• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.455-459
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• 2007

Interval-valued fuzzy sets were suggested for the first time by Gorzafczany(1983) and Turksen(1986). Based on this, Zeng and Li(2006) introduced concepts of similarity measure and entropy on interval-valued fuzzy sets which are different from Bustince and Burillo(1996). In this paper, by using Choquet integral with respect to a fuzzy measure, we introduce distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets and discuss some properties of them. Choquet integral is a generalization concept of Lebesgue inetgral, because the two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.27-40
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• 2016

In this paper, we introduce the concepts of interval-valued intuitionistic gradation of openness of fuzzy sets which is a generalization of intuitionistic gradation of openness of fuzzy sets and interval-valued intuitionistic gradation preserving mapping and then investigate their properties.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.2
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• pp.149-153
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• 2007

In this paper, we consider interval-valued fuzzy sets which were suggested by Wang and Li(1998) and Turksen(1986) and investigate entropy defined by Choquet integral on interval-valued fuzzy sets. Furthermore, we discuss some properties of them and give some examples related this entropy. This tool has drawn much attention due to numerous applications areas, such as decision making and information theory on interval-valued fuzzy sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.175-178
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• 2007

We give a geometrical interpretation of the interval-valued fuzzy set. So, based on the geometrical background, we propose new distance measures between interval-valued fuzzy sets and compare these measures with distance measures proposed by Burillo and Bustince and Grzegorzewski, respectively. Furthermore, we extend three methods for measuring distances between interval-valued fuzzy sets to interval-valued intuitionistic fuzzy sets.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.249-255
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• 2009

In [5], we introduced the concepts of IVF m-preopen sets and IVF m-precontinuous mappings on interval-valued fuzzy minimal spaces. In this paper, we introduce the concept of IVF m-preopen mapping and investigate characterizations for IVF mprecontinuous mappings and IVF m-preopen mappings.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.121-124
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• 2005

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, we define a distance measure on interval-valued fuzzy numbers using Choquet integral with respect to a classical measure and investigate their properties.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.753-774
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• 2020

We introduce the notion of interval valued intuitionistic fuzzy hyperideals, bi-hyperideals and quasi-hyperideals of an ordered semihypergroup. We characterize an interval valued intuitionistic fuzzy hyperideal of an ordered semihypergroup in terms of its level subset. Moreover, we show that interval valued intuitionistic fuzzy bi-hyperideals and quasi-hyperideals coincide only in a particular class of ordered semihypergroups. Finally, we show that every interval valued intuitionistic fuzzy quasi-hyperideal is the intersection of an interval valued intuitionistic fuzzy left hyperideal and an interval valued intuitionistic fuzzy right hyperideal.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.63-66
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• 2002

As a generalization of fuzzy sets, the concept of interval-valued fuzzy sets was introduced by Gorzalczany(GO). In this paper, we shall extend the concept of "fuzzy inclusion", introduced by Sostak[SO1], to the interval-valued fuzzy setting and study its fundamental properties for some extent.