• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.435-457
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• 2013

Using the Lukasiewicz 3-valued implication operator, the notion of an (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring is introduced, where ${\alpha},{\beta}{\in}\{{\in},q,{\in}{\wedge}q,{\in}{\vee}q\}$. We define intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) and (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$)-intuitionistic fuzzy left (right) $h$-ideal of R if and only if A is an intuitionistic fuzzy left (right) $h$-ideal with thresholds (0, 1) (or (0, 0.5) or (0.5, 1)) of R respectively. It is also shown that A is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$))-intuitionistic fuzzy left (right) $h$-ideal if and only if for any $p{\in}$ (0, 1] (or $p{\in}$ (0, 0.5] or $p{\in}$ (0.5, 1] ), $A_p$ is a fuzzy left (right) $h$-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of R if and only if for any $p{\in}(s,t]$, the cut set $A_p$ is a fuzzy left (right) $h$-ideal of R.

• East Asian mathematical journal
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• 제22권1호
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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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.37-40
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• 2003

We introduce the category IRel (H) consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the category IRel (H) in the viewpoint of the topological universe introduced by L.D.Nel. Thus we show that IRel (H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IRel (H) is cartesian closed over Set.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권1호
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• pp.33-45
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• 2005

We introduce the category ISet(H) of intuitionistic H-fuzzy sets and show that ISet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study the relation between Set(H) and ISet(H).

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.491-500
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• 2006

In this paper, we define intuitionistic fuzzy subalgebras of B-algebras which is related to several classes of algebras such as BCI/BCK-algebras. We could obtain some important results for the homomorphic image and equivalence relations on IFS(X).

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.33-36
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• 2003

We introduce the subcategory IRel$\_$R/ (H) of IRel (H) consisting of intuitionistic H-fuzzy reflexive relational spaces on sets and we study structures of IRel$\_$R/ (H) in a viewpoint of the topological universe introduce by L.D.Nel. We show that IRel$\_$R/ (H) is a topological universe over Set. Moreover, we show that exponential objects in IRel$\_$R/ (H) are quite different from those in IRel (H) constructed in [7].

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.897-914
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• 2022

Pythagorean fuzzy sets (PFSs) are capable of modelling information with more uncertainties in decision-making problems. The essential feature of PFSs is that they are described by three parameters: membership function, non-membership function and hesitant margin, with the total of the squares of each parameter equal to one. The purpose of this article is to suggest some new similarity measures and weighted similarity measures for PFSs. Numerical computations have been carried out to validate our proposed measures. Applications of these measures have been applied to some real-life decision-making problems of pattern detection and medicinal investigations. Moreover, a descriptive illustration is employed to compare the results of the proposed measures with the existing analogous similarity measures to show their effectiveness.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.29-32
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• 2003

We introduce the subcategories IRe $l_{PR}$ (H), IRe $l_{PO}$ (H) and IRe $l_{E}$(H) of IRe $l_{R}$(H) and study their structures in a viewpoint of the topological universe introduced by L.D.Nel. In particular, the category IRe $l_{R}$(H)(resp. IRe $l_{P}$(H) and IRe $l_{E}$(H)) is a topological universe eve, Set. Moreover, we show that IRe $l_{E}$(H) has exponential objects.ial objects.