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Fuzzy implicative semigroups. (English) Zbl 0879.06009
The notion of implicative semigroup [cf. W. C. Nemitz, Trans. Am. Math. Soc. 117, 126-142 (1965; Zbl 0128.24804); M. W. Chan and K. P. Shum, Semigroup Forum 46, 7-15 (1993; Zbl 0776.06012)] is extended to the fuzzy setting. The obtained results are similar to those considered for fuzzy semigroups [cf., e.g., N. Kuroki, Inf. Sci. 53, 203-236 (1991; Zbl 0714.20052)]; X.-P. Wang and W.-J. Liu, Inf. Sci. 68, 225-231 (1993; Zbl 0794.20065)].
MSC:
06F05 Ordered semigroups and monoids
20N25 Fuzzy groups
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
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