as a generalization of the triple i method, the universal triple imethod is investigated from the viewpoints of both fuzzy reasoningand fuzzy controller. the universal triple i principle is putforward, which improves the previous triple i principle. then,unified form of universal triple i method is established based onthe (0,1)-implication or r-implication. moreover, the reversibilityproperty o...

As a generalization of the triple I method, the universal triple Imethod is investigated from the viewpoints of both fuzzy reasoningand fuzzy controller. The universal triple I principle is putforward, which improves the previous triple I principle. Then,unified form of universal triple I method is established based onthe (0,1)-implication or R-implication. Moreover, the reversibilityproperty o...

This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple impli...

Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...

In this paper, the authors investigate the ordering property (OP), x y I x y ≤ ⇔ ( ) = , 1 , together with the general form of the law of importation(LI), i.e., I T x y z I x I y z , , , , ( ) ( ) = ( ) ( ) , whereT is a t-norm and I is a fuzzy implication for the four main classes of fuzzy implications. The authors give necessary and sufficient conditions under which both (OP) and (LI) holds f...

This paper is devoted to the research of full implication triple I method under Pythagorean fuzzy environment. We first propose concepts t-norm, t-conorm, residual operator (RPFIO) and biresiduum. The for modus ponens (PFMP) tollens (PFMT) are also established. In addition, properties PFMP PFMT models including robustness, continuity reversibility analyzed. Finally, a practical problem discusse...

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

In this paper, the perturbation of fuzzy connectives and the robustness of fuzzy reasoning are investigated. This perturbation of Schweizer-Sklar parameterized t-norms and its residuated implication operators are given. We show that full implication triple I algorithms based on Schweizer-sklar operators are robust for normalized Minkowski distance.

In this paper we study a connection between quasicopulas and generator triples of fuzzy preference structures. We study also conditions under which fuzzy implications can be used to construct generator triples. As we show, an important property of fuzzy implications that enables us to construct a generator triple from a fuzzy implication, is the contrapositive symmetry.