SOLUTION OF SELECTION PROBLEMS WITH FUZZY PARAMETERS

References: 17th International Multidisciplinary Scientific GeoConference SGEM 2017, www.sgem.org, SGEM2017 Conference Proceedings, ISBN 978-619-7408-01-0 / ISSN 1314-2704, 29 June - 5 July, 2017, Vol. 17, Issue 21, 595-602 pp, DOI: 10.5593/sgem2017/21/S07.076

ABSTRACT

A method of solving the selection problems with fuzzy parameters by means of a special algebraic structure is proposed. To construct such an algebraic structure, we propose a special transformation of existing fuzzy numbers to the simpler form (L or R number) while keeping the most of the initial expert information. This structure avoids deficiencies limiting applicability of the other known structures, such as unjustified extension of the uncertainty, violation of certain natural relations, openness of the carrier set with respect to the operations of multiplication and division etc. Then a more useful isomorphic algebra is constructed that also overcomes the known problem of a comparison of fuzzy numbers. This algebra defines its operations through operations on real numbers, which simplifies its usability (namely in the standard numerical computing environments). Methodology for solving problems with fuzzy numbers is presented. Example on the solution of a quadratic equation is also presented and discussed.

Keywords: optimal choice; algebraic structure; fuzzy arithmetic; LR-numbers