Showing papers on "Membership function published in 1979"

Fuzzy logic and fuzzy reasoning

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.

A measurement-informational discussion of fuzzy union and intersection

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.

Mathematical programming with fuzzy constraints and a preference on the objective

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.

Fuzzy truth definition of possibility measure for decision classification

Abstract: A new definition of possibility measure is presented which is calculated on truth space and is shown to be equivalent to Zadeh's original definition. This alternative formulation is shown to be the more natural in the context of decision classification because it clearly demonstrates the need for determining both the possibility of a category and not that category in a selection criterion. A number of useful possibility theorems are presented and their application to decision classification is demonstrated in a simplistic medical diagnosis problem, which also employs entropy measure as an additional parameter. The truth space formulation of possibility measure is shown to be of further value in problems of high dimensional state and an important possibility theorem relating to such problems is presented.

Various kinds of interactive addition of fuzzy numbers, application to decision analysis in presence of linguistic probabilities

Abstract: After a brief recall of possibility theory and of the concept of interactivity, new results concerning different kinds of addition of fuzzy numbers are given (to introduce these additions, no reference to the extension principle is needed). As an illustration, the application of one of these results to a problem (which was unsolved until now) of decision-making in presence of linguistic probabilities is presented.

Evaluation and Integration of Imprecise Information.

Abstract: : Although fuzzy set theory has been rapidly gaining popularity as a rigorous framework for incorporating imprecision into quantitative reasoning, a survey of existing literature indicates the lack of any consistently applied operational definition for the fundamental concept of membership function. In the present case, the membership of an element x in a set S is defined as the degree of truth of the statement 'x is a member of S.' It then becomes necessary to develop an empirically valid scale of truth which allows not only the binary extremes of 'true' and 'false,' but also the continuum of intermediate values. In one experiment, subjects performed two tasks: pairwise comparison; and direct numerical scaling of the relative truth of simple sentences. Results indicated that (1) the high degree of transitivity in each subject's paired-comparison judgments leads us to reject the hypothesis of a two-valued true-false logic in favor of a continuum of values; (2) ability to discriminate, as judged by the consistency between direct ratings and paired-comparison judgments, seems to be uniform along the true-false continuum, again favoring the hypothesis of a continuum of truth values over that of a binary categorical judgment; and (3) the high correlation between an item's aggregate binary preference score for a given subject and that subject's direct rating for the item indicates that at least two different methods of inferring degree of truth are highly consistent.

On fuzzy sets, subjective measurements and utility

Abstract: Fuzzy reasoning is founded on subjective measurements specified as grades of membership of property categories called fuzzy sets. These membership gradings, it is assumed, may be expressed numerically by functions or corresponding discrete representations the values of which submit to the conventional arithmetic operations. This paper raises the question as to the empirical justification of these assumptions. That is, what empirical support can be established for this approach considering the properties of subjective measurements in psychophysics and those of utility in modern microeconomics or management science. Based on a presentation of the evidence demonstrated in these disciplines a power function seems to be the tentative form of the membership gradings of fuzzy sets representing a large variety of psychophysical continua and the corporate utility under risk. However, practically no empirical evidence was found to support the submission of such power function representations to arithmetic operations. Hence, there is an urgent need to establish more empirical facts on the assignments of subjective membership gradings and, in particular, the combinations of such gradings.

A model of dialog based on fuzzy set concept

Abstract: Dialog is considered as the exchange of information between two persons who speak natural language to understand each other. However natural language is so ambiguous both in expression and logic that for understanding it is very important to supplement the information through some reasoning or imagination. In this paper, we analyze this thinking process using fuzzy sets theory and approach a modelling of dialog. The dialog in the model is characterized by the set of objects talked about, the set of their attributes, etc. There are two important factors in the process of dialog: fuzzy information on the objects given by one person and the other person's fuzzy knowledge on the objects. Both fuzzy information and knowledge are expressed by fuzzy sets. The main problem in the paper is to compare these two fuzzy sets with each other. For this purpose the concept of truth qualification in fuzzy logic is useful. The authors propose a generalized truth value instead of an ordinary one which appears in Zadeh's truth qualification rule. Then one of the two persons, say a listener in the dialog, can understand by referring the generalized truth value what the other wants to communicate.

On the satisfaction of a fuzzy relation by a set of inputs

Abstract: Some applications of Fuzzy Set theory require an indication of how well a set of fuzzy sets satisfy a relation: where the relation represents a connection between the spaces on which the fuzzy sets are defined, perhaps in the form of a hypothesis. Two measures of such satisfaction, one a scalar and one a function, are compared in this paper: and the derivation of the scalar from the function is given. The relevance of these measures to applications, approximate reasoning in particular, is indicated.

relativiste de I'information II.

Abstract: The author recently proposed a new concept for information, the so-called relativistic information, which is' basically a theory of the triplet (S, L R) in which S denotes a system which is observed by the observer R, while I is the information which is so involved by the observation process. The theory so obtained is relativistic in the way that the information is quantitatively defined by its syntax and its semantics, mutually dependent, and both depending upon the observer. After a brief background on this relativistic information and on the general system theory from where it is derived, the paper shows how it provides the Shannon information as special case under specific assumptions which are implicite in this latter although they are not always clearly mentionned, as shown with a simple example. Then, it gives a physical derivation for the Renyi entropy, therefore a new interesting meaning to it and, by this way, new prospects for its use. As a last application, the author get a new relativistic fuzzy set theory which explieitely involves the point of view of the observer �9 a relativistic fuzzy set is not defined by a membership function, but is' so by a relativistic fuzziness function with explicite composition laws regarding the observers. The concept for relativistic fuzzy variable is exhibited therefore a new fuzziness calculus which can be expanded in a way similar to that of the probability calculus.