期刊
FUZZY SETS AND SYSTEMS
卷 252, 期 -, 页码 111-124出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2013.12.004
关键词
Type-2 fuzzy sets; Normal and convex functions; Negation; Strong negation; De Morgan's laws
资金
- CICYT (Spain) [TIN2011-29827-C02-01]
- UPM-CAM
- FONACIT (Venezuela)
- UNET (Venezuela)
So far, the negation that usually has been considered within the type-2 fuzzy sets (T2FS5) framework, and hence T2FS truth values M (set of all functions from [0, 1] to [0, 1]), was obtained by means of Zadeh's extension principle and calculated from standard negation in [0, 1]. But there has been no comparative analysis of the properties that hold for the above operation and the axioms that any negation in M should satisfy. This suggests that negations should be studied more thoroughly in this context. Following on from this, we introduce in this paper the axioms that an operation in M must satisfy to qualify as a negation and then prove that the usual negation on T2FSs, in particular, is antimonotonic in L (set of normal and convex functions of M) but not in M. We propose a family of operations calculated from any suprajective negation in [0, 1] and prove that they are negations in L. Finally, we examine De Morgan's laws for some operations with respect to these negations. (C) 2013 Elsevier B.V. All rights reserved.
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