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In previous studies, based on picture fuzzy sets, full implication algorithm and quintuple implication principle have been studied. The problem is, full implication algorithm did not consider the relationship between the input and antecedent of rule, while quintuple implication principle only considered the inclusion relationship between the rule's antecedent and input. Both algorithms did not consider the similarity of rule's antecedent and input. This leads to unreasonable calculation results in some cases. Therefore, we study fuzzy reasoning methods based on picture similarity measure for generalized modus ponens and generalized modus tollens in this paper. First of all, based on picture biresiduation, a new picture similarity measure between picture fuzzy sets is constructed. Then, representations of solutions of fuzzy reasoning methods based on picture similarity measure are given. Moreover, reducibility and robustness of fuzzy reasoning methods based on picture similarity measure are studied. Finally, two issues related to medical diagnosis are addressed by the proposed methods, demonstrate the rationality and effectiveness of our suggested methods. [ABSTRACT FROM AUTHOR]

In previous studies, based on picture fuzzy sets, full implication algorithm and quintuple implication principle have been studied. The problem is, full implication algorithm did not consider the relationship between the input and antecedent of rule, while quintuple implication principle only considered the inclusion relationship between the rule's antecedent and input. Both algorithms did not consider the similarity of rule's antecedent and input. This leads to unreasonable calculation results in some cases. Therefore, we study fuzzy reasoning methods based on picture similarity measure for generalized modus ponens and generalized modus tollens in this paper. First of all, based on picture biresiduation, a new picture similarity measure between picture fuzzy sets is constructed. Then, representations of solutions of fuzzy reasoning methods based on picture similarity measure are given. Moreover, reducibility and robustness of fuzzy reasoning methods based on picture similarity measure are studied. Finally, two issues related to medical diagnosis are addressed by the proposed methods, demonstrate the rationality and effectiveness of our suggested methods. [ABSTRACT FROM AUTHOR]