Showing papers on "Fuzzy logic published in 1979"
TL;DR: It is suggested that fuzziness can be related to the lack of distinction between a set and its negation and the concept of compatibility is used to develop linguistic measures of fuzziness.
Abstract: We investigate the meaning of the concept of fuzziness. It is suggested that fuzziness can be related to the lack of distinction between a set and its negation. Using fuzzy subsets with grades of membership in the unit interval, measures of fuzziness are suggested. First, a class of measures based on metric distances is used to derive numeric measures of fuzziness of a fuzzy set. Finally, the concept of compatibility is used to develop linguistic measures of fuzziness.
556 citations
TL;DR: The results obtained in part I of the paper are specialized to the case of discrete fuzzy random variables and algorithms are derived for determining expectations, fuzzy probabilities, fuzzy conditional expectations and fuzzy conditional probabilities related to discrete fuzzyrandom variables.
491 citations
TL;DR: A three parameters representation for fuzzy numbers is shown to be very convenient to perform usual operations for normalized convex fuzzy subsets of the real line, i.e. fuzzy numbers.
399 citations
351 citations
TL;DR: This paper generalizes topological relationships among parts of a digital picture to fuzzy subsets, and develops some of their basic properties.
Abstract: Topological relationships among parts of a digital picture, such as connectedness and surroundedness, play an important role in picture analysis and description. This paper generalizes these concepts to fuzzy subsets, and develops some of their basic properties.
335 citations
TL;DR: The so-called linguistic models that arise from this notation are shown to be extremely useful for modelling highly nonlinear low-order systems and for determining, explicitly, the rules of 'optimal' fuzzy logic controllers.
283 citations
259 citations
TL;DR: An approach to approximate reasoning based upon fuzzy logic that has the advantage of being computationally very simple and efficient even for multiple compound implication statements, so allowing for easy pencil and paper calculation.
227 citations
TL;DR: In this article, a characterization of minimal prime filters in the lattice IX containing a given filter in IX by means of ultra-filters on X is presented, which enables us to characterize fuzzy compactness and fuzzy continuity.
Abstract: In the first paragraph we study filters in the lattice IX, where I is the unitinterval and X an arbitrary set. The main result of this section is a characterization of minimal prime filters in IX containing a given filter in IX by means of ultrafilters on X. In the second paragraph we apply the results of the previous section to define convergence in a fuzzy topological space which enables us to characterize fuzzy compactness and fuzzy continuity.
197 citations
TL;DR: The fuzzy logic controller is reviewed and its parameter are explicitly identified and the problem of initial selection and subsequent adjustment of the parameters are discussed in detail by example.
TL;DR: A logical calculus is developed with propositions taking their truth values in the set of fuzzy sets of [0, 1], an extension of already known multivalent logics, and the associated set theory is shown to be that of fuzzy Sets of type 2 on a given universe.
Abstract: A logical calculus is developed with propositions taking their truth values in the set of fuzzy sets of [0, 1]. This fuzzy-valued logic is an extension of already known multivalent logics, and the associated set theory is shown to be that of fuzzy sets of type 2 on a given universe. Various interpretative functions are given for the usual connectives of propositional calculus, using extended “max” and “min” operators. Examples of inference are provided and a compositional rule for fuzzy-valued fuzzy relations is suggested. Computations of truth values for composite propositions are shown to be very easy. It is hoped that such a logic will be helpful in the modelization of approximate reasoning, in natural language.
TL;DR: This paper defines and explores the properties of lower and upper inverses of fuzzy relations which extend multi-valued mappings and relates the preceeding notions to possibility distributions in natural languages and to problems of medical diagnosis.
TL;DR: A fuzzy safety measure that expresses the confidence in the objective probability and also in other, larger values of the probability of failure, and can be augmented by professional insight and experience.
Abstract: In deciding the chances of failure of a design, two types of information are available: objective and subjective. In dealing with objective information in the form of countable data, unbiased probability distributions of loading and structural capacity are obtained by employing the principle of maximum entropy. Subjective information is considered in a linguistic form and requires a transformation from the verbal to the numerical. This is attained by the use of fuzzy set theory. The fuzzy calculus is then employed to fuzzify the objective probability in light of the subjective insight. The result is a fuzzy safety measure that expresses the confidence in the objective probability and also in other, larger values of the probability of failure. In this way objective, numerical, frequency type information can be augmented by professional insight and experience.
01 Jul 1979-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: The concepts of truth value restriction and fuzzy logical relation are used to give a general approach to fuzzy logic and also fuzzy reasoning involving propositions with imprecise or vague description.
Abstract: The concepts of truth value restriction and fuzzy logical relation are used to give a general approach to fuzzy logic and also fuzzy reasoning involving propositions with imprecise or vague description.
TL;DR: The usual notion of fuzzy set is extended in such a way that the elements of fuzzy sets again can be fuzzy sets, and the fuzzy set theoretic operations are generalized up to the notion of a fuzzy mapping.
TL;DR: This definition is compared with Zadeh's definition of using the expected value of A as the probability of A and it is shown that the distinction between these two definitions is based upon the choice of definition for the cardinality of a fuzzy subset.
