Showing papers on "Fuzzy number published in 1979"
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 weighted least-square method is utilized to obtain the weights of belonging of each member to the set, which has the advantage that it involves the solution of a set of simultaneous linear algebraic equations and is thus conceptually easier to understand than the eigenvector method.
Abstract: Saaty has solved a basic problem in fuzzy set theory using an eigenvector method to determine the weights of belonging of each member to the set. In this paper, a weighted least-square method is utilized to obtain the weights. This method has the advantage that it involves the solution of a set of simultaneous linear algebraic equations and is thus conceptually easier to understand than the eigenvector method. Examples are given for estimating the relative wealth of nations and the relative amount of foreign trade of nations. Numerical solutions are obtained using both the eigenvector method and the weighted least-square method, and the results are compared.
423 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: 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
TL;DR: The results of the experiments indicate that neither the product nor the minimum fit the data sufficiently well, but the latter seems to be preferable.
263 citations
TL;DR: Methods of evaluating the parameter used in decision-making are given which can be varied to incorporate different utility functions and a new approach is described which overcomes their drawbacks.
260 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: Fuzzy concepts are shown to be very useful and easy to work with in this decision-aid problem where it seems interesting to use fuzzy sets.
192 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.
166 citations
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.
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.
TL;DR: The main purpose of this method is to describe and illustrate a formal procedure for constructing the graphic presentation of the hierarchical arrangement given the necessary information concerning the relation of each element to each other element.
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 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: It is shown how the sequence of partitions in any convex decomposition leads to a matrix for which the norm of the corresponding coefficient vector equals a scalar measure of partition fuzziness used with certain fuzzy clustering algorithms.
01 May 1979-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: This paper extends the method of approximate reasoning based upon fuzzy logic as proposed by Baldwin (1978) to arguments of a more complex nature, namely those with mixed inputs.
Abstract: In this paper we extend the method of approximate reasoning based upon fuzzy logic as proposed by Baldwin (1978) to arguments of a more complex nature, namely those with mixed inputs. Two approaches are given, both of which have their analogies in ordinary two valued logic.
TL;DR: A fuzzy subset is developed which reflects the objects ranking information in terms of grades of membership of the constraints, which are combined via intersection operation to form a fuzzy decision function.
Abstract: We investigated a fuzzy programming problem in which the constraints are a fuzzy subset over the alternatives and the objective is in the form of a linear ordering. A fuzzy subset is developed which reflects the objects ranking information in terms of grades of membership of the constraints. These two fuzzy subsets then are combined via intersection operation to form a fuzzy decision function.
TL;DR: The question of solving mathematical relationships involving fuzzy relations and numbers is investigated, first the ordinary mathematical relationship is looked at, then the fuzzy relations are investigated, and the situation where the authors have fuzzy numbers is studied.
Abstract: The question of solving mathematical relationships involving fuzzy relations and numbers is investigated. First we look at ordinary mathematical relationship. Then we investigate fuzzy relations. We then look at fuzzy quadratic equations. Finally, we study the situation where we have fuzzy numbers.
TL;DR: An improved algorithm for determining the (fuzzy) final rating of a multiple-aspect alternative according to a method proposed in an earlier paper (Baas ad Kwakernaak, 1977) is stated and proved.
Proceedings Article•
20 Aug 1979TL;DR: The discussion of the fuzzy inferences whose antecedents have fuzzy quantifiers such as "most", "some" and "many" using the authors' new methods for fuzzy conditional inferences is discussed.
Abstract: L. A. Zadeh and E. H. Mamdani proposed methods for the fuzzy reasonig in which the antecedent involves a fuzzy conditional inference "If x is A then y is B" with A and B being fuzzy concepts.
This paper points out that the consequences inferred by their methods do not always fit our intuitions, and suggests some new methods which fit our intuitions under several criteria such as modus ponens and modus tollens. This paper also contains the discussion of the fuzzy inferences whose antecedents have fuzzy quantifiers such as "most", "some" and "many" using our new methods for fuzzy conditional inferences.
TL;DR: The fuzzy entropy is applied to the seal impression problem to measure the subjective value of information under the condition of uncertainty and the effectiveness of the former method is 2.32 times higher than that of the latter method, provided that the cost of information is equal.