Reinterpreting a fuzzy subset by means of a Sincov's functional equation

Article type: Research Article

Authors: Campión, María Jesús | Catalán, Raquel G. | Induráin, Esteban | Ochoa, Gustavo

Affiliations: Departamento de Matemáticas, Universidad Pública de Navarra, Campus Arrosadía, Pamplona, Spain

Note: [] Corresponding author. Esteban Induráin, Tel.: +34948169551, Fax: +34948166057, E-mail: [email protected]

Abstract: Throughout the paper it is shown that the classical definition of a fuzzy subset carries additional structures. The concept of a fuzzy subset is regarded from an alternative point of view: namely, the characteristic function of a fuzzy subset may be reinterpreted in terms of a Sincov's functional equation in two variables. Since the solutions of a Sincov's functional equation are also closely related to the existence of representable total preorders, an special attention is paid to the relationship between fuzzy subsets and total preorders defined on a universe. Some possible applications of this approach are pointed out in the final section of the manuscript.

Keywords: Fuzzy subsets, Sincov's functional equation, representable total preorders

DOI: 10.3233/IFS-131005

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 1, pp. 367-375, 2014