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http://dx.doi.org/10.14400/JDC.2021.19.10.377

Fuzzy Deterministic Relations  

Sung, Yeoul Ouk (Department of Applied Mathematics, Kongju National University)
Lee, Hyun Kyu (Department of Applied Mathematics, Kongju National University)
Yang, Eunmok (Department of Financial Information Security, Kookmin University)
Publication Information
Journal of Digital Convergence / v.19, no.10, 2021 , pp. 377-382 More about this Journal
Abstract
A fuzzy relation between X and Y as fuzzy subset of X × Y was proposed by Zadeh. Subsequently, several researchers have applied the notion of fuzzy subsets to various branches of mathematics and computer sciences. Murali an Nemitz have studied fuzzy relations connected with fuzzy equivalence relations and fuzzy functions. Ounalli and Jaoua defined a fuzzy difunctional relation on a set. difunctional relations are versatile mathematical tool, which can be used in software design and in database theory. Their work have revealed the usefulness of difunctional relations in program specification and in defining program correctness. The main goal of this paper is to define a fuzzy deterministic relation on a set, characterize the fuzzy deterministic relation as its level subsets and investigate some properties in connection with fuzzy deterministic relation. In particular we prove that a fuzzy relation R is fuzzy deterministic iff R is a fuzzy function.
Keywords
G-reflexivity; fuzzy equivalence relation; fuzzy difunctional relation; fuzzy deterministic relation; fuzzy fuction;
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