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

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.