4.8 Article

Analysis of Data Generated From Multidimensional Type-1 and Type-2 Fuzzy Membership Functions

Journal

IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 26, Issue 2, Pages 681-693

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2017.2688342

Keywords

Fuzzy sets; membership functions (MFs); type-1 fuzzy; type-2 fuzzy; Wilcoxon signed rank (WSR); Wilcoxon rank sum (WRS)

Funding

  1. Technology Innovation Program of the Korea Institute for Advancement of Technology (KTA) from the Ministry of Trade, Industry&Energy, Republic of Korea [2015-122]

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Due to the numerous applications that utilize different types of fuzzy membership functions (MFs), it may sometimes be difficult to choose an appropriate MF for a particular application. In this paper, we establish preliminary guidelines to direct this selection by proposing a three-stage method. In the forward stage, different MFs, such as crisp MFs, type-1 (T1) fuzzy MFs, and type-2 (T2) fuzzy MFs, are generated from multidimensional data sets. Next, in the reverse stage, data is generated back from these MFs by considering different bin sizes. In doing so, various data sets may be generated for different applications which require fuzzy data. Finally, for the similarity analysis stage, we propose an iterative algorithm that makes use of the results of Wilcoxon signed rank (WSR) and Wilcoxon rank sum (WRS) tests to compare the original data and the generated data. From the results of these tests, recommendations concerning the suitability of MFs for a specific application may be suggested by observing the accuracy of representation and the requirements of the application. With this analysis, the objective is to gain insight on when T2 fuzzy sets may be considered to outperform T1 fuzzy sets, and vice versa. Several examples are provided using synthetic and real data to validate the iterative algorithm for data sets in various dimensions.

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