• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.198-204
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• 2012

We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.372-377
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• 2004

We introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a lattice, and discuss the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruence on a distributive lattice. Also we prove that for a generalized Boolean algebra, the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences. Finally, we consider the products of intuitionistic fuzzy ideals and obtain a necessary and sufficient condition for an intuitionistic fuzzy ideals on the direct sum of lattices to be representable on a direct sum of intuitionistic fuzzy ideals on each lattice.

• 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.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.351-368
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• 2009

Quick ideals and the fuzzification of quick ideals in d-algebras are considered, and some related properties are investigated. The intuitionistic fuzzification of quick ideals of a d-algebra is established, and related results are studied. The notion of equivalence relations on the family of all intuitionistic fuzzy quick ideals of a d-algebra is introduced, and then some properties are discussed.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.439-469
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• 2006

Intrinsic product of intuitionistic fuzzy sets are considered. Using this, characterizations of intuitionistic fuzzy subrings/ideals are discussed. The notions of intuitionistic fuzzy quasi ideals and intuitionistic fuzzy bi-ideals are introduced. Characterizations of regular rings are provided.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.49-64
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• 2020

In this paper, we define fuzzy prime ideals of C-algebras and investigate some of their properties. Furthermore, we study the topological properties of the space of fuzzy prime ideals of C-algebra equipped with the hull-kernel topology.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.329-342
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• 2019

In this paper, we introduce the notion of L-fuzzy semi-prime ideals and the radical of L-fuzzy ideals in universal algebras and make a theoretical study on their basic properties.

• East Asian mathematical journal
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• v.27 no.3
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• pp.349-372
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• 2011

In this paper we define interval valued (${\in}$, ${\in}{\vee}q$)-fuzzy hquasi-ideals, interval valued (${\in}$, ${\in}{\vee}q$)-fuzzy h-bi-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-quasi-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-bi-ideals and characterize different classes of hemirings by the properties of these ideals.