Showing papers on "Fuzzy logic published in 1980"
995 citations
TL;DR: The theory of Zangwill is used to prove that arbitrary sequences generated by these (Picard iteration) procedures always terminates at a local minimum, or at worst, always contains a subsequence which converges to aLocal minimum of the generalized least squares objective functional which defines the problem.
Abstract: In this paper the convergence of a class of clustering procedures, popularly known as the fuzzy ISODATA algorithms, is established. The theory of Zangwill is used to prove that arbitrary sequences generated by these (Picard iteration) procedures always terminates at a local minimum, or at worst, always contains a subsequence which converges to a local minimum of the generalized least squares objective functional which defines the problem.
965 citations
TL;DR: A general class of conectives, intersection and union, are presented for fuzzy sets, and the properties of this class are studied in comparison to the ordinary intersection andunion.
786 citations
537 citations
TL;DR: The theory of fuzzy power sets is shown very naturally to require the use of a fuzzy implication operator and emphasis is placed on the dependence of the choice of operators upon the purposes the user has in hand.
462 citations
TL;DR: This paper illustrates the application of “fuzzy subsets” concepts to goal programming in a fuzzy environment by considering a fuzzy goal-programming problem with multiple goals having equal weights associated with them and developing a solution approach based on linear programming.
Abstract: This paper illustrates the application of “fuzzy subsets” concepts to goal programming in a fuzzy environment. In contrast to a typical goal-programming problem, the goals are stated imprecisely when the decision environment is fuzzy. The paper first considers a fuzzy goal-programming problem with multiple goals having equal weights associated with them. A solution approach based on linear programming is developed. Next, the solution approach is extended to the case where unequal fuzzy weights are associated with multiple goals. Numerical examples are provided for both cases to illustrate the solution procedure.
460 citations
01 Jan 1980-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: A checklist paradigm is given, by which entirely new light is thrown upon the semantics of these operators, connecting them, in a unified way, with measures which might be made upon more refined data.
Abstract: After a brief discussion of the need for fuzzy relation theory in practical systems work, the paper explains the new triangle products of relations and the sort of results to be expected from them, starting from a crisp situation. The asymmetry of these products, in contrast to correlation, is noted as essential to the investigation of hierarchial dependencies. The panoply of multi-valued implication operators, with which the fuzzification of these products can be accomplished, is presented, and a few of their properties noted. Then, most importantly, a checklist paradigm is given, by which entirely new light is thrown upon the semantics of these operators, connecting them, in a unified way, with measures which might be made upon more refined data. Using a well-known psychological test in an actual situation, so that the finer structure is in fact available, a comparison is made between a checklist measure and several of the operator values, showing the interrelationship concretely. Finally, some products and their interpretations are presented, using further real-world data.
330 citations
TL;DR: The quality of the model is seen to be a multi-faceted concept encompassing complexity, accuracy and uncertainty.
269 citations
01 Nov 1980
TL;DR: In this article, a technique for making linguistic decsions is presented, where fuzzy sets are used to deal with uncertainty and decisions taken on the basis of such infomation must themselves be fuzzy.
Abstract: A technique for making linguistic decsions is presented. Fuzzy sets are assued to be an appropriate way of dealng with uncertainty, and it b therefore cncluded that decisions taken on the basis of such infomation must themselves be fuzzy. It b inappriate then to present the decision in numencal form; a statement in natural angug is much better. For brevity only a single-stage multlabute decsion problem is considered. Solutions to such problems are shown using ideas in linguisc approximation and truth qualiction. An extensive example illuminates the basic ideas and techniques.
250 citations
Book•
01 Nov 1980
TL;DR: McCawley supplements his earlier book with new material on the logic of conditional sentences, linguistic applications of type theory, Anil Gupta's work on principles of identity, and the generalized quantifier approach to the logical properties of determiners.
Abstract: McCawley supplements his earlier book-which covers such topics as presuppositional logic, the logic of mass terms and nonstandard quantifiers, and fuzzy logic-with new material on the logic of conditional sentences, linguistic applications of type theory, Anil Gupta's work on principles of identity, and the generalized quantifier approach to the logical properties of determiners.
