an:06404439
Zbl 1309.03021
Jesús Campión, María; Catalán, Raquel G.; Induráin, Esteban; Ochoa, Gustavo
Reinterpreting a fuzzy subset by means of a Sincov's functional equation
EN
J. Intell. Fuzzy Syst. 27, No. 1, 367-375 (2014).
1064-1246 1875-8967
2014
j
03E72 39B52
fuzzy subsets; Sincov's functional equation; representable total preorders
Summary: 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.