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Interval-valued fuzzy reasoning plays a vital role in intelligent systems with the performance of effectively reducing the loss of fuzzy information and reflecting the vagueness and uncertainty in information processing. However the existing reasoning algorithms were developed based on some special interval-valued t-norms which limits the usability and adaptation of these algorithms. This study proposes general reasoning algorithms on the basis of interval-valued fuzzy sets, that is the interval-valued fuzzy reasoning triple I algorithms based on the left-continuous t -representable t -norm T T 1 , T 2 . Furthermore, the interval-valued R -type triple I solutions of the interval-valued fuzzy reasoning triple I algorithms are given. We show that the proposed algorithms possess the reducibility. Finally, some robustness results of the interval-valued fuzzy reasoning triple I algorithms based on the left-continuous interval-valued t -representable t -norm are proved. [ABSTRACT FROM AUTHOR]

In this paper, the robustness of reverse triple I algorithms based on interval-valued fuzzy inference is discussed. As corollaries of the main results, the sensitivities of interval-valued R -type [ α , β ] -reverse triple I solutions based on three well-known interval-valued residuated implication operators are given. [ABSTRACT FROM AUTHOR]

In this paper, a new full implication algorithm based on interval-valued fuzzy inference which extends the triple I principle for fuzzy inference based on fuzzy modus ponens and fuzzy modus tollens to the case of interval-valued fuzzy sets is presented. We first give the corresponding interval-valued R -type triple I solutions and then investigate the robustness of triple I algorithms based on interval-valued fuzzy sets for fuzzy inference. The sensitivity of some special algorithms based on four important interval-valued residuated implication is given. It is shown that the robustness of interval-valued full implication algorithms for fuzzy inference directly depends on the selection of interval-valued fuzzy connectives. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we focus on the flexible inference method with parameters, that is the parametric triple I method by the combination of Schweizer–Sklar operators and triple I principles for fuzzy reasoning. Because the Schweizer–Sklar parameter m reflects the interaction between propositions in reasoning processes, the new parameterized triple I algorithms are closer to human reasoning in daily life. Also some properties of the new algorithms such as the reductivity, continuity and approximation are discussed. It is shown that some existing results are special cases of the new algorithms given here and in view of the variability of the parameter m the new algorithms have excellent flexibility in reasoning processes. [Copyright &y& Elsevier]