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 givenI-topology is given. The notion ofσ-generalized ideal is introduced and hence everyσ-generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder.
Highlights
The concepts of preideals and generalized ideals were introduced by Ramadan et al 1, as a consistent approach to the ideas of fuzzy mathematics
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
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
Summary
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. 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 every σ-generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder.
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