Affiliations: [a] B-DAT & CICAEET, School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, P.R. China | [b] School of Electrical and Electronic Engineering, The University of Adelaide, SA, Australia
Correspondence:
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Corresponding author. Sheng Chen, B-DAT & CICAEET, School of Information and Control, Nanjing University of Information Science and Technology, Nanjing 210044, P.R. China. Tel.: +86 25 58731276; +86 25 58731059; E-mail: [email protected].
Abstract: Triple I method was proven to be the effective reasoning method with solid logic foundation, however, the existing works about triple I method all neglect inconsistent bipolarity information in reasoning process, which exists in the way that our brain handles information. Considering that bipolar-valued fuzzy set theory is a powerful tool to describe inconsistent fuzzy bipolarity information, this paper introduces inconsistent bipolarity to triple I method for the first time, and systematically studies the triple I fuzzy modus tollens method with inconsistent bipolarity information based on the regular implication. First, some new concepts about inconsistent fuzzy bipolarity information are introduced. And by introducing the concept of YinYang bipolar-valued induced function, we can induce bipolar-valued operations under the YinYang order relation from the corresponding unipolar ones. Then the triple I bipolar-valued fuzzy modus tollens methods under the YinYang order relation are proposed, together with the solutions. It is proved that the solutions can degenerate into two corresponding unipolar triple I fuzzy modus tollens solutions. Lastly, reductive property, approximation property and robustness of the proposed methods are discussed.
Keywords: Fuzzy set, fuzzy reasoning, inconsistent bipolarity, triple I fuzzy modus tollens, YinYang order relation
