• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.299-303
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• 2006

In this paper, we introduce the concepts of fuzzy strongly (r, s)-semiopen sets and fuzzy strongly (r, s)-semicontinuous mappings on the intuitionistic fuzzy topological space in Sostak's sense and then we investigate some of their characteristic properties.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.515-530
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• 2019

The concept of fuzzy sets in UP-algebras was first introduced by Somjanta et al. [Fuzzy sets in UP-algebras; 2016]. In this paper, we introduce and study fuzzy proper UP-filters of UP-algebras and prove their generalizations and characteristic fuzzy sets of proper UP-filters. Moreover, we discuss the relations between fuzzy proper UP-filters and their level subsets.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.347-362
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• 2023

We introduce an algebraic structure induced by a fuzzy bipartial order on a complete residuated lattices with the double negative law. We undertake an investigation into the properties of fuzzy bi-partial orders, including their various characteristics and features. We demonstrate that the two families of l-stable and r-stable fuzzy sets can be regarded as complete lattices, and we establish that these two families are anti-isomorphic. Furthermore, we provide two examples related to them.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.9-12
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• 2000

In this paper, we are interested in counting the number of elements of a type two fuzzy set. Using concepts of type-two fuzzy sets, we can obtain some properties of these concepts and some results of possibility of type-two fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.4
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• pp.445-450
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• 2008

In order to analyze the reliabilities of the fuzzy systems, the reliabilities of the components in the fuzzy systems are represented by real values between zero and one, fuzzy numbers, intervals of confidence, vague sets, interval valued fuzzy sets, etc in the conventional researches. In this paper, we propose a method to represent and analyze the reliabilities of the fuzzy systems based on the interval valued vague sets defined in the universe of discourse [0, 1]. In the interval valued vague sets, the upper bounds and the lower bounds of the conventional vague sets[12, 14] are represented as the intervals. Therefore, it can allow the reliabilities of a fuzzy system to represent and analyze in a more flexible manner. Because the proposed method uses the simplified arithmetic operations of the fuzzy triangular numbers rather than the complicated of the fuzzy trapezoidal numbers mentioned by Kumar[14], the execution of the proposed method is faster than the one.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.441-453
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• 2002

We introduce the concepts of fuzzy r-regular open sets and fuzzy almost r-continuous maps in the fuzzy topology of Chat-topadhyay. Also we investigate the equivalent conditions of the fuzzy almost r-continuity.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.277-286
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• 2014

We define the pentagonal fuzzy sets and generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two pentagonal fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two pentagonal fuzzy sets becomes a triangular fuzzy number and give some example.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.653-663
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• 2002

We introduce and investigate the concepts of ($(T_i,T_j)$-fuzzy $\alpha-(r.s)$-semiopen $\alpha-(r.s)$-semiclosed) sets and fuzzy pairwise $\alpha-(r.s)$-semicontinuous mappings in smooth bitopological spaces.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.269-279
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• 2015

Atanassov introduced another fuzzy object, called intu- itionistic fuzzy set as a generalization of the concept of fuzzy subset. The aim of this paper is the elaboration of a representation theory of involutive interval-valued Łukasiewicz-Moisil algebras by using the notion of intuitionistic fuzzy sets.