• 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.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.711-738
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• 2010

We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.

• East Asian mathematical journal
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• v.23 no.1
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• pp.45-58
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• 2007

The notions of IVF strongly semiopen (semiclosed) sets and IVF (strong) semi-interior (IVF (strong) semi-closure) are introduced, and several examples are provided. Related properties are investigated. In particular, characterizations of an IVF strongly semiopen set are discussed.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.417-431
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• 2006

The notions of IVF strongly semiopen (semiclosed) mappings and IVF strongly semicontinuous mappings are introduced, and several examples are provided. Related properties are investigated. In particular, characterizations of an IVF strongly semiopen mapping and an IVF strongly semicontinuous mapping are discussed.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.362-365
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• 2007

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.4
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• pp.545-549
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• 2009

Microarray data sets could contain thousands of gene expression levels and have been considered as an important source from which meaningful patterns could be extracted for further analysis in biological studies. It is sometimes necessary to retrieve out specific genes or samples of analyst's interest in an effective way. This paper is concerned with a method to make use of fuzzy signature set in order to filter out genes or samples which satisfy complicated constraints as well as simple ones. Fuzzy signatures are an extension of vector valued fuzzy sets, in which elements of the vector are allowed to have a vector. Fuzzy signature sets are similar to fuzzy signatures except that their leaf elements are fuzzy sets defined on the interval [0,1]. This paper introduces an extension of fuzzy signature sets which specifies aggregation operators at each internal node and comparison operators for aggregation. It also shows how to use the extended fuzzy signature sets in microarray data retrieval and some examples of its usage.

• Journal of Internet Computing and Services
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• v.8 no.3
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• pp.99-107
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• 2007

In general, the reliabilities of the fuzzy system are represented and analyzed by real numbers between zero and one, fuzzy numbers, intervals of confidence, interval-valued fuzzy sets, vague sets, etc. This paper addresses the method to analyze the reliability of the fuzzy system for the weighted components with the weights reflected on the importance of weighted components in an system. The reliabilities and the weights of the weighted components in a fuzzy numbers and considers the weights of the weighted components in a fuzzy system, therefore, its execution is faster and more flexible than the conventional methods.

• 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.