• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.413-437
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• 2023

In this paper, we introduce the concepts of (inf, sup)-hesitant fuzzy subsemigroups and (inf, sup)-hesitant fuzzy (generalized) bi-ideals of semigroups, and investigate their properties. The concepts are established in terms of sets, fuzzy sets, negative fuzzy sets, interval-valued fuzzy sets, Pythagorean fuzzy sets, hesitant fuzzy sets, and bipolar fuzzy sets. Moreover, some characterizations of bi-ideals, fuzzy bi-ideals, anti-fuzzy bi-ideals, negative fuzzy bi-ideals, Pythagorean fuzzy bi-ideals, and bipolar fuzzy bi-ideals of semigroups are given in terms of the (inf, sup)-type of hesitant fuzzy sets. Also, we characterize a semigroup which is completely regular, a group and a semilattice of groups by (inf, sup)-hesitant fuzzy bi-ideals.

• East Asian mathematical journal
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• v.24 no.2
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• pp.145-149
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• 2008

From the notion of bi-ideals in near-rings, various generalizations of regularity conditions have been studied. In this paper, we generalize further the notion of bi-ideals and introduce the notion of weak bi-ideals in near-rings and obtain some characterizations using this concept in left self distributive near-rings.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.115-143
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• 2016

The concept of quasi-coincidence of interval valued intuitionistic fuzzy point with an interval valued intuitionistic fuzzy set is considered. By using this idea, the notion of interval valued (α, β)-intuitionistic fuzzy bi-ideals, (1,2)ideals in a semigroup introduced and consequently, a generalization of interval valued intuitionistic fuzzy bi-ideals and intuitionistic fuzzy bi-ideals is defined. In this paper, we study the related properties of the interval valued (α, β)-intuitionistic fuzzy bi-ideals, (1,2) ideals and in particular, an interval valued (Є, Є ∨q)-fuzzy bi-ideals and (1,2) ideals in semigroups will be investigated.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.95-100
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• 2006

In this paper we give some new characterizations of the intra-regular ordered semigroups in terms of bi-ideals and quasi-ideals, bi-ideals and left ideals, bi-ideals and right ideals of ordered semigroups.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.153-159
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• 2007

The notion of bi-ideals in near-rings was effectively used to characterize the near-fields. Using this notion, various generalizations of regularity conditions have been studied. In this paper, we generalize further the notion of bi-ideals and introduce the notion of weak bi-ideals in near-rings and obtain various characterizations using the same in left self distributive near-rings.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.569-596
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• 2014

In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzied algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy subsystems of ordered semigroups namely (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.449-461
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• 2019

The aim of this paper is to extend the concept of quasi and bi-ideals from left almost semigroups to left almost rings which are the generalization of one sided ideals. Further, we discuss quasi and bi-ideals in regular left almost rings and intra regular left almost rings. We then explore many interesting and elegant properties of quasi and bi-ideals.

• 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.28 no.3
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• pp.623-638
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• 2020

In this article, we initially present the concept of the fuzzy generalized m-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized m-bi-ideals, we give the important characterizations of the semigroups. We also characterize the m-regular and m-intraregular semigroups using the properties of the irreducible and strongly irreducible fuzyy generalized m-bi-ideals.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.527-537
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• 2005

The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy bi-ideals of an ordered semigroup are investigated.