General type-2 fuzzy logic systems based on refinement constraint triangulated irregular network

Article type: Research Article

Authors: Ngo, Long Thanh

Affiliations: Department of Information Systems, Le Quy Don Technical University, Ha Noi, Viet Nam

Note: [] Corresponding author. Long Thanh Ngo, Department of Information Systems, Le Quy Don Technical University, No. 100, Hoang Quoc Viet Street, Cau Giay, Ha Noi, Viet Nam. Tel.: +84 914 364 064; Fax: +84 43836 0897; E-mail: ngotlong@gmail.com

Abstract: Triangulated irregular network (TIN) has used to represent 3-dimensional surfaces by dividing domain into irregular sub-triangles and approximately represent using piecewise linear functions. Hence, TIN are also used to approximately represent membership functions of general type-2 fuzzy sets for reducing computational complexity. To support speed-up in computation of operations of type-2 fuzzy sets, a refinement CTIN is proposed by combining contour model and constraint Delaunay criteria. So a type-2 fuzzy set is also represented by RCTIN in the same way. The paper deals with the use RCTIN to represent general type-2 fuzzy sets. On the basis of RCTIN representation theorem, algorithms for operations and general type-2 fuzzy logic systems (GT2FLS) are proposed. A T2FLS is designed and implemented in comparing previous approaches under an application of obstacle avoidance of robot navigation.

Keywords: Type-2 fuzzy sets, fuzzy inference, type-2 fuzzy logic systems, robot navigation, triangulated irregular network

DOI: 10.3233/IFS-120683

Journal: Journal of Intelligent & Fuzzy Systems, vol. 25, no. 3, pp. 771-784, 2013