224 citations
01 Jan 1980
TL;DR: Fuzzy sets theory and fuzzy logic constitute the basis for the linguistic approach and models, based on this approach, can be constructed to simulate approximate reasoning.
Abstract: Fuzzy sets theory and fuzzy logic constitute the basis for the linguistic approach. Under this approach, variables can assume linguistic values. Each linguistic value is characterized by a label and a meaning. The label is a sentence of a language. The meaning is a fuzzy subset of a universe of discourse. Models, based on this approach, can be constructed to simulate approximate reasoning. The implementation of these models presents two major problems, namely how to associate a label to an unlabelled fuzzy set on the basis of semantic similarity (linguistic approximation) and how to perform arithmetic operations with fuzzy numbers. For each problem a solution is proposed. Two illustrative applications are discussed.
TL;DR: The problem of how to permit a patron to represent the relative importance of various index terms in a Boolean request while retaining the desirable properties of a Boolean system is concerned.
Abstract: This article concerns the problem of how to permit a patron to represent the relative importance of various index terms in a Boolean request while retaining the desirable properties of a Boolean system. The character of classical Boolean systems is reviewed and related to the notion of fuzzy sets. The fuzzy set concept then forms the basis of the concept of a fuzzy request in which weights are assigned to index terms. The properties of such a system are discussed, and it is shown that such systems retain the manipulability of traditional Boolean requests.
TL;DR: It is pointed out that the consequence inferred by the methods suggested does not always fit intuitions and improved methods are suggested which fit the authors' intuitions under several criteria.
TL;DR: The functions of minπ and maxπ are introduced as the analogues of nearest neighbour “propagation” signals of binary images as well as extending some already well known binary processes into grey level algorithms.
TL;DR: The problem of selecting the highest grade of membership of fuzzy subsets of type 2 and of choosing the most truthful of a group of fuzzy propositions involve making a choice among fuzzy subset on the unit interval is proposed.
Abstract: The problem of selecting the highest grade of membership of fuzzy subsets of type 2 and of choosing the most truthful of a group of fuzzy propositions involve making a choice among fuzzy subsets on the unit interval. A procedure is proposed for the selection of fuzzy subsets on the unit interval. This procedure involves selecting the subset closest to a linear membership function on the unit interval.
01 Oct 1980-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: A new operation for both multivalued implication and fuzzy inference is discussed, based upon the exponentiation operation, which investigates the problem of making inferences based on fuzzy conditional statements.
Abstract: We investigate the problem of making inferences based on fuzzy conditional statements. We discuss a new operation for both multivalued implication and fuzzy inference. This operation is based upon the exponentiation operation.
TL;DR: This paper aims to give greater understanding than hitherto, to the choice of implications rules when modelling a given situation using approximate reasoning with fuzzy logic, and asserts properties of implication which satisfy an intuitive understanding of the nature of fuzzy deduction.
TL;DR: It is proved that the core (defined in the paper) is consistent for any n-persons fuzzy game and that the Shapley values exists and it is unique for any fuzzy game with proportional values.
01 Jan 1980
TL;DR: In this paper, the consequences of changes in all these systems, to analyze them, to understand their dynamics, to influence their behaviour, make it increasingly difficult to understand the consequences.
Abstract: Increasingly complex interaction between man and nature, increasingly complex interaction between man and man-made artificial systems, make it increasingly difficult to comprehend the consequences of changes in all these systems, to analyze them, to understand their dynamics, to influence their behaviour.
TL;DR: A method of image enhancement by computer using the fuzzy set theoretic approach that involves extraction of fuzzy properties corresponding to pixels and then successive application of fuzzy operator `contrast intensification´ on the property plane is reported.
Abstract: A method of image enhancement by computer using the fuzzy set theoretic approach is reported. The algorithm involves extraction of fuzzy properties corresponding to pixels and then successive application of fuzzy operator `contrast intensification´ on the property plane. System performance with different indexes of fuzziness is demonstrated for an English script input.
TL;DR: A model of a computer-assisted diagnostic system using fuzzy subsets has been developed and provides the physician with proven diagnoses, excl~tded diagnoses and diagnostic hints, including reasons for the diagnoses displayed.
