• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.599-608
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• 1999

$H_v$-rings first were introduced by Vougiouklis in 1990. Then Darafsheh and the present author defined the $H_v$-ring of fractions $S_{-1}R$ of a commutative hyperring. The largest class of multivalued systems satisfying the module-like axioms is the Hv-module. In this paper we define $H_v$-module of fractions of a hypermodule. Some interesting results concerning this $H_v$-module is proved.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.527-543
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• 2014

The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov's axiomatization of the theory of random variable structures used an early result on the completeness theorem for Lukasiewicz's [0, 1]-valued propositional logic. In this paper, we give an elementary approach to axiomatizing the theory of random variable structures. Only well-known results from probability theory are required here.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.221-236
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• 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces and then these are used to generalize the notions of interior and closure. Further, we study the properties of semiopen soft sets, semiclosed soft sets, semi interior and semi closure of soft set in soft topological spaces. Various forms of soft functions, like semicontinuous, irresolute, semiopen and semiclosed soft functions are introduced and characterized including those of soft semicompactness, soft semiconnectedness. Besides, soft semiseparation axioms are also introduced and studied.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.141-152
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• 2003

In this paper, we define generalized quasi-preclosed sets and gqp-closed functions and obtain some new characterizations of quasi P-normal spaces and quasi P-regular spaces due to Tapi et al. [9,11]. It is shown that the pairwise continuous pre gqp-closed (resp. pairwise preopen pre gqp-closed) surjective image of quasi P-normal (resp. quasi P-regular) space is quasi P-normal (resp. quasi P-regular).

• Journal for History of Mathematics
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• v.13 no.1
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• pp.125-136
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• 2000

The notion of MV-algebra was introduced by C.C. Chang in 1958 to provide an algebraic proof of the completeness of Lukasiewicz axioms for infinite valued logic. These algebras appear in the literature under different names: Bricks, Wajsberg algebra, CN-algebra, bounded commutative BCK-algebras, etc. The purpose of this paper is to give a topological lattice completion of semisimple MV-algebras. To this end, we characterize the complete atomic center MV-algebras and semisimple algebras as subalgebras of a cube. Then we define the $\delta$-completion of semisimple MV-algebra and construct the $\delta$-completion. We also study some important properties and extension properties of $\delta$-completion.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.164-168
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• 2005

As a generalization of the notions of fuzzy $\alpha-irresolute$, fuzzy preirresolute, fuzzy irresolute and fuzzy $\beta-irresolute$ functions, we introduce the notion of fuzzy $\beta\alpha-continuous$ functions and investigate the relationships between fuzzy $\beta\alpha-continuous$ functions and fuzzy separation axioms.

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.15-21
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• 2007

We introduce the notion of pre-convergence of p-stacks and characterize the pre-interior, pre-closure, separation axioms and pre-continuity on a topological space by using pre-convergence of p-stacks. We also introduce the notion of p-precompactness and investigate its properties in terms of pre-convergence of p-stacks.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.70-76
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• 1998

The aim of this paper is to study and find characterizations of quasi-fuzzy continuous and quasi-fuzzy closed mappings between fuzzy bitopological spaces. The notion of quasi-fuzzy open sets is used to defined quasi-fuzzy Ti (i=0, 1, 2) and quasi-fuzzy regular spaces and these spaces are investigated under quasi-fuzzy continuity. Finally, quasi-fuzzy connectednss is introduced and studied to some extent.

• Journal for History of Mathematics
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• v.31 no.6
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• pp.315-337
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• 2018

Pythagorean thoerem exists in several equivalent forms in the Euclidean plane, that is, the Hilbert plane which in addition satisfies the parallel axiom. In this article, we investigate the truthness and mutual relationships of those propositions in various non-Hilbert planes which satisfy the parallel axiom and all the Hilbert axioms except the SAS axiom.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.649-658
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• 2022

In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of BCK-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.