# Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods

Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods J. Appl. Math. Comput. https://doi.org/10.1007/s12190-018-1193-9 ORIGINAL RESEARCH Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods 1 1 Moslem Javanmard · Hassan Mishmast Nehi Received: 27 February 2018 © Korean Society for Computational and Applied Mathematics 2018 Abstract Interval type-2 fuzzy numbers (IT2FNs) are a particular kind of type-2 fuzzy numbers (T2FNs). In most scientiﬁc works, since arithmetic operations required IT2FNs are simpler than those of T2FNs, mathematical calculations on IT2FNs are used more frequently rather than the T2FNs. Hence, in recent decades, the study on IT2FNs have been intensiﬁed signiﬁcantly. These numbers can be explained by trapezoidal and triangular forms. In this article, ﬁrst, the concept of general interval type-2 trapezoidal fuzzy numbers (GIT2TrFNs) and then arithmetic operations among them are introduced. Next, three new ranking methods are suggested for GIT2TrFN. Finally, several examples are used to illustrate and compare new ranking methods with others. Keywords Fuzzy number (FN) · General interval type-2 trapezoidal fuzzy number (GIT2TrFN) · General interval type-2 triangular fuzzy number (GIT2TFN) · General type-1 trapezoidal fuzzy number (GT1TrFN) · General type-1 triangular fuzzy number (GT1TFN) · Interval type-2 fuzzy number (IT2FN) · Membership function (MF) · Type-2 fuzzy number http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Mathematics and Computing Springer Journals

# Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods

, Volume OnlineFirst – May 31, 2018
34 pages

/lp/springer_journal/rankings-and-operations-for-interval-type-2-fuzzy-numbers-a-review-and-c1vGaBCq6m
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theory of Computation; Mathematics of Computing
ISSN
1598-5865
eISSN
1865-2085
D.O.I.
10.1007/s12190-018-1193-9
Publisher site
See Article on Publisher Site

### Abstract

J. Appl. Math. Comput. https://doi.org/10.1007/s12190-018-1193-9 ORIGINAL RESEARCH Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods 1 1 Moslem Javanmard · Hassan Mishmast Nehi Received: 27 February 2018 © Korean Society for Computational and Applied Mathematics 2018 Abstract Interval type-2 fuzzy numbers (IT2FNs) are a particular kind of type-2 fuzzy numbers (T2FNs). In most scientiﬁc works, since arithmetic operations required IT2FNs are simpler than those of T2FNs, mathematical calculations on IT2FNs are used more frequently rather than the T2FNs. Hence, in recent decades, the study on IT2FNs have been intensiﬁed signiﬁcantly. These numbers can be explained by trapezoidal and triangular forms. In this article, ﬁrst, the concept of general interval type-2 trapezoidal fuzzy numbers (GIT2TrFNs) and then arithmetic operations among them are introduced. Next, three new ranking methods are suggested for GIT2TrFN. Finally, several examples are used to illustrate and compare new ranking methods with others. Keywords Fuzzy number (FN) · General interval type-2 trapezoidal fuzzy number (GIT2TrFN) · General interval type-2 triangular fuzzy number (GIT2TFN) · General type-1 trapezoidal fuzzy number (GT1TrFN) · General type-1 triangular fuzzy number (GT1TFN) · Interval type-2 fuzzy number (IT2FN) · Membership function (MF) · Type-2 fuzzy number

### Journal

Journal of Applied Mathematics and ComputingSpringer Journals

Published: May 31, 2018

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