Journal
INFORMATION SCIENCES
Volume 219, Issue -, Pages 124-150Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2012.07.013
Keywords
Rough set; Interval type-2 fuzzy set; Interval type-2 fuzzy relation; Interval type-2 fuzzy rough set; Interval type-2 fuzzy topology
Categories
Funding
- National Natural Science Foundation of China [60773062, 61073121]
- Natural Science Foundation of Hebei Province of China [2008000633, 2010000318, 2012201014, 2012201033]
- Science Foundation of Hebei University [2008-125]
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This paper presents a systematic study of interval type-2 fuzzy rough sets integrating rough set theory with interval type-2 fuzzy set theory using constructive and axiomatic approaches. From the perspective of a constructive approach, a pair of lower and upper interval type-2 fuzzy rough approximation operators with respect to an interval type-2 fuzzy relation is defined. The basic properties of the interval type-2 fuzzy rough approximation operators are studied. Using cut sets of interval type-2 fuzzy sets, classical representations of interval type-2 fuzzy rough approximation operators are then presented, and the connections between special interval type-2 fuzzy relations and interval type-2 fuzzy rough approximation operators are investigated. Adopting an axiomatic approach, an operator-oriented characterization of interval type-2 fuzzy rough sets is proposed; in other words, interval type-2 fuzzy rough approximation operators are characterized by axioms. Different axiom sets of interval type-2 fuzzy set-theoretic operators guarantee the existence of different types of interval type-2 fuzzy relations that produce the same operators. Finally, the relationship between interval type-2 fuzzy rough sets and interval type-2 fuzzy topological spaces is examined. We obtain sufficient and necessary conditions for the conjecture that an interval type-2 fuzzy interior (closure) operator derived from an interval type-2 fuzzy topological space can associate with an interval type-2 fuzzy reflexive and transitive relation such that the corresponding lower (upper) interval type-2 fuzzy rough approximation operator is the interval type-2 fuzzy interior (closure) operator. (C) 2012 Elsevier Inc. All rights reserved.
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