• East Asian mathematical journal
• /
• 제31권1호
• /
• pp.1-18
• /
• 2015

In this paper we characterize different classes of hemirings by the properties of their (${\in},{\in}{\vee}q$)-fuzzy ideals, (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and (${\in},{\in}{\vee}q$)-fuzzy bi-ideals.

• 호남수학학술지
• /
• 제39권4호
• /
• pp.527-559
• /
• 2017

The main motivation of this article is to generalized the concept of fuzzy ideals, (${\alpha},{\beta}$)-fuzzy ideals, (${\in},{\in}{\vee}q_k$)-fuzzy ideals of semigroups. By using the concept of $q^{\delta}_K$-quasi-coincident of a fuzzy point with a fuzzy set, we introduce the notions of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal of a semigroup. Special sets, so called $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set, condition for the $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set-set to be left (resp. right) ideals are considered. We finally characterize different classes of semigroups (regular, left weakly regular, right weakly regular) in term of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy ideal of semigroup S.

• East Asian mathematical journal
• /
• 제27권3호
• /
• pp.349-372
• /
• 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.

• Journal of applied mathematics & informatics
• /
• 제32권3_4호
• /
• pp.405-426
• /
• 2014

The concept of interval-valued (${\alpha},{\beta}$)-fuzzy ideals, interval-valued (${\alpha},{\beta}$)-fuzzy generalized bi-ideals are introduced in LA-semigroups, using the ideas of belonging and quasi-coincidence of an interval-valued fuzzy point with an interval-valued fuzzy set and some related properties are investigated. We define the lower and upper parts of interval-valued fuzzy subsets of an LA-semigroup. Regular LA-semigroups are characterized by the properties of the lower part of interval-valued (${\in},{\in}{\vee}q$)-fuzzy left ideals, interval-valued (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and interval-valued (${\in},{\in}{\vee}q$)-fuzzy generalized bi-ideals. Main Facts.

• 호남수학학술지
• /
• 제41권2호
• /
• 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.

• Korean Journal of Mathematics
• /
• 제28권1호
• /
• pp.31-47
• /
• 2020

In this paper, we discuss in detail some of the properties of the new kind of (∈, ∈ ∨q)-fuzzy ideals in Near-ring. The concept of (∈, ∈ ∨q^δ₀)-fuzzy ideal of Near-ring is introduced and some of its related properties are investigated.