• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.184-189
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• 2011

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan's law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on generalized intuitionistic fuzzy soft sets. We discuss the basic properties of operations on generalized intuitionistic fuzzy soft sets such as necessity and possibility. Moreover, we illustrate their interconnections between each other.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.3
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• pp.389-394
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• 2011

The notion of generalized intuitionistic fuzzy soft set theory is proposed. Our generalized intuitionistic fuzzy soft set theory is a combination of the generalized intuitionistic fuzzy set theory and the soft set theory. In other words, our generalized intuitionistic fuzzy soft set theory is an extension of the intuitionistic fuzzy soft set theory. The complement, "and" and "or" operations are defined on the generalized intuitionistic fuzzy soft sets. Their basic properties for the generalized intuitionistic fuzzy soft sets are also presented and discussed.

• Korean Journal of Mathematics
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• v.25 no.1
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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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.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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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 $GIVIFS_Bs$.

• Korean Journal of Mathematics
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• v.25 no.2
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.61-64
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• 2006

Based on the geometrical representation of a generalized intuitionistic fuzzy set, we take into account all three parameters describing generalized intuitionistic fuzzy set, propose a method to calculate the correlation coefficient for generalized intuitionistic fuzzy sets in finite set and probability space, respectively, and discuss some properties of correlation and correlation coefficient of generalized intuitionistic fuzzy sets.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.317-326
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• 2006

Based on the geometrical representation of a generalized intuitionistic fuzzy set, we take into account all three parameters describing generalized intuitionistic fuzzy set and propose new methods to calculate the correlation coefficient for generalized intuitionistic fuzzy sets by means of mathematical statistics.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.5
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• pp.569-577
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• 2014

Park et al. (2011) 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, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with respect to some operations and the generalized intuitionistic fuzzy soft quotient algebra is established.