Affiliations: [a] Department of Mathematics, School of Science, Shantou University, Shantou, China
| [b]
Guangdong Provincial Key Laboratory of Digital Signal and Image Processing, Shantou, China
| [c] College of Intelligence Engineering and Mathematics, Liaoning Engineering and Technology University, Fuxin, China
Correspondence:
[*]
Corresponding author. Min-Qiang Gu, Department of Mathematics, School of Science, Shantou University, Shantou 515063, P.R.China. E-mail: mqgu@stu.edu.cn.
Note: [1] This work has been partially supported by Nation Natural Science Foundation of China (No.11471202) and the National Key Cultivation Platform of Guangdong Colleges and Universities (No.2015KGJHZ014).
Abstract: This paper defines the similarity degree of fuzzy sets with bi-implication. Based on this definition, a new fuzzy inference method, namely guaranteed similarity-degrees inference method (GSI method) is proposed. Considering the FMP problem, four kinds of calculation formulas of GSI method are exhibited. Fuzzy reasoning formulas based on the new method with the commonly used implications are discussed. As an illustration of its effectiveness, the proposed method is implemented to some numerical examples from aggregate production planning. Moreover, the authors show that under certain conditions the commonly used fuzzy reasoning methods such as the CRI method, the triple I method, and the FRI method (which based on ∧ -→ composition) all belong to GSI method, the Turksen’s AARS (the approximate analogical reasoning schema) is a partial approximation of the GSI method, and the Raha’s method is a special case of the GSI method. The proposed method is of good property to distinguish the input conditions, and its weighted mode provides the algorithm with a wide range of adaptability and flexibility and facilitates the model optimization.
