The use of parametric programming in fuzzy linear programming
type: Item
instance of: scholarly article
title: The use of parametric programming in fuzzy linear programming
zbMATH Open document ID: 0534.90056
DOI: 10.1016/S0165-0114(83)80084-0
author: Stefan Chanas
published in: Fuzzy Sets and Systems
publication date: 1983-01-01T00:00:00Z
review text: The following problem of fuzzy linear programming \[ ''\max ''\quad c'x,\quad subject\quad to\quad \sum^{n}_{i=1}a_{ij}x_ j\preccurlyeq b_ i\quad(i=1,...,m),\quad x\geq 0, \] whose constraints and goal are not crisp but fuzzy sets characterized by their membership functions, is solved by the parametric programming technique and a complete fuzzy solution (not only the maximizing alternative) is obtained. The advantages of the proposed approach are: (1) The underlying problem is not enlarged. (2) The aspiration level as well as the admissible tolerance of the objective function can be stated after the solution of the parametric problem. (3) It is not necessary to assume piecewise linearity of the membership function of the goal. (4) One obtains a complete fuzzy solution allowing to consider also other possibilities besides the maximizing variant. The presented approach is illustrated by some numerical examples.
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 94D05
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 3848965
zbMATH Keywords: multiple objective linear programming
zbMATH Keywords: parametric linear programming
zbMATH Keywords: fuzzy linear programming
zbMATH Keywords: complete fuzzy solution
reviewed by: Jaroslav Ramík
MaRDI profile type: Publication
cites work: A comparison of two methods for determining the weights of belonging to fuzzy sets
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cites work: Fuzzy sets
description: scientific article; zbMATH DE number 3848965