• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.417-425
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• 2011

In this paper, we introduce the notion of a vague filter in BE-algebras, and investigate some properties of them. Also we give conditions for a vague set to be a vague filter, and we characterize vague filters in BE-algebras.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1221-1232
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• 2008

The notions of vague d-subalgebras, vague BCK-ideals, vague d-ideals, vague $d^#$-ideals and vague $d^*$-ideals are introduced, and their properties are investigated. Relations between vague d-subalgebras, vague BCK-ideals, vague d-ideals, vague $d^#$-ideals and vague $d^*$-ideals are established.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.3
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• pp.356-361
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• 2010

M. Demirci[Vague groups, J. math. Anal. Appl. vol.230, pp. 142-156, 1999] studied the vague group operation on a crisp set as a fuzzy function and estabished the vague group structure on a crisp set. In this paper we consider bi-groups which are studied by A.A.A. Agboola and L.S. Akinola. And we also will define vague bi-groups and fuzzy bi-functions and we investigate some basic operations on the vague bi-group and fuzzy bi-functions.

• Journal of KIISE:Software and Applications
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• v.32 no.9
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• pp.927-935
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• 2005

The certainty factors of the fuzzy production rules and the certainty factors of fuzzy propositions appearing in the rules are represented by real values between zero and one. If it can allow the certainty factors of the fuzzy production rules and the certainty factors of fuzzy propositions can be represented by intervals, such as vague numbers between zero and one based on vague sets, then it can allow the reasoning of rule-based systems to perform fuzzy reasoning in more flexible manner[18]. we are also proposed an efficient algorithm to perform vague set reasoning automatically. This vague set reasoning algorithm allows the rule-based systems to perform reasoning in a more flexible and more efficient.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.43
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• pp.321-331
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• 1997

Measurement of attributes is often highly subjective and imprecise, yet most MADM methods lack provisions for handling imprecise data. Frequently, decision makers must establish a ranking within a finite set of alternatives with respect to multiple attributes which have varying degrees of importance. The problem is more complex if the evaluations of alternatives according to each attribute are not expressed in precise numbers, but rather in fuzzy numbers. Analysis must allow for lack of precision and partial truth. The advantages of a fuzzy approach for MADM are that a decision maker can obtain efficient solutions all at once without trial and error, and that this approach provides better support for judging the interactive improvement of solutions in comparison with o decision making method. The algorithm used in this study is based on the concepts of vague set theory. Linguistic variables and vague values are used to facilitate a decision maker's subjective assessment about attribute weightings and the appropriateness of alternative versus selection attributes in order to obtain final scores which are called vague appropriateness indices. A numerical example is presented to show the practical applicability of this approach.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.427-436
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• 2008

The notion of vague deductive systems in subtraction algebras is introduced, and several properties are investigated. Conditions for a vague set to be a vague deductive system are provided. Characterizations of a vague deductive system are established.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.453-465
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• 2013

The notion of vague $p$-ideals and vague $a$-ideals of BCI-algebras is introduced, and several properties of them are investigated. We show that a vague set of a BCI-algebra is a vague $a$-ideal if and only if it is both a vague $q$-ideal and a vague $p$-ideal.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.127-136
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• 2012

In this paper, we introduce the notion of an implicative vague filter in BE-algebras, and investigate some properties of them. Also we give conditions for a vague set to be an implicative vague filter, and we characterize implicative vague filters in BE-algebras. We define the notion of $n$-fold implicative vague filters in BE-algebras and we give characterizations of $n$-fold implicative vague filters and $n$-fold implicative BE-algebras.

• 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.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.297-308
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• 2008

The notions of vague BCK/BCI-algebras and vague ideals are introduced, and their properties are investigated. Conditions for a vague set to be a vague ideal are provided. Characterizations of a vague ideal are established.