On Simple Perturbation of the α-Universal Triple I Algorithm via Specific Interval Implication Operators

Fuzzy reasoning aims to describe things with fuzzy and uncertain concepts and convert them into information that computers can process. Wang thought that the inference algorithm based on Compositional Rule of Inference (CRI) had certain defective nature and proposed the triple I algorithm with fully implication operator. Later, the α-universal triple I (α-UTI) algorithm was proposed. As an important part of the fuzzy inference algorithm, the implication operator directly affects the robustness of the inference algorithm, that is, affects the quality of the inference algorithm. Besides, the quality of fuzzy reasoning algorithm can be partly determined by the robustness of reasoning algorithm. In this paper, the ordinary implication operator is extended to a more general interval implication operator. And the simple perturbation of the α-UTI algorithm is studied for some specific interval implication operators under the interval-valued environment. It is observed that the α-UTI algorithm possesses good simple perturbation performance for single rule or multi-rules, in which specific interval implications are used.