l-fuzzifying topological groups

نویسندگان

shai-yan zhang

cong-hua yan

چکیده

the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhood structure of the unit is given. it isshown that the category of $l$-fuzzifying topological groups$l$-{bf fytpg} is topological over the category of groups {bf grp}with respect to the forgetful functor. as an application, theconclusion that the product of $l$-fuzzifying topological groups isalso an $l$-fuzzifying topological group is proved. finally, it isproved the forgetful functor preserves the product.

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عنوان ژورنال:
iranian journal of fuzzy systems

ناشر: university of sistan and baluchestan

ISSN 1735-0654

دوره 9

شماره 4 2012

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