• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.362-365
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• 2008

In the conventional fuzzy system reliability analysis, the reliabilities of the fuzzy systems and the components of fuzzy systems are represented by real values between zero and one, fuzzy numbers, vague sets, interval valued fuzzy sets, etc. This paper propose a method to represent and analyze the reliabilities of the fuzzy systems based on the internal 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 are represented as the intervals, therefore it can allow the reliabilities of a fuzzy system to represent and analyze in a more flexible manner.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.335-346
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• 2000

This paper discusses the relation of fuzzy sets satisfying some types of fuzzy covering properties. We give some characterizations of such fuzzy sets and investigate a few properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.463-466
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• 2003

Fuzzy set expressing category in fuzzy rating, which is a kind of psychological scaling, is dependent on situations. This paper assumes that a mapping exists between fuzzy sets expressing categories in some situation and those expressing same categories in another situation. fuzzy sets expressing categories in some situation are obtained by fuzzy sets expressing categories in another situation and the mapping between them. The usefulness of the present method is confirmed by the experiments comparing fuzzy sets obtained by the presented method with those identified directly by fuzzy rating. The normalized distance is used to compare both fuzzy sets and the experimental results show that the normalized distances between both fuzzy sets are enough small and that the presented method is useful for psychological scaling.

• Journal of Internet Computing and Services
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• v.4 no.4
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• pp.45-51
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• 2003

In general, the values for attribute appearing in fuzzy object-oriented data models are represented by the fuzzy sets. If it can allow the attribute values in the fuzzy object-oriented data models to be represented by the interval-valued fuzzy sets, then it can allow the fuzzy object-oriented data models to represent the attribute values in more flexible manner. The attribute values of frames appearing in the inheritance structure of the fuzzy object-oriented data models are calculated by a prloritized conjunction operation using interval-valued fuzzy sets. This approach can be applied to knowledge and information processing in which degree of membership is represented as not the conventional fuzzy sets but the interval-valued fuzzy sets.

• East Asian mathematical journal
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• v.28 no.1
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• pp.1-11
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• 2012

In this paper, the concept of fuzzy soft module is introduced, some of their properties are discussed. Furthermore, the concept of fuzzy soft exactness is also given.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.121-128
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• 2023

The aim of this article is to extend hesitant fuzzy minimal open and hesitant fuzzy maximal open sets in hesitant fuzzy topological space. Further, we investigate some properties with these new sets.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1419-1430
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• 2010

Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on $\mathbb{R}$, it is natural to find a new order for normal fuzzy sets on $\mathbb{R}^n$ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order "${\preceq}_s$ for normal fuzzy sets on $\mathbb{R}^n$ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.297-308
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• 2013

We define one-sided quadrangular fuzzy sets, a left quadrangular fuzzy set and a right quadrangular fuzzy set. And then we generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two one-sided quadrangular fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two one-sided quadrangular fuzzy sets becomes a triangular fuzzy number.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.223-244
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• 2007

We introduce the notions of interval-valued fuzzy semipreopen sets (mappings), interval-valued fuzzy semi-pre interior and interval-valued fuzzy semi-pre-continuous mappings by using the notion of interval-valued fuzzy sets. We also investigate related properties and characterize interval-valued fuzzy semi-preopen sets (mappings) and interval-valued fuzzy semi-precontinuous mappings.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.136-139
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• 2005

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