Showing papers on "Membership function published in 1977"

Multiple objective decision-making using fuzzy sets

Abstract: One of the most useful aspects of fuzzy set theory is its ability to represent multio-bjective decision problems involving vague or fuzzy objectives. This paper presents a model for solving multi-objective decision problems when the objectives are of varying degrees of importance. This is done by assigning to each objective a power indicative of its importance and then raising each fuzzy set to its appropriate power. These powers are obtained by getting the eigenvector of the maximum eigenvalue of a matrix of paired comparisons of the objectives.

A procedure for multiple-aspect decision making using fuzzy sets

Abstract: In many situations one has to find the best alternative on the basis of many aspects which have varying degrees of importance. The problem is more complex if the ratings of the alternatives and the importance of the aspects are expressed using qualitative variables like good, fair, very important, etc. This paper presents a method for decision making in such situations. The qualitative terms are represented quantitatively using fuzzy sots and then the fuzzy optimal alternative is computed. The fuzzy set representing the optimal alternative gives the relative merit of each alternative and thus helps in decision making.

On programming with fuzzy constraint sets

Abstract: Two solution concepts for a FMP problem are suggested. The first one makes use of level sets of the fuzzy set of feasible alternatives. The second solution is based on the concept of Pareto maximum in vector optimization. It is shown that both solutions are equivalent in a sense that they give the same fuzzy value of a function maximized. It is suggested that if a decision‐maker is to choose a single element, then his choice must be based not only on the membership value of this element in the solution fuzzy set but also on the corresponding value of the function maximized. In this respect the situation is similar to that typical for vector optimization. The approach suggested in this paper is further used for analysing games with fuzzy sets of strategies of the players. A fuzzy equilibrium solution is introduced, which can provide a base for an agreement between the players.

Level fuzzy sets

Abstract: In practical applications of fuzzy set theory, e.g., in pattern recognition, information retrieval, etc., the reader is not advised-for the reasons of the amount of the considered object universal set and the capacity of computer memory involved-to consider fuzzy sets defined in the whole universal set, when it is sufficient-from the point of view of a given process description exactness-to take into consideration fuzzy sets determined in the universal subsets. Such a type of fuzzy set called a level fuzzy set is defined in the paper, definitions of basic operations performed on level fuzzy sets are given, and properties of these operations are presented.

On fuzzy optimization

Abstract: By fuzzy optimization we here mean optimization in a fuzzy environment, i.e., optimization with fuzzy constraints. Such a problem can be reduced to a family of ordinary optimization problems by using the representation theorem which states that a fuzzy set is a family of ordinary sets. Since it is difficult to work with a family of sets, in this paper a fuzzy set is approximated by an ordinary set. The Chebyshev norm is introduced into the set of all fuzzy sets, and a set is said to approximate a fuzzy set if the norm of a difference of its characteristic functions is smaller than a given number.

On fuzzy complements

Abstract: In [1] Bellman and Giertz showed that under reasonable restrictions the generalized operations of union and intersection for fuzzy sets have to be l.u.b, and g.l.b, in IX endowed with the usual order, where I denotes the unit interval and X is an arbitrary set. It is the purpose of this paper to characterize those operations which are acceptable as complementation. We demand that the operation would be idempotent, orderreversing and that it would be a productmap. We see that these conditions are minimal and not sufficient to guarantee the preservation of important properties of complementation with regard to sets and functions. We then define a category of fuzzy complemented spaces and give necessary and sufficient conditions for subcategories to have properties analogous to those of the category of sets and functions.

Some mathematical tools for linguistic probabilities

Abstract: Transformations of fuzzy sets are discussed using the relation between random sets and fuzzy sets. We propose the general formulation of optimization under elastic constraints. This formulation is based upon the notion of maximizing and minimizing sets. Using this formulation we justify the extension problem of possibility measures to fuzzy sets.

Inverses of fuzzy relations: Application to possibility distributions and medical diagnosis

Abstract: In this paper we define and explore the properties of lower and upper inverses of fuzzy relations which extend multi-valued mappings. With the notion of degree of inclusion of non fuzzy sets, we then relate the preceeding notions to possibility distributions in natural languages and to problems of medical diagnosis.

Structural modeling in a class of systems using fuzzy sets theory

Abstract: On the basis of fuzzy sets theory, we propose a method for structuring hierarchy for the several complex problems, and call it Fuzzy Structural Modeling (FSM) method. An important requirement for structural modeling of complex systems is that the necessary data is acquired and organized into a form such that a structural model can be developed. 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. The procedure permits an automatic development of the graphic structure that portrays the hierarchy.

Utilisation of fuzzy sets for system modelling and control

Abstract: Since L. A. Zadeh introduced fuzzy-set theory it has allowed a better grasp of certain systems in various fields, for instance, the modelization of process control. For a human observer can often supply subjective information about the evolution, the operation, or the value of certain parameters of a process he is acquainted with; and fuzzy set theory, by formalizing this subjective perception, allows one to achieve a first approach to modelizing the process, or to complete or confirm the results of objective analysis and measurements. In such a research orientation, this article devotes its first part to the formalism required for representing processes in the fuzzy system concept and in the second part, presents a method for calculating a regulation algorithm using a fuzzy model of the process.

On Some Applications of Fuzzy Algorithm in Man-Machine Communication Research

Abstract: Present paper ennuuciates some practical applications of fuzzy set theory in problems of man-machine communication. Problems are recognition of vowel speech sounds and identification of speakers from spoken words. Data used are derived from acoustic-phonetic and spectrographs analysis of large number of Hindi and Telugu (two of the major Indian Languages) speech sounds. It is explained that Fuzzy set theory provides a suitable algorithm which is substantively different from the conventional quantitative methods of system analysis yet presents an approximate but effective means of describing the behaviour of systems which are too ill-defined for precise mathematical analysis. In this paper, two decision algorithmic methods developed from fuzzy set theory and applied for machine recognition of vowels and identification of speakers with Telugu and Hindi speech sounds are presented along with the results of experiments.