Fuzzy Prime Ideals of ADL's
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Abstract
In this paper the concept of prime L-fuzzy ideals and L-fuzzy prime ideals of an ADL A with truth values in a complete lattice L satisfying the infinite meet distributive law are introduced. All prime L-fuzzy ideals of a given ADL A are determined by establishing a one-to- one correspondence between prime L-fuzzy ideals of an ADL A and the pairs (P;a), where P is a prime ideal of A and a is a prime element in L. Also, here minimal prime L-fuzzy ideals and L-fuzzy minimal prime ideals of an ADL A are introduced and characterized.
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References
L. Zadeh, “Information and control,” Fuzzy sets, vol. 8, no. 3, pp. 338–353, 1965.
J. Goguen, “L-fuzzy sets,” Journal of mathematical analysis and applications, vol. 18, no. 1, pp. 145–174, 1967.
W.-j. Liu, “Fuzzy invariant subgroups and fuzzy ideals,” Fuzzy sets and systems, vol. 8, no. 2, pp. 133–139, 1982.
T. Mukherjee and M. Sen, “On fuzzy ideals of a ring i,” Fuzzy Sets and systems, vol. 21, no. 1, pp. 99–104, 1987.
U. Swamy and K. Swamy, “Fuzzy prime ideals of rings,” Journal of Mathematical Analysis and Applications, vol. 134, no. 1, pp. 94–103, 1988.
U. Swamy and G. Rao, “Almost distributive lattices,” Journal of the Australian Mathematical Society, vol. 31, no. 1, pp. 77–91, 1981.
U. Swamy, C. S. S. Raj, and N. Teshale, “Fuzzy ideals of almost distributive lattices,” Annals of Fuzzy Mathematics and Informatics, vol. 14, no. 4, pp. 371–379, 2017.