Three-Way Fuzzy Sets and Their Applications (III)

Abstract

Three-way fuzzy inference is the theoretical basis of three-way fuzzy control. The proposed TCRI method is based on a Mamdani three-way fuzzy implication operator and uses one inference and simple composition operation. In order to effectively improve the TCRI method, this paper proposes a full implication triple I algorithm for three-way fuzzy inference and gives the triple I solution to the TFMP problem. The emphasis of our research is R0 and Go¨del triple I solution, which is related to three-way residual implication, as well as Zadeh’s and Mamdani’s triple I solution, which is based on three-way fuzzy implication operator. Then the three-way fuzzy controller is constructed by the proposed Zadeh’s and R0 triple I algorithm. Finally, the proposed triple I algorithm is applied to the three-way fuzzy control system, and its advantage is illustrated by the three-dimensional surface diagram of the control variable.

Keywords

• three-way fuzzy sets
• three-way fuzzy inference
• three-way residual implication
• Triple I Algorithm
• three-way fuzzy control system