• Journal of Convergence for Information Technology
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• v.7 no.3
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• pp.65-71
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• 2017

The quantum logic was introduced by G. Birkhoff and 1. von Neumann in order to study projections of a Hilbert space for a formulation of quantum mechanics, and Husimi proposed orthomodular law and orthomodular lattices to complement the quantum logic. Abott introduced orthoimplication algebras and its properties to investigate an implication of orthomodular lattice. The commuting relation is an important property on orthomodular lattice which is related with the distributive law and the modular law, etc. In this paper, we define a binary operation on orthoimplication algebra and the greatest lower bound by using this operation and research some properties of this operation. Also we define a homomorphism and characterize the commuting relation of orthoimplication algebra by the homomorphism.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.13-24
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• 1998

We define an LI-ideal of a lattice implication algebra and show that every LI-ideal is a lattice ideal. We give an exampl that a lattice ideal may not be an LI-ideal, and show that every lattice ideal is an LI-ideal in a lattice H implication algebra. we discuss the relationship between filters and LI-ideals, and study how to generate an LI-ideal by a set. We construct the quotient structure by using an LI-ideal, and study the properties of LI-ideals related to implication homomorphisms.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.341-355
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• 2003

The fuzzification of ${\bigotimes}-closed$ set is considered, and its basic properties we investigated. Characterizations of fuazzy ${\bigotimes}-closed$ set we given. Using a collection of ${\bigotimes}-closed$ sets with additional conditions, a fuzzy ${\bigotimes}-closed$ set is stated. The theory of fuzzy topological ${\bigotimes}-closed$ sets is discussed.