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Axioms 2018, 7(1), 16; doi:10.3390/axioms7010016

Revision of the Kosiński’s Theory of Ordered Fuzzy Numbers

Department of Investment and Real Estate, Poznan University of Economics and Business, al. Niepodleglosci 10, 61-875 Poznań, Poland
Received: 5 January 2018 / Revised: 20 February 2018 / Accepted: 26 February 2018 / Published: 2 March 2018
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
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Ordered fuzzy numbers are defined by Kosiński. In this way, he was going to supplement a fuzzy number by orientation. A significant drawback of Kosiński’s theory is that there exist such ordered fuzzy numbers which, in fact, are not fuzzy numbers. For this reason, a fully formalized correct definition of ordered fuzzy numbers is proposed here. Also, the arithmetic proposed by Kosiński has a significant disadvantage. The space of ordered fuzzy numbers is not closed under Kosiński’s addition. On the other hand, many mathematical applications require the considered space be closed under used arithmetic operations. Therefore, the Kosinski’s theory is modified in this way that the space of ordered fuzzy numbers is closed under revised arithmetic operations. In addition, it is shown that the multiple revised sum of finite sequence of ordered fuzzy numbers depends on its summands ordering. View Full-Text
Keywords: ordered fuzzy number; arithmetic operator; linear space ordered fuzzy number; arithmetic operator; linear space

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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. (CC BY 4.0).

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Piasecki, K. Revision of the Kosiński’s Theory of Ordered Fuzzy Numbers. Axioms 2018, 7, 16.

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