A parametric approach to fuzzy linear programming
type: Item
instance of: scholarly article
title: A parametric approach to fuzzy linear programming
zbMATH Open document ID: 0603.90093
DOI: 10.1016/S0165-0114(86)80028-8
author: Christer Carlsson
author: Pekka J. Korhonen
published in: Fuzzy Sets and Systems
publication date: 1986-01-01T00:00:00Z
review text: This paper is devoted to the study of linear programming problems with imprecise values of the involved parameters. Say, the parameters are unknown with varying grades of precision. The imprecision is traditionally evaluated through post-optimization analysis or by the use of stochastic programming. The fuzzy set approach is different, not traditional, but possibly better for studying some of the problems arising when the parameters are subject to error. Generally the decision-maker is able to fix intervals for the parameters of the problem or to give some ranking of the possible values of them. Then the Bellman-Zadeh principle may be used and strict optimization and constraints may be replaced by a gradual attainment of aspiration levels \((z_ 0,b_ 0)\). An overview of this problem is given in section 2 and the handling of the imprecision by the different approaches is analyzed. In section 3 a theorem states that the solution of an LP problem is an increasing function of the parameters. Then using the knowledge of the intervals where they should be located and assuming parametric dependent and monotonically decreasing membership functions ways for obtaining the parameters for the LP problem are developed. Linear parametric programming techniques provide the tools for solving the corresponding applications. Section 4 is devoted to the solution of a numerical example and the behaviour of the proposed approach is illustrated.
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 3974728
zbMATH Keywords: fuzzy parametric programming
zbMATH Keywords: fuzzy linear programming
reviewed by: Carlos Narciso Bouza Herrera
MaRDI profile type: Publication
cites work: Decision-Making in a Fuzzy Environment
cites work: The use of parametric programming in fuzzy linear programming
cites work: Goal programming and multiple objective optimizations. Part I
cites work: Fuzzy sets and systems. Theory and applications
cites work: Q3874179
cites work: Linear programming under randomness and fuzziness
cites work: Q4103341
cites work: Interactive computer programs for fuzzy linear programming with multiple objectives
cites work: Q3343779
cites work: Fuzzy programming and linear programming with several objective functions
cites work: Applications of fuzzy set theory to mathematical programming
full work available at URL: s0165-0114(86)80028-8
OpenAlex ID: W2022793254
description: scientific article; zbMATH DE number 3974728