Title: Rough approximations of multi-fuzzy sets

Authors: Gayathri Varma; Sunil Jacob John

Addresses: Department of Mathematics, National Institute of Technology, Calicut – 673 601, India ' Department of Mathematics, National Institute of Technology, Calicut – 673 601, India

Abstract: Rough sets have been invented to cope with uncertainty and to deal with intelligent systems characterised by insufficient and incomplete information. This paper proposes a general framework for the study of relation-based multi-fuzzy rough approximation operators. We define rough multi-fuzzy sets and study their properties. An arbitrary multi-fuzzy relation is used to approximate multi-fuzzy sets. A pair of lower and upper rough approximation operators is hence obtained and basic properties of these approximation operators will be examined. By introducing the cut sets of multi-fuzzy sets, we study the connections between multi-fuzzy rough approximation operators and crisp approximation operators. Finally, the multi-fuzzy approximation operators will be defined by axioms.

Keywords: multi-fuzzy sets; multi-fuzzy relations; rough sets; rough multisets; approximation operators; cut sets; axioms; fuzzy sets.

DOI: 10.1504/IJGCRSIS.2014.068037

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2014 Vol.3 No.4, pp.327 - 344

Received: 21 Oct 2014
Accepted: 18 Dec 2014

Published online: 10 Mar 2015 *

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