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Showing papers on "Fuzzy logic published in 1982"


Journal ArticleDOI
TL;DR: This paper deals successively with differentiation of ordinary functions at a fuzzy point and with differentiation at a nonfuzzy point, and with practical methods of computation are presented.

592 citations


Journal ArticleDOI
TL;DR: This paper deals with the properties of their methods in the case of 'generalized modus tollens', and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems.

493 citations


Journal ArticleDOI
Ronald R. Yager1
TL;DR: A new approach to the summarization of data based upon the theory of fuzzy subsets allows for a linguistic summary of the data and is useful for both numeric and nonnumeric data.

441 citations


Book
01 Jan 1982

328 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that if the scores are additive for different events and if the person chooses admissible values only, then there exists a known transform of the values x to values which are probabilities.
Abstract: : Let a person express his uncertainty about an event E, conditional upon an event F, by a number x and let him be given, as a result, a score which depends on x and the truth or falsity of E when F is true. It is shown that if the scores are additive for different events and if the person chooses admissible values only, then there exists a known transform of the values x to values which are probabilities. In particular, it follows that values x derived by significance tests, confidence intervals or by the rules of fuzzy logic are inadmissible. Only probability is a sensible description of uncertainty.

325 citations


Journal ArticleDOI
TL;DR: An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short) as discussed by the authors, which is actually set functions which are monotonic with respect to set inclusion.
Abstract: An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short). Fuzzy measures are actually set functions which are monotonic with respect to set inclusion. Triangular norms and conorms are semi-groups of the unit interval which have been thoroughly studied in the literature of functional equations. The proposed class encompasses probability measures, Zadeh's possibility measures and the dual notion of necessity measures. Any set function of the class can be expressed in terms of a density, and constructively defined out of this density. This feature makes the proposed framework attractive from a practical point of view for the representation and manipulation of subjective evidence. The link between t-norm and t-conorm based set functions and Shafer's belief functions is invesligaled.

304 citations


Book
01 Jan 1982
TL;DR: In this article, the authors present 44 articles by 74 contributors from 17 different countries on membership functions, composite fuzzy relations, fuzzy logic and inference, classifications and similarity measures, expert systems and medical diagnosis, psychological measurements and human behaviour, approximate reasoning and decision analysis, and fuzzy clustering algorithms.
Abstract: The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.

272 citations


Journal ArticleDOI
TL;DR: The uniform data function is a function which assigns to the output of the fuzzy c-means (Fc-M) or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm.
Abstract: The uniform data function is a function which assigns to the output of the fuzzy c-means (Fc-M) or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm. For the preselected number of cluster c, the Fc-M algorithm produces c vectors in the space in which the data lie, called cluster centers, which represent points about which the data are concentrated. It also produces for each data point c-membership values, numbers between zero and one which measure the similarity of the data points to each of the cluster centers. It is these membership values which indicate how the point is classified. They also indicate how well the point has been classified, in that values close to one indicate that the point is close to a particular center, but uniformly low memberships indicate that the point has not been classified clearly. The uniform data functional (UDF) combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows. For each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio (indicating better classification) from a clustering of a standard data set in which there is no cluster structure. These probabilities are then averaged over the data set to obtain the values of the UDF.

221 citations


Journal ArticleDOI
TL;DR: Pattern‐directed inference systems are among the most largely used tools in A.I. to‐day in order to represent and exploit knowledge, but the lack of flexibility in the matching remains a drawback in this kind of system.
Abstract: Pattern‐directed inference systems (P.D.I.S.) are among the most largely used tools in A.I. to‐day in order to represent and exploit knowledge. Generally, P.D.I.S.'s use production rules triggered by matching between rule patterns and elements of the data base. However, the lack of flexibility in the matching remains a drawback in this kind of system. In the framework of the communication in natural language with robots, approximate descriptions of real world situations and approximately specified rules are needed; furthermore, similarity in the matching process does not always need to be perfect. Thus, the pervading fuzziness of natural language can be taken into account. The following levels, belonging to the real interval [0,1], are evaluated: The possibility of similarity between referents designated in the data and in the pattern respectively; the necessity that a referent designated in the data is similar to a referent designated in the pattern. Designations are fuzzy when the pattern or the data are fuzzy, which is usual with words of a natural language.

183 citations


Journal ArticleDOI
TL;DR: The family of all the solutions of a fuzzy relation equation on a finite set is considered, characterized by the set ofall the lower solutions, which can be obtained by a combinatorial algorithm.

181 citations


Journal ArticleDOI
TL;DR: Two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described, under the restrictive assumption that for any x in X, the membership function of Rχ has a ‘complementary function’.

Journal ArticleDOI
TL;DR: The min-bounded sum operator is suggested which is a compensatory one, has some desired properties and is supported by empirical arguments and allows a considerable decrease of the computational burden in the substitute problem and leads to a solution which is attractive from the stand-point of efficiency.

Journal ArticleDOI
TL;DR: The paper considers the determination of optimal inventory policy of firms from a global viewpoint of top management, represented as a fuzzy conditional statement equated with a fuzzy relation which is the firm's optimal fuzzy replenishment rule.

