Fuzzy Systems Based on Universal Triple I Method and Their Response Functions

Yiming Tang and Fuji Ren
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Yiming Tang: Information and Communication Engineering, Postdoctoral Research Station, Hefei University of Technology, Heifei 230009, China2AnHui Province Key Laboratory of Affective, Computing and Advanced Intelligent Machine, School of Computer and Information, Hefei University of Technology, Hefei 230009, China
Fuji Ren: AnHui Province Key Laboratory of Affective, Computing and Advanced Intelligent Machine, School of Computer and Information, Hefei University of Technology, Hefei 230009, China3Institute of Technology and Science, The University of Tokushima, Minami Josanjima, Tokushima 770-8506, Japan

International Journal of Information Technology & Decision Making (IJITDM), 2017, vol. 16, issue 02, 443-471

Abstract: The fuzzy systems based on the universal triple I method are investigated, and then their response functions are analyzed. First, the conclusions show that 100 fuzzy systems via the universal triple I method are approximately interpolation functions, which can be used in practical systems, and that 90 ones are approximately fitted functions, which may be usable. Second, as its special cases, the Compositional Rule of Inference (CRI) method and the triple I method are discussed, with the results that 19 fuzzy systems via the CRI method and 2 ones via the triple I method are practicable. Therefore, the universal triple I method has larger effective choosing space, which can obtain more usable fuzzy systems than the others. Lastly, it is found that the first implication and second implication, respectively, embody the function of rule base and reasoning mechanism, further demonstrating the reasonability of the universal triple I method.

Keywords: Fuzzy system; fuzzy reasoning; response function; triple I method; CRI method (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0219622014500746

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