RU and (U,N)-implications satisfying Modus Ponens |
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Institution: | Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa, km 7.5, 07122 Palma de Mallorca, Spain |
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Abstract: | In this paper it is investigated when some kinds of fuzzy implication functions derived from uninorms satisfy the Modus Ponens with respect to a continuous t-norm T, or equivalently, when they are T-conditionals. The study is done for RU-implications and -implications with N a continuous fuzzy negation leading to a lot of solutions in both cases. For RU-implications T-conditionality only depends on the underlying t-norm of the uninorm used to derive the residual implication. On the contrary, for -implications the underlying t-norm is never relevant and only the region out of the t-norm is so. Even the t-conorm can be not relevant also in some cases. |
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Keywords: | Fuzzy implication function Residual implication Modus Ponens Uninorm |
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