Next Article in Journal
Categorically Closed Topological Groups
Next Article in Special Issue
Orness For Idempotent Aggregation Functions
Previous Article in Journal
The SIC Question: History and State of Play
Previous Article in Special Issue
Assigning Numerical Scores to Linguistic Expressions
Article Menu

Export Article

Open AccessArticle

New Order on Type 2 Fuzzy Numbers

Departamento Matemática y Física, Universidad Nacional Experimental del Táchira (UNET), San Cristóbal, 5001 Táchira, Venezuela
Departamento Matemática Aplicada a las TIC, Universidad Politécnica de Madrid, 28660 Boadilla del Monte, Madrid, Spain
Author to whom correspondence should be addressed.
Axioms 2017, 6(3), 22;
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)
PDF [1403 KB, uploaded 28 July 2017]


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

Figure 1

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).
Printed Edition Available!
A printed edition of this Special Issue is available here.

Share & Cite This Article

MDPI and ACS Style

Hernández, P.; Cubillo, S.; Torres-Blanc, C.; Guerrero, J.A. New Order on Type 2 Fuzzy Numbers. Axioms 2017, 6, 22.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top