• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.133-154
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• 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.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.309-330
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• 2004

In this paper, we apply the concept of intuitionistic fuzzy sets to theory of semigroups. We give some properties of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.665-676
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• 2012

Fuzzifications of the notion of n-fold strong ideals are considered. Characterizations of fuzzy $n$-fold strong ideals are given.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.333-351
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• 2024

In this paper, the concept of Pythagorean fuzzy sets are used to describe in semigroups. Then, some characterizations of regular (resp., intra-regular) semigroups by means of Pythagorean fuzzy left (resp., right) ideals and Pythagorean fuzzy (resp., generalized) bi-ideals of semigroups are investigated. Furthermore, the class of both regular and intra-regular semigroups by the properties of many kinds of their Pythagorean fuzzy ideals also being studied.

• East Asian mathematical journal
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• v.22 no.1
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• pp.93-109
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• 2006

The concept of intuitionistic fuzzy set was first introduced by Atanassov in 1986. In this paper, we define the intuitionistic(S,T)-fuzzy left h-ideals of a hemiring by using an s-norm S and a t-norm T and study their properties. In particular, some results of fuzzy left h-ideals in hemirings recently obtained by Jun, $\"{O}zt\"{u}rk$, Song, and others are extended and generalized to intuitionistic (S,T)-fuzzy ideals over hemirings.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.499-509
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• 2000

In [9], the concept of fuzzy sets is applied to the theory of Ζ-ideals in a BCI-semigroup (it was renamed as an IS-algebra for the convenience of study), and a characterization of fuzzy Ζ-ideals by their level Ζ-ideals was discussed. In this paper, we study further properties of fuzzy Ζ-ideals. We prove that the homomorphic image and preimage of a fuzzy Ζ-ideal are also fuzzy Ζ-ideals.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1049-1056
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• 2008

Intuitionistic Fuzzifications of strong hyper K-ideals and hyper K-subalgebras in hyper K-algebras are discussed, and related properties are investigated. Relations between intuitionistic fuzzy hyper K-subalgebras, intuitionistic fuzzy weak hyper K-ideals and intuitionistic fuzzy strong hyper K-ideals are provided.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.33-40
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• 2000

We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.419-430
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• 2005

In this paper, we introduce the notions of ($\in,\;{\in} V q$)-fuzzy subnear-ring, ($\in,\;{\in} V q$)-fuzzy ideal and ($\in,\;{\in}V q$)-fuzzy quasi-ideal of near-rings and find more generalized concepts than those introduced by others. The characterization of such ($\in,\;{\in}V q$)-fuzzy ideals are also obtained.

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