• Korean Journal of Mathematics
• /
• 제29권2호
• /
• pp.305-320
• /
• 2021

In this paper, the relations between L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of a poset and L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of the lattice of all ideals of a poset are established. A result analogous to Separation Theorem is obtained using L-fuzzy semi-prime ideals.

• Journal of applied mathematics & informatics
• /
• 제28권5_6호
• /
• pp.1217-1225
• /
• 2010

In this paper we define fuzzy interior $\Gamma$-ideals in ordered $\Gamma$-semigroups. We prove that in regular(resp. intra-regular) ordered $\Gamma$-semigroups the concepts of fuzzy interior $\Gamma$-ideals and fuzzy $\Gamma$-ideals coincide. We prove that an ordered $\Gamma$-semigroup is fuzzy simple if and only if every fuzzy interior $\Gamma$-ideal is a constant function. We characterize intra-regular ordered $\Gamma$-semigroups in terms of interior (resp. fuzzy interior) $\Gamma$-ideals.

• Journal of applied mathematics & informatics
• /
• 제11권1_2호
• /
• pp.255-263
• /
• 2003

Fuzzifications of n-fold quasi-associative ideals are considered. Conditions for a fuzzy ideal to be a fuzzy n-fold quasi-associative ideal are given. Using a collection of n-fold quasi-associative ideals, fuzzy n-fold quasi-associative ideals are constructed. Finally, the extension property for fuzzy n-fold quasi-associative ideals is established.

• 대한수학회보
• /
• 제43권1호
• /
• pp.141-148
• /
• 2006

Fuzzy (weak) implicative hyper K-ideals are introduced, and relations among fuzzy weak implicative hyper K-ideals, fuzzy implicative hyper K-ideals and fuzzy hyper K-ideals are discussed.

• 호남수학학술지
• /
• 제46권1호
• /
• pp.82-100
• /
• 2024

The main objective of the study is to introduce ideals of Sheffer stroke Hilbert algebras by means of fuzzy points, and investigate some properties. The process of making (fuzzy) ideals and fuzzy deductive systems through the fuzzy points of Sheffer stroke Hilbert algebras is illustrated, and the (fuzzy) ideals and the fuzzy deductive systems are characterized. Certain sets are defined by virtue of a fuzzy set, and the conditions under which these sets can be ideals are revealed. The union and intersection of two fuzzy ideals are analyzed, and the relationships between aforementioned structures of Sheffer stroke Hilbert algebras are built.

• Journal of applied mathematics & informatics
• /
• 제34권5_6호
• /
• pp.405-419
• /
• 2016

The notion of Γ-semiring was introduced by M. Murali Krishna Rao [8] as a generalization of Γ-ring as well as of semiring. In this paper fuzzy k-ideals, k-fuzzy ideals and fuzzy-2-prime ideals in Γ-semirings have been introduced and study the properties related to them. Let μ be a fuzzy k-ideal of Γ-semiring M with |Im(μ)| = 2 and μ(0) = 1. Then we establish that M_μ is a 2-prime ideal of Γ-semiring M if and only if μ is a fuzzy prime ideal of Γ-semiring M.

• Journal of applied mathematics & informatics
• /
• 제41권1호
• /
• pp.133-154
• /
• 2023

In this paper, we introduce the concept of tripolar fuzzy sub-semigroups, tripolar fuzzy ideals, tripolar fuzzy quasi-ideals, and tripolar fuzzy bi-ideals of an ordered semigroup and study some algebraic properties of them. Moreover, we prove that tripolar fuzzy bi-ideals and quasi-ideals coincide only in a particular class of ordered semigroups. Finally, we prove that every tripolar fuzzy quasi-ideal is the intersection of a tripolar fuzzy left and a tripolar fuzzy right ideal.

• 한국지능시스템학회논문지
• /
• 제17권1호
• /
• pp.118-122
• /
• 2007

In this paper, we consider the intuitionistic fuzzification of the notion of a interior ideal in ordered semigroup S, and investigate some properties of such ideals. In terms of intuitionistic fuzzy set, characterizations of intuitionistic fuzzy interior ideals in ordered semigroups are discussed. Using a collection of interior ideals with additional conditions, an intuitionistic fuzzy interiror ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy interior ideals of an ordered semigroup are investigated. We also give a characterization of a intuitionistic fuzzy simple semigroup in terms of intuitionistic fuzzy interior ideals.

• 호남수학학술지
• /
• 제25권1호
• /
• pp.43-52
• /
• 2003

The fuzzification of positive implicative hyper K-ideals in hyper K-algebras is considered, Relations between fuzzy positive implicative hyper K-ideal and fuzzy hyper K-ideal are given. Characterizations of fuzzy positive implicative hyper K-ideals are provided. Using a family of positive implicative hyper K-ideals we make a fuzzy positive implicative hyper K-ideal. Using the notion of a fuzzy positive implicative hyper K-ideal, a weak hyper K-ideal is established.

• Kyungpook Mathematical Journal
• /
• 제56권2호
• /
• pp.371-386
• /
• 2016

Using the hesitant intersection (${\Cap}$), the notions of ${\Cap}$-hesitant fuzzy subalgebras, ${\Cap}$-hesitant fuzzy ideals and ${\Cap}$-hesitant fuzzy p-ideals are introduced,and their relations and related properties are investigated. Conditions for a ${\Cap}$-hesitant fuzzy ideal to be a ${\Cap}$-hesitant fuzzy p-ideal are provided. The extension property for ${\Cap}$-hesitant fuzzy p-ideals is established.