Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders | Zendy

G. Elsalamony | Zendy

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Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders

Author(s) -

G. Elsalamony

Publication year - 2009

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2009/567482

Subject(s) - mathematics , ideal (ethics) , network topology , preorder , fuzzy logic , fuzzy mathematics , topology (electrical circuits) , discrete mathematics , algorithm , fuzzy set , algebra over a field , computer science , pure mathematics , fuzzy number , combinatorics , artificial intelligence , epistemology , philosophy , operating system

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 I-topology is given. The notion of σ-generalized ideal is introduced and hence every σ-generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder

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