• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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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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• v.55 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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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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• v.27 no.4
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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.

• Honam Mathematical Journal
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• v.37 no.2
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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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• v.40 no.3_4
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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}.

• The Pure and Applied Mathematics
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• v.30 no.3
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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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• v.14 no.3
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.207-219
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• 2008

We give some properties of intuitionistc fuzzy left, right, and two-sided ideals and bi-ideals of a semigroup. And we characterize a regular semigroup, a semigroup that is a lattice of left(right) simple semigroups, a semigroup that is a semilattice of left(right) groups and a semigroup that is a semilattice of groups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.311-324
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• 2010

We prove that a regular ordered semigroup S is left simple if and only if every intuitionistic fuzzy left ideal of S is a constant function. We also show that an ordered semigroup S is left (resp. right) regular if and only if for every intuitionistic fuzzy left(resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ for every $a\;{\in}\;S$. Further, we characterize some semilattices of ordered semigroups in terms of intuitionistic fuzzy left(resp. right) ideals. In this respect, we prove that an ordered semigroup S is a semilattice of left (resp. right) simple semigroups if and only if for every intuitionistic fuzzy left (resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ and $\mu_A(ab)\;=\;\mu_A(ba)$, $\gamma_A(ab)\;=\;\gamma_A(ba)$ for all a, $b\;{\in}\;S$.