Showing papers on "Fuzzy number published in 1985"
TL;DR: An extensive survey on fuzzy set-theoretic operations is provided, and the relevance of the theory of functional equations in the axiomatical construction of classes of such operations and the derivation of functional representations is emphasized.
932 citations
TL;DR: The concept of maximizing set and minimizing set is introduced to decide the ordering value of each fuzzy number and these values are used to determine the order of the n fuzzy numbers.
875 citations
TL;DR: This work investigates the problem of employing expert opinion to rank alternatives across a set of criteria and employs fuzzy arithmetic to compute an issue's fuzzy ranking.
492 citations
TL;DR: It is shown that any of such operators is generated by a family of fuzzy subsets, which gives the way to construct F-indistinguishabilities, and facilitates new applications of fuzzy relations.
428 citations
TL;DR: The inequality relation between two fuzzy numbers is investigated and a certain type of such a relation motivated by practical interpretation is proposed, and its correspondence with the usual lattice-type relation generated by the extended maximum and minimum operators is proposed.
348 citations
TL;DR: This paper surveys major models and theories in this area of fuzzy set theory and offers some indication on future developments which can be expected.
323 citations
TL;DR: The method of fuzzy c -means is described in detail and used to create fuzzy groups for two sets of climatic data, one from Australia and the other from China, showing the inherent continuity of the data and a reasonable geographical contiguity.
249 citations
01 Jan 1985
TL;DR: It is demonstrated that fuzzy set theory is applicable to a wide range of practical problems and that simple fuzzy control algorithms do give good results.
Abstract: A state-of-the-art review of the literature related to applications of fuzzy set theory, with special emphasis on fuzzy industrial controllers, is presented. It is demonstrated that fuzzy set theory is applicable to a wide range of practical problems and that simple fuzzy control algorithms do give good results.
239 citations
TL;DR: In this article, the concept of a normal fuzzy random variable was defined and the following representation theorem was proved: every normal fuzzy variable equals the sum of its expected value and a mean zero random vector.
Abstract: In this paper we define the concept of a normal fuzzy random variable and we prove the following representation theorem: Every normal fuzzy random variable equals the sum of its expected value and a mean zero random vector.
234 citations
TL;DR: A systematic investigation of the cardinality of a fuzzy set is performed which unifies and improves previous attempts and the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized.
01 Nov 1985
TL;DR: An energy `measure' of a fuzzy dynamic system is proposed, and `an energy function' is formulated, and a heuristic algorithm for determining the stability of the fuzzy system is also proposed.
Abstract: A dynamic system is stable if its total energy decreases monotonically until a state of equilibrium is reached. The stability of a fuzzy dynamic system is based on a generalization of this notion. If a free fuzzy dynamic system has an asymptotically stable equilibrium state, the stored energy of the system displaced within the domain of attraction decays with time until it assumes its minimum value at the equilibrium state. An energy `measure' of a fuzzy dynamic system is proposed, and `an energy function' is formulated. A heuristic algorithm for determining the stability of the fuzzy system is also proposed. To illustrate the applications of the algorithm, some numerical examples are given.
18 Aug 1985
TL;DR: Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness.
Abstract: Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness. Prolog-ELF inherits all the desirable basic features of Prolog. In addition to assertions with truth-values between 1.0 and 0.5 (0 for exceptional cases), fuzzy sets can be very easily manipulated. An application of fuzzy logical database is illustrated.
TL;DR: The influence of fuzzy implication operators and the connective Also on the accuracy of a fuzzy model of a d.c. series motor is considered and the best types of fuzzy relations, representing fuzzy models of a real system, are chosen.
TL;DR: The first part contains an extensive presentation of the resolution of fuzzy relational equations; the applicational aspects of these equations in systems analysis, decision-making, and arithmetic of fuzzy numbers are presented.
TL;DR: The classical model of decision-making under uncertainty is extended to the case when the consequences of a decision are only roughly described and their probabilities of occurrence modeled by intervals or fuzzy numbers.
TL;DR: In this article, the inverse problem concerned with fuzzy relations is investigated and conditions for the existence of a solution are shown and an analytical solution is given, and a method for the improvement of the solution is proposed.
TL;DR: It is shown that antecedents and consequents are related in terms of a fuzzy relation and fuzzy relational equations form an effective and plausible tool for implementations of reasoning methods with fuzzy premises.
01 Dec 1985
TL;DR: The method makes use of the lambda-cut representations of fuzzy sets and interval analysis to perform extended algebraic operations such as those encountered in risk and decision analysis under fuzzy conditions with accuracy which is much better than the conventional discretization approach.
Abstract: This paper describes an algorithm for performing extended algebraic operations such as those encountered in risk and decision analysis under fuzzy conditions. The method makes use of the lambda-cut representations of fuzzy sets and interval analysis. It is an approximate computational technique but is highly efficient compared with the exact method of nonlinear programming, with an accuracy which is much better than the conventional discretization approach. The effectiveness and utility of the procedure are illustrated with examples of fuzzy risk and decision analysis taken from available literature.
01 Jan 1985
TL;DR: An extension of multi attribute utility analysis for the multiple-agent decision problem is presented and a computer package for ensuring the transistivity of collective preference ordering in an agreement level is demonstrated for assessment of fuzzy multiattribute utility functions.
