Inclusion principle of fuzzy arithmetic results

Article type: Research Article

Authors: Piegat, Andrzej | Pluciński, Marcin^{; *}

Affiliations: Faculty of Computer Science and Information Systems, West Pomeranian University of Technology, Żołnierska, Szczecin, Poland

Correspondence: [*] Corresponding author. M. Pluciński, Faculty of Computer Science and Information Systems, West Pomeranian University of Technology, Żołnierska 49, 71-210 Szczecin, Poland. E-mail: mplucinski@wi.zut.edu.pl.

Abstract: The paper presents the inclusion principle of fuzzy arithmetic results. This principle explains what features should have the span of the result of calculations realized with use of the fuzzy arithmetic. If some kind of fuzzy arithmetic provides results that do not comply with this principle, it means that the arithmetic has incomplete reliability, has errors in its theoretical assumptions and should either be verified or rejected. The principle contributes to the ordering of fuzzy arithmetic rules and thus to its practical applicability.

Keywords: Fuzzy arithmetic, interval arithmetic, multidimensional fuzzy arithmetic, principle of results inclusion

DOI: 10.3233/JIFS-210980

Journal: Journal of Intelligent & Fuzzy Systems, vol. 42, no. 6, pp. 4987-4998, 2022