Fuzzy goals under fuzzy constraints
type: Item
instance of: scholarly article
title: Fuzzy goals under fuzzy constraints
zbMATH Open document ID: 0599.90063
DOI: 10.1016/0022-247X(86)90302-1
author: M. Prevot
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The paper deals with a classical problem of decision making in a fuzzy environment, viz. in situations where a goal G as well as constraints \(C_ 1,C_ 2,...,C_ n\) imposed are viewed as fuzzy sets defined in a certain universe of discourse. Discussed are two forms of aggregation of goals and constraints: (1) intersection of G and the \(C_ i's\). The fuzzy decision is hence obtained via \(D=G\cap C_ 1\cap C_ 2\cap...\cap C_ n\) (where \(\cap\) stands for taking the minimum of their membership functions), (2) their convex combination, \(D(x)=a_ 0G(x)+\sum^{n}_{i=1}a_ iC_ i(x)\) with \(a_ 0+a_ 1+...+a_ n=1\), \(x\in X.\) A definition of optimum decision (in the sense of Pareto) and its existence for both formulations given above is discussed in detail. Secondly, some computational hints useful for determining the optimum (resulting from an analysis of the Lagrange saddle point and the formulation of the Lagrange problem) are provided.
Mathematics Subject Classification ID: 90B50
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 3968310
zbMATH Keywords: decision making in a fuzzy environment
zbMATH Keywords: aggregation of goals and constraints
zbMATH Keywords: Lagrange saddle point
zbMATH Keywords: Lagrange problem
MaRDI profile type: Publication
cites work: Q3846725
cites work: Q5675516
cites work: Q3863747
cites work: Q4091811
description: scientific article; zbMATH DE number 3968310