• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.359-365
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• 2012

The fuzzy set framework has a number of properties that make it suitable to formulize uncertain information in medical diagnosis. This study introduces a fuzzy diagnostic method based on the interval-valued interview chart and the interval-valued intuitionistic fuzzy weighted arithmetic average(IIFWAA) operator. An issue in the use of the IIFWAA operator is to determine the weights. In this study, we propose the occurrence information of symptoms as the weights. An illustrative example is provided to demonstrate its practicality and effectiveness.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.370-373
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• 2006

In this paper, we consider set-valued aggregation operators and investigate some properties of them. Moreover, we define interval-valued Choquet integral aggregation operators and discuss their characterizations.

• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.4
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• pp.323-326
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• 2002

In this paper, we consider Choquet integrals of interval number-valued functions(simply, interval number-valued Choquet integrals). Then, we prove convergence theorem for interval number-valued Choquet integrals with respect to an autocontinuous fuzzy measure.

• 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.28 no.2
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• pp.241-259
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• 2006

Using the concept of interval-valued fuzzy (IVF) sets, the notions of IVF semiopen (semiclosed) sets, IVF preopen (preclosed) sets and IVF $\alpha$-open ($\alpha$-closed) sets are introduced, and interrelations are investigated. Also, the concepts of IVF open mappings, IVF preopen mappings, IVF semiopen mappings and IVF $\alpha$-open mappings are introduced, and interrelations are discussed.

• International conference on construction engineering and project management
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• 2011.02a
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• pp.468-473
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• 2011

The goal of a project manager is generally to minimize the cost of the project and also to cope with uncertainty. This paper deals with the problem of project scheduling a set of activities satisfying precedence constraints in order to minimize the sum of the costs associated with the starting times of the activities in the network with imprecise activity durations, represented by means of interval or fuzzy numbers. So far this problem has been completely solved by several authors when the activities durations have crisp values. However, they do not consider the imprecision in activity durations in their models. Here the framework of possibility theory is proposed to solve this problem. In fuzzy arithmetic, usually, the interval calculations are used for the aim of complexity reduction and simplification. Thus the case of interval-valued durations is first addressed, and then extended to fuzzy intervals. A numerical example is used to illustrate the developed concept.

• 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.

• 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.