01 Jul 1979-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: This paper gives a critical appraisal of “fuzzy logic” from the viewpoint of a logician and concludes that no acceptable case has been made for the need for it.
Abstract: This paper gives a critical appraisal of “fuzzy logic” from the viewpoint of a logician and concludes that no acceptable case has been made for the need for it
01 Dec 1979
TL;DR: The concepts of truth value restriction and fuzzy logical relation are used to give a general approach to fuzzy logic and also fuzzy reasoning involving propositions with imprecise or vague description as discussed by the authors.
Abstract: The concepts of truth value restriction and fuzzy logical relation are used to give a general approach to fuzzy logic and also fuzzy reasoning involving propositions with imprecise or vague description.
01 Jun 1979
TL;DR: A fuzzy approach to DM is described, incorporating linguistic variables, relations, and algorithms, which helps to solve the problem of partial utilities and their interdependence.
Abstract: Multiattribute decisionaking (DM) is treated as a special kind of structured human problem solving. Emphasis is placed on the use of the available knowledge about utilities, which is obtained by combining heuristics and traditional aggregation methods. In this way, the problem of partial utilities and their interdependence may be solved. A fuzzy approach to DM is described, incorporating linguistic variables, relations, and algorithms. It is summarized in a formal model and illustrated by an example.
01 Mar 1979-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: It is shown that Zadeh's max and min operations are the only possible extension of the classic union and intersection operations which are meaningful in the face of ordinal information on degrees of membership.
Abstract: The question of obtaining fuzzy membership grades is discussed. It is then shown that Zadeh's max and min operations are the only possible extension of the classic union and intersection operations which are meaningful in the face of ordinal information on degrees of membership. A discussion of ratio type information-meaningful operations is also presented.
TL;DR: Stimuli were generated by factorially varying two sets of features that distinguish between two letter patterns and subjects rated the degree to which each stimulus was an instance of one letter rather than the alternative.
Abstract: Stimuli were generated by factorially varying two sets of features that distinguish between two letter patterns. Subjects rated the degree to which each stimulus was an instance of one letter rather than the alternative. The obtained ratings were relatively continuous and systematic functions of the feature manipulations. The results were well accounted for by a model in which (a) each feature has an associated fuzzy predicate that is used to independently evaluate the degree to which it is true that the feature is present in the stimulus; (b) the featural truth values are integrated according to fuzzy logical expressions that correspond directly to propositional descriptions of each letter pattern; and (c) the resulting goodness of match to the stimulus for each letter is compared to that of the alternatives to determine the final identification. Language: en
01 May 1979-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: Various interpretations of conditional propositions are considered, which include relational definitions using Łukasiewicz logical implication rule and Zadeh's Maximin rule, and theorems for reducing dimensionality are presented.
Abstract: Various interpretations of conditional propositions are considered, which include relational definitions using Łukasiewicz logical implication rule and Zadeh's Maximin rule. Theorems are presented which describe the relationship between the interpretations. An example of reasoning in ordinary set theory is presented as a special case of the method used for approximate reasoning with fuzzy propositions. Models of reasoning from multiple conditional propositions of high dimensional state are constructed and theorems for reducing dimensionality are presented. Problems of dimensionality using the Łukasiewicz implication rule are discussed and an alternative method based on fuzzy logic is indicated briefly.
TL;DR: A branch‐and‐bound algorithm for solving the problem of determining a maximizing decision in the multistage control of a fuzzy system in a fuzzy environment is proposed and is simple and relatively efficient.
Abstract: In this paper, the problem of determining a maximizing decision in the multistage control of a fuzzy system in a fuzzy environment is considered. In the fuzzy system under control, the state is assumed to be fuzzy, while the control, not fuzzy. The fuzzy environment is given by fuzzy constraints and fuzzy goals imposed on particular control stages. The number of control stages, i.e. the termination time, is assumed to be fixed and specified; the same applies to the initial state. The fuzzy decision is defined as the intersection of fuzzy goals and fuzzy constraints. For solving the above problem, a branch‐and‐bound algorithm is proposed. The algorithm is simple and relatively efficient. Two examples are given.
TL;DR: A generalized Tanimoto coefficient measuring attitudinal similarity provides the fundamental basis for location and analysis of potential coalitions in a group decision‐making task.
Abstract: After noting several limiting features and procedural disadvantages of typical game theoretic studies of coalition formation, a new measurement procedure based on fuzzy set theory is described A generalized Tanimoto coefficient measuring attitudinal similarity provides the fundamental basis for location and analysis of potential coalitions in a group decision‐making task The results of a pilot study using fuzzy preference matrices and α‐level sets to determine the existence and structural evolution of coalitions over time are presented Finally, some conjectures concerning the definition and future study of coalitions are advanced
TL;DR: The problem of optimization under elastic constraints is formulated which will be served to justify the extension of possibility measure to linguistic variables, and the mathematical notion of possibility is presented, in the setting of set-functions, as a special case of Choquet capacities.