On polygonal fuzzy sets and numbers

Authors:
A. D. BáEz-SáNchez;A. C. Moretti;M. A. Rojas-Medar
Affiliations:
DMA, IMECC-UNICAMP, C.P. 6065, 13083-970 Campinas-SP, Brazil;School of Applied Science-UNICAMP, Rua Pedro Zaccaria, 1300, CEP 13484-350 Limeira-SP, Brazil;GMA, Dpto. Ciencias Básicas, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

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.