Proceedings of the Korean Institute of Intelligent Systems Conference (한국지능시스템학회:학술대회논문집)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Intuitionistic Fuzzy Ideals on A Distributive Lattice

분배속 상의 직관적 퍼지 아이디얼

  • Kul Hur (Division of Mathematics and Informational Statistics, and Institute of Basic Natural Science Wonkwang University) ;
  • Kang, Hee-Won (Division of Mathematics and Informational Statistics, and Institute of Basic Natural Science Wonkwang University) ;
  • Song, Hyeong-Kee (Division of Mathematics and Informational Statistics, and Institute of Basic Natural Science Wonkwang University)
  • Published : 2004.04.01
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Abstract

We introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a lattice, and discuss the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruence on a distributive lattice. Also we prove that for a generalized Boolean algebra, the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences. Finally, we consider the products of intuitionistic fuzzy ideals and obtain a necessary and sufficient condition for an intuitionistic fuzzy ideals on the direct sum of lattices to be representable on a direct sum of intuitionistic fuzzy ideals on each lattice.

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