Abstract: An extension of multiattribute utility analysis for the multiple-agent decision problem is presented. Although multiattribute utility analysis is concerned with decision-making under uncertainty, assessment of the parameters of the multiattribute utility functions is actually performed deterministically by the single decision-maker. The authors are concerned with fuzzy evaluation of the multiattribute utility function, which is based on fuzzy preference ordering and scaling constants using membership functions of fuzzy set theory. The fuzzy approach treats a conceptual imprecision that accrues from a multiplicity of evaluation. A fuzzy multiattribute utility function with multiple agent evaluation is derived. A computer package, ICOPSS/FR, for ensuring the transistivity of collective preference ordering in an agreement level is demonstrated for assessment of fuzzy multiattribute utility functions.
TL;DR: In the presented procedure, optimum structural design with fuzzy constraints is transformed into a set of ordinary optimum problems by a level cuts approach which results in a sequence of optimum design schemes with different design levels.
Abstract: It is pointed out that there exists a vast amount of fuzzy information in both objective and constraint functions of optimum design of structures (ODS) Thus, relatively reasonable optimum designs can only be obtained by fuzzy programming methods. While all fuzzy constraints enclose a fuzzy feasible region in decision-making space, the fuzzy optimum solution will be a sequence of points in a small fuzzy optimum subregion. In the presented procedure, optimum structural design with fuzzy constraints is transformed into a set of ordinary optimum problems by a level cuts approach which results in a sequence of optimum design schemes with different design levels. The concept of optimum design level corresponding to the most suitable scheme among the obtained sequence is also advanced in this paper.
TL;DR: The probability of fuzzy events is defined as a denumerable additivity measure based on a non-conventional approach of separativity between fuzzy subsets that fulfils all properties analogous to the properties of classical probability in the crisp case.
TL;DR: By means of the asymptotic structural characteristics of fuzzy measure, four forms of generalization are given for both Egoroff's theorem, Riesz's theorem and Lebesgue's theorem respectively, and the almost everywhere (pseudo-almost everywhere) convergence theorem is proved.
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TL;DR: In this article, the notions of a subspace, a sum, and a product are extended to fuzzy closure spaces (or fcs's), and the hereditary, additivity, and productivity behaviour of compactness in fcss is investigated.
TL;DR: Three kind of convergences are defined on a space of fuzzy sets and some comments on the fixed point property are represented.
TL;DR: It is proved that if σ is a fuzzy subset of S and μσ is the strongest fuzzy relation on S that is a fuzzier relation on σ, then μσ are a fuzzy subgroup if and only if �x is a furry subgroup.
TL;DR: In Part II the same problem will be discussed using a competitive-like pooling, and some solution concepts are considered: cores, minimax (opposition) sets, consensus winners, etc.
Abstract: Starting from individual fuzzy preference relations, some (sets of) socially best acceptable options are determined, directly or via a social fuzzy preference relation. A fuzzy majority rule is assumed to be given by a fuzzy linguistic quantifier, e.g., “most, ” Zadeh's conventional approach to linguistic quantifiers, based on the cardinalities of fuzzy sets, yields a consensory-like pooling of individual opinions. Some solution concepts are considered: cores, minimax (opposition) sets, consensus winners, etc. In Part II the same problem will be discussed using a competitive-like pooling.
TL;DR: This paper focuses on multiobjective linear fractional programming problems with fuzzy parameters and presents a new interactive decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method.
Abstract: In this paper, we focus on multiobjective linear fractional programming problems with fuzzy parameters and present a new interactive decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method. The fuzzy parameters in the objective functions and the constraints are characterized by fuzzy numbers. The concept of a-Pareto optimality is introduced in which the ordinary Pareto optimality is extended based on the α-level sets of the fuzzy numbers. In our interactive decision making method, in order to generate a candidate for the satisficing solution which is also a-Pareto optimal, if the DM specifies the degree α of the a-level sets and the reference objective values, the minimax problem is solved by combined use of the bisection method and the linear programming method and the DM is supplied with the corresponding α-Pareto optimal solution together with the trade-off rates among the values of the objective functions and the d...
TL;DR: It is shown that a linear fuzzy neighborhood space is probabilistic normable iff it is Hausdorff and it has an n-bounded convex fuzzy neighborhood of zero.
TL;DR: A tutorial approach is adopted in the explanation of the basic concepts of fuzzy set theory and it is shown how fuzzy logic can be used to develop a fuzzy control algorithm by means of the fuzzy conditional statement.
Abstract: The purpose of this paper is to present to the reader who is unfamiliar with fuzzy set theory the basic concepts in a straightforward manner. Thus a tutorial approach is adopted in the explanation of these concepts. After describing fuzzy sets, it is shown how fuzzy logic can be used to develop a fuzzy control algorithm by means of the fuzzy conditional statement. In order to unify the ideas that are presented, a detailed description of the development of a fuzzy controller is discussed. Computer simulation results are shown of the fuzzy controller with heading error and yaw rate as input and rudder demand as output activating the non-linear yaw dynamics of a ship during course-changing manoeuvres. For the simulation ship study, the model was derived from full-scale sea trials on a Royal Navy frigate.