Characterizations of non associative ordered semigroups by the properties of their fuzzy ideals with thresholds (α, β]

In this paper, we give the characterizations of regular (intra-regular, both regular and intra-regular) ordered AG-groupoids by the properties of fuzzy (left, right, quasi-, bi-, generalized bi-) ideals with thresholds (а, β]

Neutrosophic Set Approach for Characterizations of Left Almost Semigroups

In this paper we have defined neutrosophic ideals, neutrosophic interior ideals, netrosophic quasi-ideals and neutrosophic bi-ideals (neutrosophic generalized bi-ideals) and proved some results related to them. Furthermore, we have done some characterization of a neutrosophic LA-semigroup by the properties of its neutrosophic ideals

Theory of Abel Grassmann\u27s Groupoids

It is common knowledge that common models with their limited boundaries of truth and falsehood are not su¢ cient to detect the reality so there is a need to discover other systems which are able to address the daily life problems. In every branch of science problems arise which abound with uncertainties and impaction. Some of these problems are related to human life, some others are subjective while others are objective and classical methods are not su¢ cient to solve such problems because they can not handle various ambiguities involved. To overcome this problem, Zadeh [67] introduced the concept of a fuzzy set which provides a useful mathematical toolfordescribingthebehaviorofsystemsthatareeithertoocomplexorare ill-dened to admit precise mathematical analysis by classical methods. The literature in fuzzy set and neutrosophic set theories is rapidly expanding and application of this concept can be seen in a variety of disciplines such as articialintelligence,computerscience,controlengineering,expertsystems, operating research, management science, and robotics. Zadeh introduced the degree of membership of an element with respect to a set in 1965, Atanassov introduced the degree of non-membership in 1986, and Smarandache introduced the degree of indeterminacy (i.e. neither membership, nor non-membership) as independent component in 1995 and defined the neutrosophic set. In 2003 W. B. Vasantha Kan- dasamy and Florentin Smarandache introduced for the rst time the I- neutrosophic algebraic structures (such as neutrosophic semigroup, neutro- sophic ring, neutrosophic vector space, etc.) based on neutrosophic num- bers of the form a + bI, wher

Regular ag-groupoids characterized by (∈, ∈ ∨ q k)-fuzzy ideals

In this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in AG -groupoids. Generalizing the concepts of (∈, ∈ ∨q) -fuzzy bi-ideals (interior ideal), we define (∈, ∈ ∨ q k) -fuzzy bi-ideals, (∈, ∈ ∨ q k )-fuzzy left (right)-ideals and ( , ) k ? ? ?q -fuzzy interior ideals in AG -groupoids and discuss some fundamental aspects of these ideals in AG -groupoids. We further define ( ∈, ∈ ∨ q k) -fuzzy bi-ideals and (∈, ∈ ∨ q k)-fuzzy interior ideals and give some of their basic properties in AG -groupoids. In the last section, we define lower/upper parts of (∈, ∈ ∨ q k ) -fuzzy left (resp. right) ideals and investigate some characterizations of regular and intera-regular AG -groupoids in terms of the lower parts of ( ∈, ∈ ∨ q k ) -fuzzy left (resp. right) ideals and ( ∈, ∈ ∨ q k )-fuzzy bi-ideal of AG -groupoids

On Ordered (p; q)-Lateral Ideals in Ordered Ternary Semigroups

In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary semigroups. Also, some properties of (p; q)-lateral simple ordered ternary semigroup have been examined. Further, we characterize the relationship between minimal (resp., maximal) ordered (p; q)- lateral ideals and (p; q)-lateral simple ordered ternary semigroups

A new generalization of fuzzy ideals in LA-semigroups

Abstract. In this article, the concept of (∈γ, ∈γ ∨ q δ )-fuzzy LAsubsemigroups, (∈γ, ∈γ ∨ q δ )-fuzzy left(right) ideals, (∈γ, ∈γ ∨ q δ )-fuzzy generalized bi-ideals and (∈γ, ∈γ ∨ q δ )-fuzzy bi-ideals of an LA-semigroup are introduced. The given concept is a generalization of (∈, ∈ ∨ q)-fuzzy LA-subsemigroups, (∈, ∈ ∨ q)-fuzzy left(right) ideals, (∈, ∈ ∨ q)-fuzzy generalized bi-ideals and (∈, ∈ ∨ q)-fuzzy bi-ideals of an LA-semigroup. We also give some examples of (∈γ, ∈γ ∨ q δ )-fuzzy LA-subsemigroups ( left, right, generalized bi-and bi) ideals of an LA-semigroup. We prove some fundamental results of these ideals. We characterize (∈ γ , ∈γ ∨ q δ )-fuzzy left(right) ideals, (∈γ, ∈γ ∨ q δ )-fuzzy generalized bi-ideals and (∈γ, ∈γ ∨ q δ )-fuzzy bi-ideals of an LA-semigroup by the properties of level sets

An investigatiozn on Prime and Semiprime fuzzy hyperideals in po-ternary semihypergroups

The aim of this paper is to apply the concept of fuzzification on prime hyperideals and semiprime hyperideals in po-ternary semihypergroups and look for some of their related characteristics. Moreover, a number of characterizations for intra-regular po-ternary semihypergroups had been given by using the concept of fuzzy hyperideals