Paper Info
Title
Interval Type-2 Fuzzy Differential Equations and Stability
Abstract
This article is devoted to present a framework for studying type-2 fuzzy calculus. Some new concepts pertaining to interval type-2 fuzzy functions (IT2FF) and interval type-2 fuzzy differential equations (IT2FDE) with their stability analysis are introduced. A new definition of type-2 fuzzy derivative called type-2 granular derivative (T2gr-derivative) is defined to overcome the disadvantages of the previous definitions of type-2 fuzzy derivatives. Furthermore, the definitions of elementary arithmetic on the set of interval type-2 fuzzy numbers (IT2FNs) and the set of interval type-2 fuzzy complex numbers are presented. The notion of granular metric on the set of IT2FNs is also defined. Besides, the concepts of continuity, integral, and limit of IT2FFs are introduced. Using the concept of type-2 granular fuzzy Laplace transform and the approximations of T2gr-derivative proposed in this article, the exact and approximate solutions of interval T2FDE are presented. Then, some new concepts such as fuzzy node, fuzzy saddle spiral point, fuzzy star, and so forth lay the groundwork for the analysis of interval T2FDE stability. Several examples are given to illustrate the presented notions.
Year
DOI
Venue
2022
10.1109/TFUZZ.2021.3097810
IEEE Transactions on Fuzzy Systems
Keywords
DocType
Volume
Interval type-2 fuzzy complex number (IT2FCN),interval type-2 horizontal membership functions (IT2HMFs),multidimensional relative-distance-measure (M-RDM) arithmetic,stability,type-2 granular derivative (T2gr-derivative),type-2 granular fuzzy Laplace transform (T2gr-Laplace transform)
Journal
30
Issue
ISSN
Citations 
8
1063-6706
0
PageRank 
References 
Authors
0.34
17
2
Name
Order
Citations
PageRank
Marzieh Najariyan100.34
Li Qiu200.34