TY - JOUR

T1 - Multicriteria Choice Based on Fuzzy Information

AU - Noghin, V. D.

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research (projects 16-29-12864, 17-07-00371, 17-29-03236). Publisher Copyright: © 2020, Allerton Press, Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - Abstract: This paper proposes a new method for solving the problem of multicriteria optimization of a numerical vector function on a fuzzy set. The membership function of a fuzzy feasible set is joined to the original set of criteria that allows the original problem of multi-criteria optimization to be treated as the task of finding a suitable compromise (Pareto-optimal) solution with respect to an extended set of criteria. It is assumed that in a search for the “best” compromise solution there is only fuzzy information about the preferences of decision maker in the form of information quanta. At the first stage of the proposed method, the search for a compromise is made on the basis of an axiomatic approach, with which the Pareto set is reduced. The result of the reduction is a fuzzy set with a membership function, which is determined on the basis of the used fuzzy information. At the second stage, the obtained membership function is added to the extended set of criteria, after which the scalarization procedure based on the idea of goal programming is used to solve the formed multicriteria problem.

AB - Abstract: This paper proposes a new method for solving the problem of multicriteria optimization of a numerical vector function on a fuzzy set. The membership function of a fuzzy feasible set is joined to the original set of criteria that allows the original problem of multi-criteria optimization to be treated as the task of finding a suitable compromise (Pareto-optimal) solution with respect to an extended set of criteria. It is assumed that in a search for the “best” compromise solution there is only fuzzy information about the preferences of decision maker in the form of information quanta. At the first stage of the proposed method, the search for a compromise is made on the basis of an axiomatic approach, with which the Pareto set is reduced. The result of the reduction is a fuzzy set with a membership function, which is determined on the basis of the used fuzzy information. At the second stage, the obtained membership function is added to the extended set of criteria, after which the scalarization procedure based on the idea of goal programming is used to solve the formed multicriteria problem.

KW - fuzzy set

KW - goal programming

KW - multicriteria choice

KW - multicriteria optimization

KW - quanta of fuzzy information

KW - reduction of the Pareto set

KW - scalarization

UR - http://www.scopus.com/inward/record.url?scp=85101918850&partnerID=8YFLogxK

U2 - 10.3103/S0147688220050044

DO - 10.3103/S0147688220050044

M3 - Article

AN - SCOPUS:85101918850

VL - 47

SP - 275

EP - 283

JO - Scientific and Technical Information Processing

JF - Scientific and Technical Information Processing

SN - 0147-6882

IS - 5

ER -