas of fuzzy set theory in general, and of the linguistic approach to risk analysis in particular, are discussed
362 citations
TL;DR: If it turns out that random measures have their fuzzy meanings then this paper presents a way to deal with fuzzy measures of fuzzy sets by use of a classical mathematical method, such as measure theory, functional analysis and topology.
248 citations
TL;DR: The notion of @q-crisp fuzzy numbers is introduced, and, in particular, it is shown that this class of fuzzyNumbers is homeomorphic to the Hilbert cube.
213 citations
TL;DR: In this paper a new fuzzy compactness defined by fuzzy nets, called N-compactness, is given and the notion of R-neighborhood is introduced instead of Qneighbourhood to establish the Moore-Smith convergence theory, for it is perhaps more convennient to use.
164 citations
TL;DR: The idea of fuzzy relational equation with generalized connectives is introduced and algorithms of resolution of this class equations are presented in details, showing some types of well-known fuzzy relational equations can be treated as special cases of a wise class of equations under discussion.
TL;DR: This paper suggests a method of multi-dimensional fuzzy reasoning concerned with both modus ponens and modus tollens, and discusses an example to show how the method works.
TL;DR: The proposed learning procedure consists in iterative finding such k and W which minimize the error rate estimate by the leaving 'leaving one out' method.
TL;DR: The basic idea behind the approaches is to translate the original problem in deterministic terms via tools provided by fuzzy sets theory to get a classical one.
01 Oct 1983
TL;DR: What is commonly called "commonsense knowledge" may be viewed as a collection of "dispositions": propositions with implied fuzzy logic.
Abstract: What is commonly called "commonsense knowledge" may be viewed as a collection of "dispositions": propositions with implied fuzzy logic.
01 Jan 1983
TL;DR: This chapter discusses the application of Fuzzy Set Theory to a Risk Analysis Model of Computer Security, and a concept of A FuzzY Ideal for Multicriteria Conflict Resolution is proposed.
Abstract: Fuzzy Set Theory: Past, Present and Future.- Advances in Fuzzy Sets - An Overview.- A Survey of Some Aspects on the Research Work of Fuzzy Topology in China.- Some Properties of Fuzzy Convex Sets.- "Non-standard" Concepts in Fuzzy Topology.- The Spaces of Fuzzy Probability and Possibility.- An Algebraic System Generalizing the Fuzzy Subsets of a Set.- From the Fuzzy Statistics to the Falling Random Subsets.- On Fuzzy Relations and Partitions.- Fuzzy Set Structure with Strong Implication.- Inference Regions for Fuzzy Propositions.- Fuzzy Tree Grammar and Fuzzy Forest Grammar.- Fuzzy Production Rules: A Learning Methodology.- Decision Support with Fuzzy Production Systems.- Imprecision in Computer Vision.- Fuzzy Programming: Why and How? - Some Hints and Examples.- A Fuzzy, Heuristic, Interactive Approach to the Optimal Network Problem.- Application of Fuzzy Set Theory to Economics.- Use of Fuzzy Logic for Implementing Rule-Based Control of Industrial Processes.- A New Approach to Design of Fuzzy Controller.- Advanced Results on Applications of Fuzzy Switching Functions to Hazard Detection.- The Application of Fuzzy Set Theory to a Risk Analysis Model of Computer Security.- Fuzzy Models of Human Problem Solving.- A Concept of A Fuzzy Ideal for Multicriteria Conflict Resolution.- Appendix I: Fuzzy Set Research in People's Republic of China.- Author Index.
TL;DR: Convergence of powers of a fuzzy transitive matrix is considered and some conditions for convergence are given under the max-min operation on fuzzy matrices, which show graph-theoretic properties of fuzzyMatrices and are useful when the authors consider convergence of systems represented by fuzzy matrix.
TL;DR: A new concept of “disjointness” for fuzzy is introduced and studied, and a concept of an “additive class of fuzzy sets” is defined to be a class of fuzzy sets closed under some ‘additive operations’.
TL;DR: The relational algebra for such fuzzy data model is defined, namely, the union, intersection, difference and extended Cartesian product are similarly defined as those in fuzzy set theory and the special relational operations are newly defined for fuzzy databases.
TL;DR: In this paper, it was shown that the canonical topology of the real line is uniformizable in the sense of Hutton and Sarkar, and furthermore, this uniformity induces a pseudometric which induces the topology.
TL;DR: The addition of fuzzy numbers denoted ⊕, and defined via a sup- t- norm convolution, is now well-understood from both theoretical and computational points of view, at least for the t-norm ’min’.
TL;DR: In this paper, some algorithms which have minimization properties about the fuzziness of solutions in the maxmin fuzzy relation equations are introduced.
TL;DR: F fuzzy reflexive, symmetric and transitive relations on fuzzy subsets are studied and the possible fuzzy partitioning of a fuzzy subset is investigated.