Journal ArticleDOI
TL;DR: Rational inference procedures are described in this paper on the basis of established Bayesian theory and Dempster and Shafer's theory of evidence to include fuzzy knowledge.

Journal ArticleDOI
TL;DR: For a large class of triangular norms each T-fuzzy ρ-algebra is generated, i.e., consists of all functions μ:X → [0, 1] being measurable with respect to some σ- algebra on X.

Journal ArticleDOI
TL;DR: A binary operation ⊕ is constructed on the L-fuzzy real line R (L) which reduces to the usual addition on R if ⊆ is restricted to the embedded image of R in R ( L), which yields a partially ordered, abelian cancellation semigroup with identity, and which is jointly fuzzy continuous on R (l).

Journal ArticleDOI
TL;DR: The present article seeks to show that these inadequacies are the consequence of embracing fuzzy-set theory within prototype theory, and proposes an alternative, more adequate version of prototype theory in which concep! gal gradedness is represented ordinally rather than by fuzzy sets.

Journal ArticleDOI
TL;DR: The main result is the existence and uniqueness of the probabilistic completion of L-fuzzy uniform spaces and the applicability of this theory is given.
Abstract: Basic properties of probabilistic topologies associated with L-fuzzy uniformities are studied, e.g. regularity, uniform continuity and 1-completeness. The main result is the existence and uniqueness of the probabilistic completion of L-fuzzy uniform spaces. Moreover with respect to the applicability of this theory we also give concrete representations of the probabilistic completion of compact as well as of Polish spaces.

Journal ArticleDOI
TL;DR: FUZZY QMODEL utilizes the fuzzy c-means algorithm of Bezdek to provide an alternative initial mixing polyhedron and so can produce suitable solutions in the presence of noisy or “messy” data points.
Abstract: Many data sets can be viewed as a collection of samples representing mixtures of a relatively small number of end members. When end members are present in the sample set, the algorithm QMODEL by Klovan and Miesch can efficiently determine proportionate contributions. EXTENDED QMODEL by Full, Ehrlich, and Klovan was designed to deduce the composition of realistic end members when the end members are not represented by samples. However, in the presence of high levels of random variation or outliers not belonging to the system of interest, EXTENDED QMODEL may not be reliable inasmuch as it is largely dependent on extreme values for definition of an initial mixing polyhedron. FUZZY QMODEL utilizes the fuzzy c-means algorithm of Bezdek to provide an alternative initial mixing polyhedron. This algorithm utilizes the collective property of all the data rather than outliers and so can produce suitable solutions in the presence of noisy or “messy” data points.

Journal ArticleDOI
TL;DR: This paper proposes a further concept of fuzzy uniformities—so-called fuzzy T- spaces, introduced by Lowen, which are equivalent to fuzzy U- spaces in the real world.

Journal ArticleDOI
TL;DR: An algorithm for solving transportation problems with fuzzy constraints is proposed and the relationship between the algebraic structure of the optimum solution of the deterministic problem and its fuzzy equivalent is investigated.

Journal ArticleDOI
TL;DR: A dynamic programming functional equation for a multi-stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation, an extension of the Bellman-Zadeh model.

Journal ArticleDOI
TL;DR: This article showed that much of what these articles propose is but a rediscovery of well-known results and suggested that most of what they propose is just a re-discovered result.
Abstract: An earlier paper and subsequent commentaries in Decision Sciences described purportedly new methods for formulating and solving goal programming problems with fuzzy goals. This note suggests that much of what these articles propose is but a rediscovery of well-known results.

Journal ArticleDOI
Jean Siskos1
TL;DR: A special multiple criteria decision making approach for solving problems in context with fuzzy individual preferences, i.e. a highway plan choice problem and a problem in marketing research dealing with the launching of a new product.

Journal ArticleDOI
TL;DR: Fuzzy set theory has been developed for and applied to problems involving complex systems like ecosystems as mentioned in this paper, where fuzzy compartmentalization of ecosystem components allows greater diversity of behavior than deterministic or probabilistic methods.

Journal ArticleDOI
TL;DR: This paper will show that the mathematical requirements placed on the generalization in order that the lattice structures of the fuzzy subset theory be preserved are really quite minimal.

Journal ArticleDOI
TL;DR: A theorem equivalent to the Ford and Fulkerson one concerning the classic task of maximum flow is proved and an algorithm for searching maximum flow assuming integer values of flows on network arcs is presented.

Journal ArticleDOI
TL;DR: The problem to be addressed and tackled in this paper arose as a byproduct from some efforts at solving problems involving multiple goals by linking linear and goal programming models that some forms for interdependence among the goals could not be handled in the programming models.


Journal ArticleDOI
Ronald R. Yager1
TL;DR: In this paper, the definition of the and operation in multivalued logic and decision making is investigated, and a set of basic properties for selecting an appropriate operator are given, as well as a general class of connectives.
Abstract: We investigate the definition of the “and” operation in multivalued logic and decision making. A set of basic properties are suggested. Rules for selecting an appropriate operator are given. A general class of connectives is also suggested.