Showing papers on "Membership function 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: 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
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.
131 citations
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.
119 citations
TL;DR: The need for a measure of correlation between two membership functions and the properties that the correlation measure may possess are examined and the definition is extended to the cases when (a) the domain is finite and (b) thedomain is a subset of R^n.
108 citations
TL;DR: Results of empirical research are presented which focused on the problem of modelling vagueness, i.e. determining membership functions of fuzzy sets which are considered as quantitative representations of vague concepts such as ‘young man’, ‘long sticks’), etc.
107 citations
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.
101 citations
01 Nov 1985
TL;DR: A new interactive fuzzy satisficing method for multiobjective nonlinear programming is presented which considers that the decision-maker (DM) has fuzzy goals for each of the objective functions through the interaction with the DM.
Abstract: A new interactive fuzzy satisficing method for multiobjective nonlinear programming is presented which considers that the decision-maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting corresponding membership functions. In order to generate a candidate for the satisficing solution (Pareto optimal) after determining the membership functions, if the DM specifies his/her reference membership values, the augmented minimax problem is solved. The DM is thus supplied with the corresponding Pareto optimal solution together with the tradeoff rates between the membership functions. Then by considering the current values of the membership functions as well as the tradeoff rates, the DM acts on this solution by updating his/her reference membership values. A time-sharing computer program is written to implement man-machine interactive procedures based on this method. An application to an industrial pollution control problem is demonstrated.
93 citations
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: Two necessary and sufficient conditions are given in order to decompose an assigned fuzzy relation in two fuzzy sets.
TL;DR: This paper extends certain results of Sanchez (Resolution of eigen fuzzy sets equations, Fuzzy Sets and Systems 1 (1978) 69-75) to the context of fuzzy numbers and uses a slight modification of the Dubois-Prade definition of fuzzyNumbers.
TL;DR: Two methods to transfer information given by fuzzy observations to fuzzy sets on the parameter region of a given explicit functional relationship are suggested: expected cardinality and fuzzy expectation.
TL;DR: Concepts of T;-continuous functions in a fuzzy setting in connection with the fuzzy continuity and fuzzy separation axioms are introduced and generalised.
TL;DR: This paper investigates the use of fuzzy data in a fuzzy decision problem by identifying a class of optional decisions from the data into the set of actions with maximum membership in some fuzzy set.
TL;DR: The deterministic performance evaluation of nonlinear optimization methods is extended: a pairwise comparison is carried out using fuzzy estimates of the performance ratios to obtain fuzzy final scores of the methods under consideration, using the concept of fuzzy numbers with triangular membership functions.
Abstract: In this paper we extend the deterministic performance evaluation of nonlinear optimization methods: we carry out a pairwise comparison using fuzzy estimates of the performance ratios to obtain fuzzy final scores of the methods under consideration. The key instrument is the concept of fuzzy numbers with triangular membership functions. The algebraic operations on them are simple extensions of the operations on real numbers; they are exact in the parameters (lower, modal, and upper values), not necessarily exact in the shape of the membership function. We illustrate the fuzzy performance evaluation by the ranking and rating of five methods (geometric programming and four general methods) for solving geometric-programming problems, using the results of recent computational studies. Some general methods appear to be leading, an outcome which is not only due to their performance under subjective criteria like domain of applications and conceptual simplicity of use; they also score higher under more objective criteria like robustness and efficiency.
01 Oct 1985-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: An interactive fuzzy decision-making method by assuming that the decision-maker (DM) has fuzzy goals for each of the objective functions in multi-objective non-linear programming problems that can be derived efficiently from among a Pareto optimal solution set by updating his reference membership intervals.
Abstract: This paper presents an interactive fuzzy decision-making method by assuming that the decision-maker (DM) has fuzzy goals for each of the objective functions in multi-objective non-linear programming problems. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. After determining the membership functions for each of the objective functions, in order to generate a candidate for the satisficing solution which is also Pareto optimal, the DM is asked to specify his reference intervals for each of the membership functions, called reference membership intervals. For the DM's reference membership intervals, the corresponding augmented weighted minimax problem is solved and the DM is supplied with the Pareto optimal solution which is in a sense close to his requirement together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his reference membership intervals. In this way the satisficing solution for the DM can be derived efficiently from among a Pareto optimal solution set by updating his reference membership intervals. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the corresponding computer outputs.
01 Jan 1985
TL;DR: The functional information energy if formally similar to the Onicescu's information energy, which used an analogy to kinetic energy from mechanisms, although it is conceptually different.
