Search results for "Fuzzy measure theory"
showing 5 items of 5 documents
Decomposable Measures and Measures of Information for Crisp and Fuzzy Sets
1983
Abstract There exist bijections between the decomposable informations of Kampe de Feriet and Forte (1967a) and the decomposable measures of Weber (1982). Using integrals for Archimedean decomposable operations, introduced by Weber (1982), informations and measures of this type are extended from crisp to fuzzy sets. For ∨-decomposable measures, Sugeno’s (1974) integral is used. For ∧-decomposable informations, Nguyen’s (1977) construction and a modification are discussed.
On a multiplication and a theory of integration for belief and plausibility functions
1987
Abstract Belief and plausibility functions have been introduced as generalizations of probability measures, which abandon the axiom of additivity. It turns out that elementwise multiplication is a binary operation on the set of belief functions. If the set functions of the type considered here are defined on a locally compact and separable space X , a theorem by Choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of X , the so-called basic probability assignment. This is basic for defining two new types of integrals. One of them may be used to measure the degree of non-additivity of the belief or plausibility function. The other o…
Fuzzy methods for analysing fuzzy production environment
1998
Abstract Very recently, in production management research literature, the necessity to extend production systems analysis techniques, such as queue theory, Mean Value Analysis (MVA) and discrete simulation, to Fuzzy Production Environments, i.e. to those production situations in which data are vague, has emerged. Fuzzy set theory is a powerful tool to model vagueness and, therefore, fuzzy mathematics can be used to extend classical production system analysis techniques. This paper proposes a methodology based on fuzzy relation algebra to extend classical MVA and discrete event simulation.
A theory of spatial general equilibrium in a fuzzy economy
1984
Let an economic space be characterized by the existence of a given distribution of locations, i.e. consumers' residential locations and producers' plants. It is equipped with a system of prices. The economy is fuzzy because the economic behaviors of agents are imprecise. In this context, spatial partial equilibria theories are applications of a fuzzy economic calculation model. The aim of the present paper is to study the conditions which must be fulfilled in order that the compatibility of consumers' equilibria and producers' equilibria be verified. Mathematical tools are Butnariu's theorems which extend the Brouwer's and Kakutani's theorems to the cases of fuzzy functions and fuzzy point-…
Fuzzy expected utility
1984
Decision making under uncertainty requires not only measures of the uncertainty of situations that we try to recognize , but also an estimate of the imprecision from which they are determined. This imprecision can be the result either of a lack of exactness in the measure of the elements which are necessary to the determination of the states of nature or the purely subjective interpretation of these states. Through a subjective measure of the non-measurable imprecision, the purpose of the fuzzy expected utility, which is investigated, is to translate with a great accuracy the imprecise behaviour of the decision-maker in an uncertain world. Consequently we propose to introduce first the prob…