Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
A course in fuzzy systems and control
A course in fuzzy systems and control
Unified forms of fully implicational restriction methods for fuzzy reasoning
Information Sciences: an International Journal
Distributivity of residual implications over conjunctive and disjunctive uninorms
Fuzzy Sets and Systems
Information Sciences: an International Journal
A Note on the Unified Forms of Triple I Method
Computers & Mathematics with Applications
Reverse triple I method of fuzzy reasoning for the implication operator RL
Computers & Mathematics with Applications
Unified full implication algorithms of fuzzy reasoning
Information Sciences: an International Journal
Triple I method based on pointwise sustaining degrees
Computers & Mathematics with Applications
Continuity of triple I methods based on several implications
Computers & Mathematics with Applications
Unified forms of Triple I method
Computers & Mathematics with Applications
IEEE Transactions on Fuzzy Systems
On the Law of Importation in Fuzzy Logic
IEEE Transactions on Fuzzy Systems
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As a generalization of the triple I method, differently implicational universal triple I method of (1, 2, 2) type (universal triple I method for short) is investigated. First, the concepts of residual operators and strongly residual operators are given, and then related conclusions of residual pairs are provided. Second, the related universal triple I solutions (including FMP-solutions, FMT-solutions and so on) are strictly defined by the infimum, where such solutions are divided into two parts respectively corresponding to the minimum and infimum. Then, we put emphasis on the FMP-solutions, in which the unified forms of FMP-solutions w.r.t. strongly residual operators and a new idea for getting FMP-solutions w.r.t. infimum are achieved. Third, as a result of analyzing the logic basis of a sort of CRI (Compositional Rule of Inference) method, it is found that their CRI solutions can be regarded as special cases of FMP-solutions. Lastly, the response functions of fuzzy systems via universal triple I method are discussed, which demonstrates that the universal triple I method can provide bigger choosing space and get better fuzzy controllers by contrast with the triple I method and CRI method.