Abstract
The aim of this paper is to introduce the notion of interval-valued fuzzy subspace with its flags and interval-valued fuzzy n-normed linear space. We define the operations intersection, sum, directsum and tensor product of intervalvalued fuzzy subspaces and obtain their corresponding flags. Further we provide some results on interval-valued fuzzy n-normed linear space. AMS Subject Classification : 46S40, 03E72.
Highlights
The theory of 2-norm and n-norm on a linear space has been introduced by Gahler in [9, 10] and subsequently studied by several authors [11, 14, 19, 20]
After the introduction of fuzzy subspace of a vector space by Katsaras and Liu s [12], many researchers [1, 2, 3, 16, 18, 21] engaged themselves in the development of fuzzy subspace of a vector space
G.Lubczonok and V.Murali introduced an interesting theory of flags and fuzzy subspaces of vector spaces [17]
Summary
The theory of 2-norm and n-norm on a linear space has been introduced by Gahler in [9, 10] and subsequently studied by several authors [11, 14, 19, 20]. A detailed theory of fuzzy norm on a linear space can be viewed in [4, 5, 6, 7, 8, 13, 15, 23]. We have introduced the notion of fuzzy n-normed linear space [22]. G.Lubczonok and V.Murali introduced an interesting theory of flags and fuzzy subspaces of vector spaces [17]. Zadeh in his pioneering work introduced the theory of interval-valued fuzzy subset in [24]. In this paper we introduce the notions of interval-valued fuzzy subspace and interval-valued fuzzy n-normed linear space. Further we establish some properties of interval-valued fuzzy n-normed linear space
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