Abstract: In order to define a measure of the information processed by a fuzzy event and by a partition of fuzzy events, the `information energy' provided by a fuzzy event and a partition of fuzzy events is considered. This measure integrates the statistical uncertainty resulting from the occurrence of events and the uncertainty of meaning of events that is expressed by the membership function. The functional information energy if formally similar to the Onicescu's information energy, which used an analogy to kinetic energy from mechanisms, although it is conceptually different.
15 Dec 1985
TL;DR: This tutorial contains a brief discussion of the current trends in simulation which the authors believe justify the need of this new tool, which is best known under the name of Fuzzy Set Theory.
Abstract: The objective of this tutorial is to introduce to the simulation community another tool that is now available. This tool is best known under the name of Fuzzy Set Theory. This tutorial contains a brief discussion of the current trends in simulation which we believe justify the need of this new tool. Kept to a minimum, the Introduction to fuzzy sets will be strictly limited to the case of a finite number of elements. Most attention will be devoted to fuzzy logic. It is precisely fuzzy logic which lends itself to growth in the simulation of situations that arise in real life either because of the inexactness of the environment, or because of the inexactness/imprecision of the available data.
TL;DR: Liapounoff's Theorem for fuzzy measures is proved and it is applied to extend a theorem of Aumann and Shapley concerning the existence of the value for non-atomic games.
TL;DR: The fuzzy beta possibility distribution is introduced in decision analysis: both the rewards and probabilities are modelled using fuzzy sets and arbitrary specification of the membership functions of the fuzzy probabilities may lead to internal inconsistencies.
TL;DR: A model is proposed that is capable of handling two distinct forms of imprecision, viz. randomness and fuzziness, and is required to cope with both of them while modeling a variety of problems in management, medical diagnosis, and unsupervised pattern recognition.
Abstract: The paper deals with a problem of modeling of fuzzy systems in random environments. A model is proposed that is capable of handling two distinct forms of imprecision, viz. randomness and fuzziness. The model is required to cope with both of them while modeling a variety of problems in management, medical diagnosis, and unsupervised pattern recognition. The models proposed in the paper are constructed and evaluated in a formal framework established by fuzzy relation equations. Randomness is introduced as additional constraints imposed on the structure of the fuzzy relation equation (hence: structured fuzzy models). The forecasting (prediction) problem is studied in detail.
TL;DR: Fuzzy duality is presented, and an extension of the initial fuzzy problem arises immediately from it, and existence and uniqueness theorems are given.
TL;DR: In this paper, the authors examined the use of a matrix structure for representing collections of performance measures as ordinary subsets of organizational activities and showed that the fuzzy representation can be used to compare alternative collection of performance measure and provide insights to the value of these collections of measures for decision-making and control purposes.
01 Jan 1985
TL;DR: In order to prevent confusion about fuzzy measures and measures of fuzziness, this work shall first briefly describe the meaning and features of fuzzy measures.
Abstract: In order to prevent confusion about fuzzy measures and measures of fuzziness, we shall first briefly describe the meaning and features of fuzzy measures. In the early 1970s, Sugeno defined a fuzzy measure as follows [Sugeno 1977]: 𝓑 is a Borel field of the arbitrary set (universe) X.
TL;DR: The interactive fuzzy goal programming which can determine the satisfying solution ensuring the Pareto-optimality of the decision maker is proposed, and an interactive computer program was constructed.
Abstract: This paper considers the situation where the decision-maker has a fuzzy goal for each of the object functions in a multiobjective nonlinear programming problem, and proposes the interactive fuzzy goal programming which can determine the satisfying solution ensuring the Pareto-optimality of the decision maker. The decision-maker has a fuzzy goal for each of the object functions in the multiobjective nonlinear programming problem. For example, “The function should nearly be a or less,” or “The function should be approximately b.” Such a fuzzy goal of the decision-maker is determined by evaluating interactively the corresponding membership function. After determining the membership function for each of the object functions, the decision-maker sets the goal membership value for each membership function on a subjective basis. Then the difference between the membership function value and the goal membership value is minimized, determining the corresponding Pareto-optimal solution. The decision-maker is either satisfied with the given Pareto-optimal solution, or subjectively updates the goal membership value by noting the difference between the membership function value for the obtained Pareto-optimal solution and the goal membership value. By this process, the satisfying solution is derived eventually for the decision-maker, ensuring the Pareto-optimality. Based on the proposed algorithm, an interactive computer program was constructed, which is shown in this paper, together with the example of computer output for numerical example.