期刊
FUZZY SETS AND SYSTEMS
卷 209, 期 -, 页码 54-65出版社
ELSEVIER
DOI: 10.1016/j.fss.2012.04.003
关键词
Fuzzy numbers; Polygonal fuzzy numbers; Generalized Hausdorff metric; Approximation of fuzzy numbers
资金
- CNPq-Brazil
- CNPq [306538/2010-5]
- Fondecyt-Chile [1080628]
In this paper, we propose a new mathematical formalization of the concept of polygonal fuzzy numbers and an extension of this notion to fuzzy sets on R-n. We study the mathematical structure of these families of fuzzy sets and show that each family is a complete and separable metric space when endowed with the generalized Hausdorff metric. Moreover, we show that for n = 1, the families of polygonal fuzzy numbers are isomorphic to some convex and closed convex cone of a finite dimensional space. We obtain generalizations and extensions of some previous results on polygonal fuzzy numbers and simplified proofs of some well-known results about approximation of fuzzy n-dimensional quantities. Finally, some developments about the approximation of families of fuzzy sets are introduced. (C) 2012 Elsevier B.V. All rights reserved.
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