Abstract: A model of a computer-assisted diagnostic system using fuzzy subsets has been developed. The physician documents symptom-diagnosis presence relationships and symptom-diagnosis conclusiveness relationships by means of labels of the fuzzy subsets never, almost nevm·, very very seldom, very seldom, seldom, m01·e or less seldom, not known, more 01· less often, often, very often, ve1·y ve1·y often, almost always, always. Symptoms are regarded as fuzzy subsets of reference sets. The reference set includes all values the symptom may assume. The degree of membership of a value in the fuzzy subset of a symptom is calculated when the patient's symptom pattern is available. By means of compositions of fuzzy relations, four different diagnostic indications are determined for every diagnosis under consideration: presence indication, conclusiveness indication, non-p1·esence indication and non-symptom presence indication. By performing the diagnostic process, the system provides the physician with proven diagnoses, excl~tded diagnoses and diagnostic hints, including reasons for the diagnoses displayed. Proposals for further investigations may also be requested.
TL;DR: The product of fuzzy σ-algebras is introduced which is a generalisation of the family of fuzzy events considered by L.A. Zadeh and is a comparison between classical measurability of functions and fuzzy measurable defined in this paper.
TL;DR: Two implication operators and resulting relationships between fuzzy sets are studied and the results compared with previous ones obtained with other implication operators are compared.
01 Jan 1980
TL;DR: A new measure of consensus in small groups based on fuzzy mathematics which overcomes the difficulties found in other fuzzy consensus measures is examined, useful in analyzing how groups reach a decision.
Abstract: This paper examines a new measure of consensus in small groups based on fuzzy mathematics which overcomes the difficulties found in other fuzzy consensus measures. The method involves the construction of α-Consensus measures from fuzzy relations. These measures are integrated over a to produce a measure of small group consensus. This procedure is useful in analyzing how groups reach a decision. Results of an experimental application of this fuzzy analysis procedure are given to illustrate the proposed technique.
TL;DR: This paper briefly reviews the method from an operational viewpoint, isolating the individual processes that are used in the method, and presenting a feasible algorithm for computing each process.
01 Jan 1980-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: Although the prescriptive rules were found to be an inadequate model of the kiln operators, analysis indicated that the rules had the potential to produce better kiln control.
Abstract: This paper describes the investigation into the control skills of cement kiln operators with a view to modelling these skills by a fuzzy algorithm. The operators' strategies were studied by observing and making a detailed record of the operators' behaviour as they controlled the kiln. Analysis of the observational record suggested that many aspects of the operators' control behaviour could be modelled by a threshold logic controller. An improvement to the threshold model was attempted by comparing the operators' performance with the performance produced by a set of prescriptive control rules. Although the prescriptive rules were found to be an inadequate model of the kiln operators, analysis indicated that the rules had the potential to produce better kiln control. The implementation of the prescriptive rules as a fuzzy controller is discussed.
01 Jan 1980
TL;DR: An economic interpretation is given and properties of the fuzzy dual problems are derived, leading to a pair of “fuzzy dual” optimization problems.
Abstract: In classical duality theory of linear programming the saddlepoint of the Lagrangian is the solution of the max-min problem as well as of the min-max problem. In using the theory of fuzzy sets these problems are interpreted in a new sense — leading to a pair of “fuzzy dual” optimization problems. An economic interpretation is given and properties of the fuzzy dual problems are derived.
01 Jan 1980
TL;DR: This short note is an exploratory paper where the difference of nature between probabilistic knowledge and possibilistic knowledge is emphasized in the framework of queuing problems.
Abstract: This short note is an exploratory paper where the difference of nature between probabilistic knowledge and possibilistic knowledge is emphasized in the framework of queuing problems. While the arrival have usually to be modelled by a stochastic process (provided that its correct identification is possible), a queuing system may also exhibit another kind of uncertainty regarding the service time or the service rule which are not always precisely known or defined. Fuzziness, rather than randomness corresponds to the deep nature of this uncertainty. Thus, it is dealt with fuzzy service time and fuzzy service rule in a queuing problem. Hints for solutions are given in various situations. Moreover, an entirely possibilistic model is discussed.