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Axioms 2012, 1(1), 21-32; doi:10.3390/axioms1010021
Article

Axiomatic of Fuzzy Complex Numbers

University National UNED, Department of Fundamental Mathematics, Faculty of Sciences, Paseo Senda del Rey, 9, Madrid 28040, Spain
Received: 5 January 2012 / Revised: 5 April 2012 / Accepted: 5 April 2012 / Published: 20 April 2012
(This article belongs to the Special Issue Axioms: Feature Papers)
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Abstract

Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead to very complicated calculi. Moreover, fuzzy numbers with a simpler shape of membership functions often have more intuitive and more natural interpretations. But not only must we apply the concept and the use of fuzzy sets, and its particular case of fuzzy number, but also the new and interesting mathematical construct designed by Fuzzy Complex Numbers, which is much more than a correlate of Complex Numbers in Mathematical Analysis. The selected perspective attempts here that of advancing through axiomatic descriptions.
Keywords: mathematical analysis; number theory; non-classical logics; fuzzy logic; fuzzy sets; fuzzy measure theory; fuzzy systems; A.I. mathematical analysis; number theory; non-classical logics; fuzzy logic; fuzzy sets; fuzzy measure theory; fuzzy systems; A.I.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Garrido, A. Axiomatic of Fuzzy Complex Numbers. Axioms 2012, 1, 21-32.

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