• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권3호
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• pp.139-151
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• 2007

We introduce the concept of intuitionistic fuzzy semiprimality of a semigroup which is an extension of semiprimality in it. And we obtain a characterization of a semigroup that is a semilattice of simple semigroups in terms of intuitionistic fuzzy semiprime interior ideals.

• 대한수학회보
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• 제44권2호
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• pp.359-367
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• 2007

We consider the intuitionistic fuzzification of the concept of several ${\Gamma}$-ideals in a ${\Gamma}$-semigroup S, and investigate some properties of such ${\Gamma}$-ideals.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.51-62
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• 2015

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.855-866
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• 2024

The set of all prime L-fuzzy ideals of an ADL A with truth values in a frame L is topologized and the resulting space is denoted by 𝓕_L Spec (A), called fuzzy Stone space of A. Certain properties of the space 𝓕_L Spec (A) are discussed, and it is proved that 𝓕_L Spec (A) is homeomorphic with the product space Spec (A) × Spec (L).

• 대한수학회논문집
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• 제30권3호
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• pp.143-154
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• 2015

Characterizations of hesitant fuzzy left (right) ideals are considered. The notion of hesitant fuzzy (generalized) bi-ideals is introduced, and related properties are investigated. Relations between hesitant fuzzy generalized bi-ideals and hesitant fuzzy semigroups are discussed, and characterizations of (hesitant fuzzy) generalized bi-ideals and hesitant fuzzy bi-ideals are considered. Given a hesitant fuzzy set $\mathcal{H}$ on a semigroup S, hesitant fuzzy (generalized) bi-ideals generated by $\mathcal{H}$ are established.

• Korean Journal of Mathematics
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• 제27권4호
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• pp.1077-1108
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• 2019

The notions of intuitionistic fuzzy UP-subalgebras and intuitionistic fuzzy UP-ideals of UP-algebras were introduced by Kesorn et al. [13]. In this paper, we introduce the notions of intuitionistic fuzzy near UP-filters, intuitionistic fuzzy UP-filters, and intuitionistic fuzzy strong UP-ideals of UP-algebras, prove their generalizations, and investigate their basic properties. Furthermore, we discuss the relations between intuitionistic fuzzy near UP-filters (resp., intuitionistic fuzzy UP-filters, intuitionistic fuzzy strong UP-ideals) and their upper t-(strong) level subsets and lower t-(strong) level subsets in UP-algebras.

• 호남수학학술지
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• 제37권2호
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• pp.187-205
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• 2015

We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.445-460
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• 2022

In this paper, we studied on 𝛽-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of 𝛽-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any 𝛽-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime 𝛽-fuzzy filters and some topological concepts on the collection of prime 𝛽-fuzzy filters of a Stone ADL. Further we show that the collection 𝓣 = {X^𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec_𝛽(A) where X^𝛽(λ) = {𝜇 ∈ 𝓕Spec_𝛽(A) : λ ⊈ 𝜇}.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.221-236
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• 2023

In this paper, we define the notions of (3, 2)-fuzzy ideal of subtraction semigroup and near subtraction semigroup. Also, we discuss some of its properties with examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권3호
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• pp.181-187
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• 2014

Dealing with uncertainty is always a challenging problem. Intuitionistic fuzzy sets was presented to manage situations in which experts have some membership and non-membership value to assess an alternative. Hesitant fuzzy sets was used to handle such situations in which experts hesitate between several possible membership values to assess an alternative. In this paper, the concept of intuitionistic hesitant fuzzy set is introduced to provide computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values. Distance measure is defined between any two intuitionistic hesitant fuzzy elements. Fuzzy technique for order preference by similarity to ideal solution is developed for intuitionistic hesitant fuzzy set to solve multi-criteria decision making problem in group decision environment. An example is given to illustrate this technique.