• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.459-476
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• 2017

Interval valued intuitionistic fuzzy sets (IVIFSs) is widely used to model uncertainty, imprecise, incomplete and vague information. In this paper, newly defined modal operators over an extensional generalized interval valued intuitionistic fuzzy sets ($GIVIFS_Bs$) are proposed. Some of the basic properties of the new operators are discussed and few theorems were proved. The actual contribution in this paper is to discuss ten operators on $GIVIFS_Bs$.

• 한국지능시스템학회논문지
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• 제24권2호
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• pp.201-208
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• 2014

Park et al. introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, we introduce new operations such as restricted union and restricted intersection and study their basic properties, and deal with the algebraic structure of generalized intuitionistic fuzzy soft sets. The lattice structures of generalized intuitionistic fuzzy soft sets are constructed.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.1-18
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

• 한국지능시스템학회논문지
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• 제17권4호
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• pp.546-549
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• 2007

When we deal with crisp data, it is common to find the correlation between variables. In this paper, we propose a method to calculate the correlation coefficient for intuitionistic fuzzy data, by adopting the concepts from the conventional statistics. The value of the correlation coefficient computed from our formula not only provides us the strength of the relationship of intuitionistic fuzzy sets, but also shows that the intuitionistic fuzzy sets are positively or negatively related.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2002년도 춘계학술대회 및 임시총회
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• pp.114-118
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• 2002

As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [1]. By using intuitionistic fuzzy sets, we introduce and study the concept of intuitionistic fuzzy filters and define the concept of Hausdorffness on intuitionistic fuzzy filters, which can not be defined in crisp theory of filters, and study their properties for some extent.

• 한국지능시스템학회논문지
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• 제12권6호
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• pp.583-588
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• 2002

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. Tt is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of $F\bigcapF^c and F\bigcupF^c$, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of $F\bigcapF^c and F\bigcupF^c$.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2002년도 추계학술대회 및 정기총회
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• pp.13-16
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• 2002

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] Proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. It is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/.

• 충청수학회지
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• 제35권3호
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• pp.243-254
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• 2022

In this paper, we introduce three different concepts of closed sets on the intuitionistic fuzzy topological spaces, i.e., the generalized fuzzy (r, s)-closed, semi-generalized fuzzy (r, s)-closed, and generalized fuzzy (r, s)-semiclosed sets on intuitionistic fuzzy topological spaces in Šostak's sense. Also we investigate their properties and the relationships among these generalized fuzzy closed sets.

• Korean Journal of Mathematics
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• 제25권2호
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• pp.261-278
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized closed and open sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized continuous mappings and then investigate some of their properties.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.563-576
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• 2021

In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebra of a PMS-algebra. The idea of level subsets of an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra is introduced. The relation between intuitionistic fuzzy sets and their level sets in a PMS-algebra is examined, and some interesting results are obtained.