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Axioms 2017, 6(3), 22; doi:10.3390/axioms6030022

New Order on Type 2 Fuzzy Numbers

1
Departamento Matemática y Física, Universidad Nacional Experimental del Táchira (UNET), San Cristóbal, 5001 Táchira, Venezuela
2
Departamento Matemática Aplicada a las TIC, Universidad Politécnica de Madrid, 28660 Boadilla del Monte, Madrid, Spain
*
Author to whom correspondence should be addressed.
Received: 5 June 2017 / Revised: 14 July 2017 / Accepted: 24 July 2017 / Published: 28 July 2017
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
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Abstract

Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get more adequate and flexible models of inference processes, where uncertainty, imprecision or vagueness is present. Type 2 fuzzy sets comprise one of such extensions. In this paper, we introduce and study an extension of the fuzzy numbers (type 1), the type 2 generalized fuzzy numbers and type 2 fuzzy numbers. Moreover, we also define a partial order on these sets, which extends into these sets the usual order on real numbers, which undoubtedly becomes a new option to be taken into account in the existing total preorders for ranking interval type 2 fuzzy numbers, which are a subset of type 2 generalized fuzzy numbers. View Full-Text
Keywords: type 2 fuzzy sets; fuzzy numbers; partial order type 2 fuzzy sets; fuzzy numbers; partial order
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Hernández, P.; Cubillo, S.; Torres-Blanc, C.; Guerrero, J.A. New Order on Type 2 Fuzzy Numbers. Axioms 2017, 6, 22.

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