• Korean Journal of Mathematics
• /
• v.13 no.2
• /
• pp.203-208
• /
• 2005

We define a product fuzzy group, which is weaker than the standard fuzzy group defined by Rosenfeld, and characterize some properties of product fuzzy groups, product fuzzy ideals, and product fuzzy subrings.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.1
• /
• pp.118-122
• /
• 2007

In this paper, we consider the intuitionistic fuzzification of the notion of a interior ideal in ordered semigroup S, and investigate some properties of such ideals. In terms of intuitionistic fuzzy set, characterizations of intuitionistic fuzzy interior ideals in ordered semigroups are discussed. Using a collection of interior ideals with additional conditions, an intuitionistic fuzzy interiror ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy interior ideals of an ordered semigroup are investigated. We also give a characterization of a intuitionistic fuzzy simple semigroup in terms of intuitionistic fuzzy interior ideals.

• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.1-6
• /
• 2012

In [K. J. Lee and C. H. Park, Some questions on fuzzifications of ideals in subtraction algebras, Commun. Korean Math. Soc. 22 (2007), no. 3, 359-363], Lee and Park posed three questions. In this paper, the affirmative answers to their questions are provided, and characterizations of fuzzy ideals are investigated.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.9 no.5
• /
• pp.509-512
• /
• 1999

We study semiprime fuzzy ideals semiprimary fuzzy ideals and their properties. We investigate that if a fuzzy ideal is semiprime and semiprimary then it is prime.

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

• The Pure and Applied Mathematics
• /
• v.14 no.3
• /
• pp.223-230
• /
• 2007

We give an answer to the following question: Question. Let S be a subset of [0,1] containing a maximal element m > 0 and let C :=$\{I_{t}\;{\mid}\;t{\in}S\}$ be a decreasing chain of ideals of a BCK/BCI-algebra X. Then does there exists a fuzzy ideal ${\mu}(X)=S\;and\;C_{\mu}=C?$.

• Honam Mathematical Journal
• /
• v.41 no.2
• /
• pp.285-300
• /
• 2019

This research focuses on the characterization of an ordered semigroups (OS) in the frame work of generalized bipolar fuzzy interior ideals (BFII). Different classes namely regular, intra-regular, simple and semi-simple ordered semigroups were characterized in term of $({\alpha},{\beta})$-BFII (resp $({\alpha},{\beta})$-bipolar fuzzy ideals (BFI)). It has been proved that the notion of $({\in},{\in}{\gamma}q)$-BFII and $({\in},{\in}{\gamma}q)$-BFI overlap in semi-simple, regular and intra-regular ordered semigroups. The upper and lower part of $({\in},{\in}{\gamma}q)$-BFII are discussed.

• Communications of the Korean Mathematical Society
• /
• v.8 no.2
• /
• pp.225-231
• /
• 1993

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1447-1457
• /
• 2009

In this paper we define intuitionistic fuzzy interior ideals in ordered semigroups. We prove that in regular(resp. intra-regular and semisimple) ordered semigroups the concepts of intuitionistic fuzzy interior ideals and intuitionistic fuzzy ideals coincide. We prove that an ordered semi group is intuitionistic fuzzy simple if and only if every intutionistic fuzzy interior ideal is a constant function. We characterize intra-regular ordered semi groups in terms of interior (resp. intuitionistic fuzzy interior) ideals.

• Honam Mathematical Journal
• /
• v.32 no.4
• /
• pp.593-617
• /
• 2010

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.