Fuzzy bounded linear operators

Authors:
T. Bag;S. K. Samanta
Affiliations:
Department of Mathematics, Visva-Bharati, Santiniketan, 731235, West-Bengal, India;Department of Mathematics, Visva-Bharati, Santiniketan, 731235, West-Bengal, India
Venue:
Fuzzy Sets and Systems
Year:
2005

Citing 3
Cited 19

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Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms

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Best simultaneous approximation in fuzzy anti-normed linear spaces

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Abstract

In this paper, a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types (strong and weak) of fuzzy bounded linear operators are defined. Relation between fuzzy continuity and fuzzy boundedness is studied. Definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed. The Hahn-Banach theorem, the Open mapping theorem, the Closed graph theorem and the Uniform boundedness principle theorem are established.