This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals) from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R) is isom...

Probability theory is the standard economic representation of uncertainty, although it is not always an accurate one. Fuzzy logic is an alternative representation that does not require individual beliefs regarding the explicit functional form of uncertainty. This paper applies fuzzy logic to an oligopoly trigger pricing game. The fuzzy trigger pricing game reverses the standard cyclical price w...

If V is a variety of algebras, let L(V) denote the prevariety of all lattices embeddable in congruence lattices of algebras in V . We give some criteria for the first-order axiomatizability or nonaxiomatizability of L(V). One corollary to our results is a nonconstructive proof that every congruence n-permutable variety satisfies a nontrivial congruence identity.

With every monoid, one can associate various binary relations, in particular the so-called principal quasi-order, principal order and principal congruence. The aim of this paper is to show that any compatible quasiorder, order and congruence can be obtained as an intersection of the corresponding principal relations. The particular case of languages -subsets of free monoids generated by an alph...

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...