01 Feb 1983
TL;DR: The analytical approaches outlined here enable the analyst to use the information in a fuzzy form for narrowing down the scope of alternative decisions, by discarding those of them for which better alternatives can be found.
Abstract: A fuzzy set is a mathematical model of a collection of elements (objects) with fuzzy boundaries, which involves the possibility of gradual transition from complete belongness to nonbelongness of an element to a collection. This concept is introduced in the Fuzzy Sets Theory as the means to model mathematically fuzzy notions that are used by human beings in describing their understanding of real systems, their preferences, goals, etc. This introductory paper outlines various classes of problems of decision-making in a fuzzy environment, that is, in which information is modeled in terms of fuzzy sets and relations. The analytical approaches outlined here enable the analyst to use the information in a fuzzy form for narrowing down the scope of alternative decisions, by discarding those of them for which better alternatives can be found. A number of illustrative examples are discussed.
TL;DR: A calculus of linguistically quantified statements based upon fuzzy sets and possibility theory is used and an optimal sequence of controls is sought which maximizes the membership function of the fuzzy decision which is assumed to be the intersection of fuzzy constraints and fuzzy goals.
Abstract: Multistage incision-making (control) under fuzziness is considered. At each control stage, a fuzzy constraint is imposed on the control applied, and a fuzzy goal is imposed on the state attained. An optimal sequence of controls is sought which maximizes the membership function of the fuzzy decision which is assumed to be the intersection of fuzzy constraints and fuzzy goals. Thin is basically equivalent to the determination of an optimal sequence of controls which ‘ best satisfies the fuzzy constraints and fuzzy goals at nil the control stages ’. The generalization proposed in the paper replaces the strict ‘ all ’ the something milder, for example ‘ most ’: Thus, we seek an optimal sequence of controls which ‘ best satisfies the fuzzy constraints and fuzzy goals at, for example, most of the control stages ’. A calculus of linguistically quantified statements based upon fuzzy sets and possibility theory is used. First, the algebraic method is employed. The resulting control problem is solved by dy...
TL;DR: In this paper, the meaning of a proposition containing one or more fuzzy quantifiers is represented as a system of elastic constraints whose domain is a collection of fuzzy relations in a relational database.
Abstract: The generic term fuzzy quantifier is employed in this paper to denote the collection of quantifiers in natural languages whose representative elements are: several, most, much, not many, very many, not very many, few, quite a few, large number, small number, close to five, approximately ten, frequently, etc. In our approach, such quantifiers are treated as fuzzy numbers which may be manipulated through the use of fuzzy arithmetic and, more generally, fuzzy logic.
A concept which plays an essential role in the treatment of fuzzy quantifiers is that of the cardinality of a fuzzy set. Through the use of this concept, the meaning of a proposition containing one or more fuzzy quantifiers may be represented as a system of elastic constraints whose domain is a collection of fuzzy relations in a relational database. This representation, then, provides a basis for inference from premises which contain fuzzy quantifiers. For example, from the propositions “Most U's are A's” and Most A's are B's,” it follows that “Most2U's are B's,” where most2 is the fuzzy product of the fuzzy proportion most with itself.
The computational approach to fuzzy quantifiers which is described in this paper may be viewed as a derivative of fuzzy logic and test-score semantics. In this semantics, the meaning of a semantic entity is represented as a procedure which tests, scores and aggregates the elastic constraints which are induced by the entity in question.
TL;DR: In this paper a generalisation of fuzzy relations is introduced - fuzzy relations are defined on fuzzy subsets and properties like ordered reflexivity, symmetry, transitity, transitive closures of such generalised relations and operations on them are discussed.
TL;DR: The thesis advanced here is that within certain bounds (which are specified) there are many ways of representing uncertainty and in particular the ideas of probability and fuzzy sets are shown to be entirely compatible.
Abstract: In spite of the fact the engineers are familiar with the idea that physical systems can be modelled in various ways, it is often stated that probability theory is the only way of modelling uncertainties and degrees of belief about those uncertainties. The thesis advanced here is that within certain bounds (which are specified) there are many ways of representing uncertainty. In particular the ideas of probability and fuzzy sets are shown to be entirely compatible. A voting model is used to illustrate the argument before the basis of the formal treatment is outlined. Finally a set of conjectures are advanced about the types of problem that might best be tackled by probabilistic and fuzzy inference.
TL;DR: All possible negation operations which are optimal in some precise sense are fully described and turn out to be Lowen's fuzzy complements, Yager's intuitionistic negation, and a dual to the latter.
TL;DR: A new solution of the vectormaximum problem will be defined in terms of fuzzy mathematics and may be called the fuzzy solution, which will overcome difficulties which appear if otherwise solved by nonfuzzy mathematics.