• 호남수학학술지
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• 제38권3호
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• pp.643-659
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• 2016

In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.481-489
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• 2005

We first show that any complete MV-algebra whose Boolean subalgebra of idempotent elements is atomic, called a complete MV-algebra with atomic center, is isomorphic to a product of unit interval MV-algebra 1's and finite linearly ordered MV-algebras of A(m)-type $(m{\in}{\mathbb{Z}}^+)$. Secondly, for a semi-simple MV-algebra A, we introduce a completion ${\delta}(A)$ of A which is a complete, MV-algebra with atomic center. Under their intrinsic topologies $(see\;{\S}3)$ A is densely embedded into ${\delta}(A)$. Moreover, ${\delta}(A)$ has the extension universal property so that complete MV-algebras with atomic centers are epireflective in semi-simple MV-algebras

• 한국수학사학회지
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• 제13권1호
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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.

• 호남수학학술지
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• 제32권1호
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• pp.131-139
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• 2010

Several types of skeletons in a hyper MV-algebra are introduced, and their relations are investigated.

• 대한수학회지
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• 제42권6호
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• pp.1111-1120
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• 2005

Hong and Nel in [8] obtained a number of spectral dualities between a cartesian closed topological category X and a category of algebras of suitable type in X in accordance with the original formalism of Porst and Wischnewsky[12]. In this paper, there arises a dual adjointness S $\vdash$ C between the category X = Lim of limit spaces and that A of MV-algebras in X. We firstly show that the spectral duality: $S(A)^{op}{\simeq}C(X^{op})$ holds for the dualizing object K = I = [0,1] or K = 2 = {0, 1}. Secondly, we study a duality between the category of Tychonoff spaces and the category of semi-simple MV-algebras. Furthermore, it is shown that for any $X\;\in\;Lim\;(X\;{\neq}\;{\emptyset})\;C(X,\;I)$ is densely embedded into a cube $I^/H/$, where H is a set.

• Korean Journal of Mathematics
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• 제10권1호
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• pp.37-44
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• 2002

In this paper, we obtain an algebraic structure which is equivalent to an MV-algebra. Moreover, we show that $t$-norm and $t$-conorm can be obtained from MV-algebras.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.475-489
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• 2006

After the introduction of fuzzy sets by Zadeh [8], there have been a number of generalizations of fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. An intuitionistic fuzzy set is also called a bifuzzy set according to [5]. In this paper, we apply the concept of a bifuzzy set to (implicative) ideals in pseudo MV-algebras. The notion of a bifuzzy (implicative) ideal of a pseudo MV-algebra is introduced, and some related properties are investigated. Conditions for a bifuzzy set to be a bifuzzy ideal are given, and characterizations of a bifuzzy (implicative) ideal are provided. Using a family of ideals, bifuzzy ideals are established.

• 한국지능시스템학회논문지
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• 제11권7호
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• pp.649-652
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• 2001

In this paper, we introduce neighborhood systems in an L-fuzzy topology using complete MV-algebras. We investigate the relationship between L-fuzzy topologies and the neighborhood systems. We study the properties of neighborhood system.

• 대한수학회논문집
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• 제25권4호
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• pp.537-545
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• 2010

The notions of (weak) hyper MV-deductive systems and (weak) implicative hyper MV-deductive systems are introduced, and several properties are investigated. Relations among hyper MV-deductive systems, weak hyper MV-deductive systems, implicative hyper MV-deductive systems and weak implicative hyper MV-deductive systems are discussed. A characterization of a hyper MV-deductive system is provided. A condition for a weak hyper MV-deductive system to be a weak implicative hyper MV-deductive system is given.

• 한국수학사학회지
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• 제20권1호
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• pp.73-82
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• 2007

본 논문은 Wajsberg hoops, BCK-대수와 MV-대수의 도입과 그 발전과정을 간단히 소개하고, Wajsberg hoops, MV-대수, 그리고 가환 BCK-대수의 관계를 살펴본다. 특히 모든 Wajsberg 대수는 가환 BCK-대수가 됨을 규명한다.