Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders

G. Elsalamony

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-16

Abstract:

The present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is obtained. As a particular consequence of the results in this paper, a construction of fuzzifying topology generated by generalized ideals of fuzzy subsets via a given -topology is given. The notion of -generalized ideal is introduced and hence every -generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:567482

DOI: 10.1155/2009/567482

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