Continuous triangular norm based fuzzy topology
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For each continuous t-norm &, a class of fuzzy topological spaces, called &-topological spaces, is introduced. The motivation stems from the idea that to each many-valued logic there may correspond a theory of many-valued topology, in particular, each continuous t-norm may lead to a theory of fuzzy topology. It is shown that for each continuous t-norm &, the subcategory consisting of &-topological spaces is simultaneously reflective and coreflective in the category of fuzzy topological spaces, hence gives rise to an autonomous theory of fuzzy topology. Topologizing a fuzzy pre-ordered set with the fuzzy Scott topology yields a functor from the category of fuzzy pre-ordered sets and maps that preserve suprema of flat ideals to the category of &-topological spaces. It is proved that this functor is a full one if and only if the t-norm & is Archimedean.
KeywordsContinuous triangular norm Fuzzy topology Fuzzy pre-order Fuzzy Scott topology
Mathematics Subject Classification54A40 18B30 06F30 03B52
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We thank sincerely Dr. Hongliang Lai for stimulating discussion during the preparation of this paper.
- 7.Flagg, R.C., Sünderhauf, P., Wagner, K.R.: A logical approach to quantitative domain theory. Topology Atlas Preprint No. 23 (1996). http://at.yorku.ca/e/a/p/p/23.htm
- 22.Lai, H., Zhang, D., Zhang, G.: Flat ideals in the unit interval with the canonical fuzzy order. J. Sichuan Univ. (Nat. Sci. Ed.) 55, 905–911 (2018)Google Scholar