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Arithmetics of extensional fuzzy numbers - part II: Algebraic framework

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2 Author(s)
Michal Holčapek ; Centre of Excellence IT4Innovations, Division of the University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 70103, Czech Republic ; Martin Štěpnička

In the first part of this contribution, we proposed extensional fuzzy numbers and a working arithmetic for them that may be abstracted to so-called many identities algebras (MI-algebras, for short). In this second part, we show that the proposed MI-algebras give a framework not only for the arithmetic of extensional fuzzy numbers, but also for other arithmetics of fuzzy numbers and even more general sets of real vectors used in mathematical morphology. This entitles us to develop a theory of MI-algebras to study general properties of structures for which the standard algebras are not appropriate. Some of the basic concepts and properties are presented here.

Published in:

Fuzzy Systems (FUZZ-IEEE), 2012 IEEE International Conference on

Date of Conference:

10-15 June 2012