Paper Info
Title
High order α-planes integration: A new approach to computational cost reduction of General Type-2 Fuzzy Systems.
Abstract
Nowadays, there are different representations of Generalized Type-2 Fuzzy Sets that consider a non-uniform distribution of the uncertainty, for example, the Geometric approach, the Z-Slices method and the α-planes approximation. Each representation has advantages and disadvantages, however, the present work is focused on the α-planes representation, and this representation consists on realizing a horizontal discretization, the solution of each horizontal slice, and then the integration of these planes. Each horizontal slice results in an Interval Type-2 Fuzzy System, so, the computational cost is proportional to the discretization level, which means, is proportional to the number of α-planes used for modeling the Generalized Type-2 FS. The aim of this work is reducing the computational cost of Generalized Type-2 FS by a new approach of α-planes representation. In this paper the Newton–Cotes quadrature for the α-planes integration is proposed, achieving in this way a high-level discrete integration compared with the conventional α-planes integration. The proposed approach aims at reducing the number of α-planes necessary to obtain a good approximation of Generalized Type-2 FS. In order to validate the proposed approach, a set of experiments was realized with a randomly generated Generalized Type-2 Fuzzy Sets, and they are realized with a different number of α-planes in order to compare the performance of the proposed approach with respect to the conventional approach. On the other hand, the proposed approach was also applied to a control problem, as an example of applications of the proposed approach to real-world problems.
Year
DOI
Venue
2018
10.1016/j.engappai.2018.06.013
Engineering Applications of Artificial Intelligence
Keywords
Field
DocType
α-planes,Type-2 Fuzzy Logic,General Type-2 Fuzzy Logic
Discretization,Mathematical optimization,Computer science,Algorithm,Fuzzy set,Quadrature (mathematics),Fuzzy control system,Cost reduction
Journal
Volume
ISSN
Citations 
74
0952-1976
9
PageRank 
References 
Authors
0.46
20
3
Name
Order
Citations
PageRank
Emanuel Ontiveros1221.71
Patricia Melin24009259.43
Oscar Castillo35289452.83