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2015•Journal of Intelligent & Fuzzy SystemsRequires access

The comparative study of gradual and fuzzy normed linear spaces

Ildar Sadeqi, Farnaz Yaqub Azari

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Abstract

In this paper, a comparative study of two types of norms on a linear space, namely gradual norm and fuzzy norm has been made and it is shown that they are equivalent in general. Because a gradual normed linear space is a locally convex space so a fuzzy normed linear space is also a locally convex space in classical sense. Therefore, most of results in classical locally convex spaces do hold in fuzzy normed linear spaces.

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What this paper is about

In this paper, a comparative study of two types of norms on a linear space, namely gradual norm and fuzzy norm has been made and it is shown that they are equivalent in general. Because a gradual normed linear space is a locally convex space so a fuzzy normed linear space is also a locally convex space in classical sense. Therefore, most of results in classical locally convex spaces do hold in fuzzy normed linear spaces.

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Available abstract

In this paper, a comparative study of two types of norms on a linear space, namely gradual norm and fuzzy norm has been made and it is shown that they are equivalent in general. Because a gradual normed linear space is a locally convex space so a fuzzy normed linear space is also a locally convex space in classical sense. Therefore, most of results in classical locally convex spaces do hold in fuzzy normed linear spaces.

Key concepts: Normed vector space, Strictly convex space, Mathematics, Reflexive space, Norm (philosophy), Locally convex topological vector space, Normed algebra, Continuous linear operator

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