On the Monotonicity of Fuzzy Inference Models
Hirosato Seki* and Kai Meng Tay**
*Department of Mathematical Sciences, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan
**Faculty of Engineering, Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia
Monotonicity property is very important in real systems. The monotonicity may need to be satisfied in a variety of application domains, e.g., control, medical diagnosis, educational evaluation, etc. A search in the literature reveals that the importance of the monotonicity in fuzzy inference system has been highlighted. Therefore, this paper surveys the works relating the monotonicity for various fuzzy inference systems. It firstly focuses on the monotonicity of the Mamdani inference model. Themonotonicity ofMamdani model is shown by using a defuzzification method in cases of three t-norms. Secondly, the monotonicity conditions and applications of the T–S inference model are stated. Finally, the monotonicity of the single input type fuzzy inference models is surveyed.
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