Representation and application of fuzzy numbers

Fuzzy Sets and SystemsPublished 1 October 1997

Stanisław Heilpern

DOI10.1016/s0165-0114(97)00146-2

Source URL

Citations178

SJR quartileQ1

SJR score0.75

SNIP1.25

TL;DR

Some types of representation of fuzzy numbers are described and the notions of the distance and orders between fuzzy numbers based on these representations are studied.

Abstract

In this paper we present the theoretical background of fuzzy numbers connected with the possibility and Dempster-Shafer theories. We describe some types of representation of fuzzy numbers and we study the notions of the distance and orders between fuzzy numbers based on these representations. The second part is devoted to the application of fuzzy numbers in data analysis, artificial intelligence and decision making.

Keywords

Computer ScienceDecision SciencesMathematics

Information SciencesThe concept of a linguistic variable and its application to approximate reasoning-III

12,148 Citations1975L. A. Zadeh

Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.

Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—I

12,036 Citations1975Lotfi A. Zadeh

It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc.

Mathematics in Science and Engineering/Mathematics in science and engineeringFuzzy Sets and Systems - Theory and Applications

6,430 Citations1980Didier Dubois, Henri Prade

Fuzzy Sets and SystemsA review of some methods for ranking fuzzy subsets

940 Citations1985G. Bortolan, R. Degani

Fuzzy Sets and SystemsMetric spaces of fuzzy sets

765 Citations1990Phil Diamond, Peter E. Kloeden

A characterisation of compact and locally compact subsets is given in terms of boundedness and p-mean equileft-continuity, and the spaces shown to be locally compact, complete and separable metric spaces.

Fuzzy Sets and SystemsThe expected value of a fuzzy number

500 Citations1992Stanisław Heilpern

The expected interval is defined as the expectedvalue of an interval random set generated by the fuzzy number and the expected value of this number isdefined as the centre of the expected interval.

International Journal of Man-Machine StudiesQuantified propositions in a linguistic logic

110 Citations1983Ronald R. Yager

The formalism of fuzzy subset theory is used to provide a framework in which to interpret linguistic quantifiers in binary logic and the problem of making quantified statements based upon the observation of a sample from a set of objects is studied.

Fuzzy Sets and SystemsFuzzy subsets of the space of probability measures and expected value of fuzzy variable

15 Citations1993Stanisław Heilpern

This paper investigates the properties of the fuzzy set of all probability measures for which the probability of fuzzy event A is equal to fuzzy probability Q and calculates the expected value of the variable generated by the fuzzy evidence.

Fuzzy Sets and SystemsApproximation of functional relationships to fuzzy observations

15 Citations1992M. Albrecht

An approximation method using Hausdorff-like distances is proposed naturally containing the crisp observation case and leading to a crisp function for crisp observations, which leads to well-known approximation principles from classical theory and can be realized by standard computer software.

European Journal of Operational ResearchDeriving expected values from probabilities of fuzzy subsets

8 Citations1991Stefan Chanas, B. Florkiewicz

The presented approach is an essential improvement of the method proposed before that by Yager and is possible to develope solution algorithms which are more effective than classical methods known in linear programming.