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Open AccessArticle

A New gH-Difference for Multi-Dimensional Convex Sets and Convex Fuzzy Sets

1
Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, Italy
2
Department of Mathematics, DIGIPEN Institute of Technology, 9931 Willows Rd NE, Redmond, WA 98052, USA
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(2), 48; https://doi.org/10.3390/axioms8020048
Received: 19 March 2019 / Revised: 15 April 2019 / Accepted: 16 April 2019 / Published: 24 April 2019
(This article belongs to the Special Issue Softcomputing: Theories and Applications)
In the setting of Minkowski set-valued operations, we study generalizations of the difference for (multidimensional) compact convex sets and for fuzzy sets on metric vector spaces, extending the Hukuhara difference. The proposed difference always exists and allows defining Pompeiu-Hausdorff distance for the space of compact convex sets in terms of a pseudo-norm, i.e., the magnitude of the difference set. A computational procedure for two dimensional sets is outlined and some examples of the new difference are given. View Full-Text
Keywords: convex set-valued gH-difference; set-valued Analysis; multidimensional fuzzy gH-difference convex set-valued gH-difference; set-valued Analysis; multidimensional fuzzy gH-difference
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Stefanini, L.; Bede, B. A New gH-Difference for Multi-Dimensional Convex Sets and Convex Fuzzy Sets. Axioms 2019, 8, 48.

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