Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

A Minimax Criterion Approach to Treat the Inexactness in Feasible Set of a Linear Programming Problem

Authors
Zhenzhong Gao, Masahiro Inuiguchi
Corresponding Author
Zhenzhong Gao
Available Online 30 August 2021.
DOI
https://doi.org/10.2991/asum.k.210827.035How to use a DOI?
Keywords
Inexact Linear Programming, Interval Linear Programming, Robustness Analysis, Inexact Feasible Set, Minimax Criterion, Weighted Lp-Norm
Abstract

The robustness analysis investigates the optimality of a solution in a linear programming problem that contains uncertainties. Conventionally, researchers concentrated on the one with a fixed feasible set, while in this paper, we focus on an inexact one. Since an inexact feasible set usually makes a solution infeasible in some situations, we consider it a penalty for the objective function. To accomplish it, we utilise the minimax criterion and propose an updated programming problem, which has an objective function that includes a weighted Lp-norm to represent the penalty. For the application, we only consider L1-norm (absolute-value norm) and L2-norm (Euclidean norm). We show that for the L1-norm, an approach based on linear programming can treat it with low computational complexity. In contrast, we show that an approach based on derivative can treat the case of L2-norm. Finally, we compare our approach with conventional fuzzy linear programming for the merit and drawback of our approach.

Copyright
© 2021, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Cite this article

TY  - CONF
AU  - Zhenzhong Gao
AU  - Masahiro Inuiguchi
PY  - 2021
DA  - 2021/08/30
TI  - A Minimax Criterion Approach to Treat the Inexactness in Feasible Set of a Linear Programming Problem
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 258
EP  - 265
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.035
DO  - https://doi.org/10.2991/asum.k.210827.035
ID  - Gao2021
ER  -