Fuzzy ideals of almost distributive lattices
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The notion of an Almost Distributive Lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalization of Boolean algebra and Boolean rings. In this paper, we introduce the notion of $L$-fuzzy ideal of an ADL with truth values in a complete lattice $L$ satisfying the infinite meet distributive law and prove certain properties of these. Mainly, it is proved that the class of $L$-fuzzy ideals of an ADL forms a complete distributive lattice.
Abstract
The notion of an Almost Distributive Lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalization of Boolean algebra and Boolean rings. In this paper, we introduce the notion of $L$-fuzzy ideal of an ADL with truth values in a complete lattice $L$ satisfying the infinite meet distributive law and prove certain properties of these. Mainly, it is proved that the class of $L$-fuzzy ideals of an ADL forms a complete distributive lattice.
참고문헌 (12)
- G. Birkhoff, "Lattice Theory, Colloquium Publications", Amer. Math. Soc., 25 (1967)
- J. A. Goguen, "L-fuzzy sets", J. Math. Anal. Appl, 18, pp.145~174 (1967)
- W. J. Liu, "Fuzzy invariant subgroups and fuzzy ideals", fuzzy sets and systems, 8, pp.133~139 (1982)
- T. Ramarao, "Fuzzy Ideals and Filters of lattices", Asian Journal of current Engineering and Maths, 2, pp.297~300 (2013)
- A. Rosenfeld, "Fuzzy groups", J. Maths. Anal. Appl, 35, pp.512~517 (1971)
- U. M. Swamy, "Almost Distributive Lattices", J. Australian Math. Soc., 31, pp.77~91 (1981)
- U. M. Swamy, "Algebraic Fuzzy systems", Fuzzy sets and systems, 41, pp.187~194 (1991)
- U. M. Swamy, "Irriducibility in Algebraic Fuzzy systems", Fuzzy sets and systems, 41, pp.233~241 (1991)
- U. M. Swamy, "Fuzzy ideals and congruences of lattices", Fuzzy sets and systems, 95, pp.249~253 (1998)
- U. M. Swamy, "Fuzzy Prime Ideals of Rings", J. Math. Anal. Appl, 134, pp.94~103 (1988)
- B. Venkateswarlu, "Associate elements in ADLs", Asian-European Journal of mathematics, 7(4), pp.1450066~ (2014)
- L. A. Zadeh, "Fuzzy set", Information and control, 8, pp.338~353 (1965)