Abstract
Improving the efficiency of type-reduction algorithms continues to attract research interest. Recently, there has been some new type-reduction approaches claiming that they are more efficient than the well-known algorithms such as the enhanced Karnik–Mendel (EKM) and the enhanced iterative algorithm with stopping condition (EIASC). In a previous paper, we found that the computational efficiency of an algorithm is closely related to the platform, and how it is implemented. In computer science, the dependence on languages is usually avoided by focusing on the complexity of algorithms (using big O notation). In this article, the main contribution is the proposal of two novel type-reduction algorithms. Also, for the first time, a comprehensive study on both existing and new type-reduction approaches is made based on both algorithm complexity and practical computational time under a variety of programming languages. Based on the results, suggestions are given for the preferred algorithms in different scenarios depending on implementation platform and application context.
Highlights
D URING the past few years, there has been a steady increase of interest in developing type-2 fuzzy logic systems, and in particular interval type-2 fuzzy logic systems [1]
While some of the recent work on type-reduction approaches is based on continuous algorithms or general type2 fuzzy systems [22, 23], this paper focuses on discrete type-reduction approaches which are based on computing the centroid of an interval type-2 fuzzy set
Let an interval type-2 (IT2) fuzzy set Abe based on xi ∈ X, Ji ≡ [ ̄ui, ui], i = 1, 2, ..., N 0 ̄ui ui 1 where xi is the primary variable in the discrete universe of discourse X, Ji represents the membership grade interval for the primary variable xi, and N is the number of discrete points in the universe of discourse of the IT2 fuzzy set
Summary
Chao Chen, Member, IEEE, Dongrui Wu, Senior Member, IEEE, Jonathan M. Senior Member, IEEE, Jamie Twycross, and Jerry M. Abstract—Improving the efficiency of type-reduction algorithms continues to attract research interest. There have been some new type-reduction approaches claiming that they are more efficient than the well-known algorithms such as the enhanced Karnik-Mendel (EKM) and the enhanced iterative algorithm with stopping condition (EIASC). We found that the computational efficiency of an algorithm is closely related to the platform, and how it is implemented. For the first time, a comprehensive study on both existing and new type-reduction approaches is made based on both algorithm complexity and practical computational time under a variety of programming languages. Suggestions are given for the preferred algorithms in different scenarios depending on implementation platform and application context
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