The purpose of this paper is to study some properties of cartesian product of fuzzy completely prime ideals and fuzzy completely semiprime ideals of Γ-semigroups. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between cartesian product of fuzzy ideals (fuzzy completely prime ideals, fuzzy completely semiprime ideals) of a Γ-semigroup and that of it...

we generalize concepts of left hyperfilters, right hyperfilters and an ordered semihypergroup by introducing left-m-hyperfilters, right-n-hyperfilters (m,n)-hyperfilters semihypergroup. Then, some properties these generalized have been studied. Finally, left-m-hyperfilters (resp. right-n-hyperfilters, (m,n)-hyperfilters) (m, 0)-regular (0,n)-regular, (m,n)-regular) semihypergroups characterize in terms...

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

A ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if (I ∩ J) = (I) + (J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f (x) = a0 + a1x + ··· + amx, g(x) = b0 + b1x + ··· + bnx ∈ R[x] satisfy f (x)g(x) = 0, then aibj = 0 for each ...

  Multiple criteria decision making (MCDM) problem is one of the famous different kinds of decision making problems. In more cases in real situations, determining the exact values for MCDM problems is difficult or impossible. So, the values of alternatives with respect to the criteria or / and the values of criteria weights, are considered as fuzzy values (fuzzy numbers). In such conditions, th...

Definition 1.1. Let A be an involutive algebra over C with involution ξ 7→ ξ (resp. ξ 7→ ξ). We say A is a left (resp. right) Hilbert algebra if A has a inner product (· | ·) satisfying: a. Multiplication on the left (resp. right) is a bounded operator; that is, ∀ξ ∈ A the map πl(ξ) : η 7→ ξη (resp. πr(ξ) : η 7→ ηξ) is bounded on A. b. (ξη | ζ) = (η | ξζ) (resp. (ξη | ζ) = (ξ | ζη)). c. The inv...

After the introduction of fuzzy sets by Zadeh [20] in 1965, several researchers have been working on the generalization of the fuzzification. In 1986, Atanassov [2] introduced the notion of intuitionistic fuzzy sets. For more details on the intuitionistic fuzzy sets, we refer to [2-4]. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true [18]. Kim and Jun [7, 8] int...

In this paper, a new approach to LA-semigroup theory is proposed by obtaining significant characterizations of regular, intra-regular, completely regular, weakly regular and quasi-regular LA-semigroups via soft intersection left (right, two-sided) ideals, (generalized) bi-ideals, interior ideals, quasi-ideals of LA-semigroups.

The intersection of all two-sided ideals of an ordered semigroup, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup (S, ·,≤) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L′ of (S, ·,≤), I is properly contained in L′ and L′ is contained in L imply L′ = L. The notions of simple right and two-s...