Algebraic fuzzy systems

Uniqueness results in the representation of families of sets by fuzzy sets

“…They gave necessary and sufficient conditions for the existence of such a fuzzy set, [19,Theorem 1], [20,Theorem p. 91], and [22,Theorems 1 and 2]. Also see references cited in [22,1,7,14,32,31,34]. These representation theorems, representation of a family of subsets of a set R by a fuzzy subset of R, were used to study several fuzzy concepts such as fuzzy topological spaces and fuzzy algebraic structures, [19].…”

L-Fuzzy Prime Ideals in Universal Algebras

“…As suggested by Gougen [10], the unit interval [0, 1] is not sufficient to take the truth values of general fuzzy statements. U. M. Swamy and D. V. Raju [11,12] studied the general theory of algebraic fuzzy systems by introducing the notion of a fuzzy L− subset of a set corresponding to a given class L of subsets of having truth values in a complete lattice satisfying the infinite meet distributive law. Swamy and Swamy [13] defined the commutator (or the product) of −fuzzy ideals and of a ring as follows:…”

The Commutator of Fuzzy Congruences in Universal Algebras

“…U.M.Swamy and D.V. Raju [42] showed that the set FCon(A) of all L-fuzzy congruences of an algebra A forms an algebraic closure fuzzy set system, where L is a complete lattice satisfying the infinite meet distributive law. In particular, if L is the unit interval [0, 1], then FCon(A) is an algebraic lattice and this result coincides with that of Murali [43].…”