Fuzzy congruence relations on almost distributive lattices
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In this paper we give several characterizations for fuzzy ideals, fuzzy homomorphisms, and fuzzy congruences of an almost distributive lattice. In addition, the quotient of an almost distributive lattice induced by a fuzzy congruence is also presented in the paper. Furthermore, we obtain a kind of fuzzy congruences for which their quotient is a distributive lattice and for which it is not. Mainly, we construct a monomorphism of the lattice of fuzzy ideals into the lattice of fuzzy congruences of almost Boolean rings, and we give a necessary and sufficient condition for this monomorphism to become a lattice isomorphism.
Abstract
In this paper we give several characterizations for fuzzy ideals, fuzzy homomorphisms, and fuzzy congruences of an almost distributive lattice. In addition, the quotient of an almost distributive lattice induced by a fuzzy congruence is also presented in the paper. Furthermore, we obtain a kind of fuzzy congruences for which their quotient is a distributive lattice and for which it is not. Mainly, we construct a monomorphism of the lattice of fuzzy ideals into the lattice of fuzzy congruences of almost Boolean rings, and we give a necessary and sufficient condition for this monomorphism to become a lattice isomorphism.
참고문헌 (11)
- A. B. Chakraborty, "Fuzzy homomorphism and algebraic structures", Fuzzy Sets and Systems, 59, pp.211~221 (1993)
- W. J. Liu, "Fuzzy invariant subgroups and fuzzy ideals", Fuzzy Sets and Systems, 8, pp.133~139 (1982)
- D. S. Malik, "Fuzzy homomorphism of rings", Fuzzy Sets and Systems, 46, pp.139~146 (1992)
- Y. S. Pawar, "Congruence Relations on Almost Distributive Lattices", Southeast Asian Bull. Math, 36, pp.519~527 (2012)
- A. Rosenfeld, "Fuzzy Groups", J. Math. Anal. Appl, 35, pp.512~517 (1971)
- U. M. Swamy, "Fuzzy ideals of almost distributive lattices", Ann. Fuzzy Math. Inform.
- U. M. Swamy, "Fuzzy Ideals and congruences of lattices", Fuzzy Sets and Systems, 95, pp.249~253 (1998)
- U. M. Swamy, "Birkho center of an almost distributive lattice", Int. Jour. Algebra, 11, pp.539~346 (2009)
- U. M. Swamy, "Almost distributive lattice", J. Aust. Math. Soc., 5(31), pp.77~91 (1981)
- Y. Bo, "Fuzzy ideals on a distributive lattice", Fuzzy Sets and Systems, 35, pp.231~240 (1990)
- L. A. Zadeh, "Fuzzy Sets", Information and Control, 8, pp.338~353 (1965)