Uniqueness of solution in FLP under parameter perturbations
type: Item
instance of: scholarly article
title: Uniqueness of solution in FLP under parameter perturbations
zbMATH Open document ID: 0692.90093
DOI: 10.1016/0165-0114(90)90157-2
author: B. Shafai
author: George R. Sotirov
published in: Fuzzy Sets and Systems
publication date: 1990-01-01T00:00:00Z
review text: Given is the following interval linear programming problem: \[ (1)\quad \min cx,\quad s.t.\quad Ax\leq B\quad and\quad x\geq 0, \] in which the coefficients on the right hand side (i.e. the components of the vector B) are intervals. The authors establish necessary and sufficient conditions for all the problems due to (1), with varying vector b (b\(\in B)\), having the same unique optimal solution. Subsequently, the authors propose to use this result in the stability (sensitivity) analysis of the solution of a fuzzy linear programming problem with varying values of some parameters in the membership functions of the fuzzy goal and the constraints. This is possible because in such a case the fuzzy linear programming problem resolves itself into a certain crisp equivalent problem of the form (1). It should be said, however, that this concerns only the uniqueness of the solution of the problem dual to this equivalent one. The authors do not draw any conclusions about the properties of the optimal solution of the original problem, although both the title of the paper and the abstract seem to announce such conclusions.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 4133854
zbMATH Keywords: parameter perturbations
zbMATH Keywords: sensitivity analysis
zbMATH Keywords: interval linear programming
zbMATH Keywords: fuzzy linear programming
reviewed by: Stefan Chanas
MaRDI profile type: Publication
full work available at URL: 0165-0114(90)90157-2
OpenAlex ID: W1979732844
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description: scientific article; zbMATH DE number 4133854