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 of Applied Mathematics and Computing – Springer Journals
Published: May 31, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera