• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.316-322
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• 2008

We introduce the concept of interval-valued intuitionistic fuzzy soft sets, which is an extension of the interval-valued fuzzy soft set. We also introduce the concepts of operations for the interval-valued intuitionistic fuzzy soft sets and study basic some properties.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.371-386
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• 2016

Using the hesitant intersection (${\Cap}$), the notions of ${\Cap}$-hesitant fuzzy subalgebras, ${\Cap}$-hesitant fuzzy ideals and ${\Cap}$-hesitant fuzzy p-ideals are introduced,and their relations and related properties are investigated. Conditions for a ${\Cap}$-hesitant fuzzy ideal to be a ${\Cap}$-hesitant fuzzy p-ideal are provided. The extension property for ${\Cap}$-hesitant fuzzy p-ideals is established.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.621-628
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• 2003

We investigate some related properties of fuzzy filters and fuzzy implicative filters in lattice implication algebras. We find a characterization of fuzzy filters and fuzzy implicative filters, and we discuss a relation between fuzzy filters and fuzzy implicative filters in lattice implication algebras. Also we give an extension theorem of fuzzy implicative filters.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.93-101
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• 2003

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-470
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• 2006

As a continuation of [4], characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCk-algebra X with respect to a fuzzy set $\={A}$ in X, we construct a fuzzy implicative ideal of X containing $\={A}$.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.279-288
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• 2007

The notion of fuzzy n-fold implicative ordered filters in implicative semigroups is introduced, and related properties are investigated. Relations between fuzzy ordered filters and fuzzy n-fold implicative ordered filters are provided. Characterizations of a fuzzy n-fold implicative ordered filter are given, and an extension property for a fuzzy n-fold implicative ordered filter is obtained.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.202-206
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• 2008

We introduce the concept of interval-valued minimal structure which is an extension of the interval-valued fuzzy topology. And we introduce and study the concepts of IVF m-continuous and several types of compactness on the interval-valued fuzzy m-spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.2
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• pp.231-236
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• 2003

Recently, Oussalah 〔Fuzzy Sets and Systems 128(2002) 247-260〕 investigated some theoretical results about some invariance properties concerning the relationships between the defuzzification outcomes and the arithmetic of fuzzy numbers. But, in this note we introduce some explicit calculations of the resulting fuzzy set or possibility distribution when the matter is the determination of the defuzzified value pertaining to the result of some manipulation of fuzzy quantities under t-norm based fuzzy arithmetic operations.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.255-263
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• 2003

Fuzzifications of n-fold quasi-associative ideals are considered. Conditions for a fuzzy ideal to be a fuzzy n-fold quasi-associative ideal are given. Using a collection of n-fold quasi-associative ideals, fuzzy n-fold quasi-associative ideals are constructed. Finally, the extension property for fuzzy n-fold quasi-associative ideals is established.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.22-24
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• 2002

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy Quantities based on the extension principle suggested by Mares (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous f-norm which holds the distributivity under f-norm based fuzzy arithmetic operations.