• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.5
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• pp.603-608
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• 2009

In this paper, a similarity measure between interval-valued vague sets is proposed. In the interval-valued vague sets representation, the upper bound and the lower bound of a vague set are represented as intervals of interval-valued fuzzy set respectively. Proposed method combines the concept of geometric distance and the center-of-gravity point of interval-valued vague set to evaluate the degree of similarity between interval-valued vague sets. We also prove three properties of the proposed similarity measure. It provides a useful way to measure the degree of similarity between interval-valued vague sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.129-132
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• 2005

In this paper, we consider comonotonically additive compact set-valued functionals instead of interval-valued functionals and study some characterizations of them. And we also investigate some relation between compact set-valued functionals and compact set-valued Choquet integrals.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.170-173
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• 2005

We note that Jang et at. studied closed set-valued Choquet integrals with respect to fuzzy measures. In this paper, we consider Choquet integrals of compact set-valued functions, and prove some properties of them. In particular, using compact set-valued functions, instead of interval valued we investigate characterization of compact set-valued Choquet integrals.

• Journal of Information Processing Systems
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• v.14 no.3
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• pp.790-800
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• 2018

The simplified neutrosophic set (SNS) is a generalization of fuzzy set that is designed for some practical situations in which each element has truth membership function, indeterminacy membership function and falsity membership function. In this paper, we propose a new method to construct similarity measures of single valued neutrosophic sets (SVNSs) and interval valued neutrosophic sets (IVNSs), respectively. Then we prove that the proposed formulas satisfy the axiomatic definition of the similarity measure. At last, we apply them to pattern recognition under the single valued neutrosophic environment and multi-criteria decision-making problems under the interval valued neutrosophic environment. The results show that our methods are effective and reasonable.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.350-354
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• 2009

Y. R$\acute{e}$ball$\acute{e}$[Fuzzy Sets and Systems, vol.157, pp.3025-2039, 2006] discussed the representation of necessity measure through the Choquet integral criterian. He also considered a decision maker who ranks necessity measures related with Choquet integral representation. Our motivation of this paper is that a decision maker have an "ambiguity" necessity measure to present preferences. In this paper, we discuss the representation of interval-valued necessity measures through the Choquet integral criterian.