This paper aims to study the correlation between intuitionistic fuzzy sets obtained as image of intuitionistic fuzzy t-norms and t-conorms. We consider the action of automorphisms and the class of strong fuzzy negations in order to verify the conditions under which the correlation coefficient related to such fuzzy connectives and their corresponding conjugate and dual constructions are obtained. We attend to present algebraic expressions of correlation relationship by considering t-representable intuitionistic fuzzy t-norms and t-conorms.
Fuzzy logic is a powerful theory to make a decision which is usually irresolute for one thing or another, making it difficult to reach a final agreement. So, fuzzy connectives have been extensively studied in computer science and widely used in practical applications such as decision-making pattern recognition also including medical diagnosis, clustering analysis and image processing [3].Fuzzy implications and aggregation functions are mainly study in this work in order to obtain new representative members in the class of fuzzy QL-operators by analysing related mathematical properties.Thus, the aggregating fuzzy QL-subimplications are introduced. They are obtained by action of the OWA-operator performed over the family of the product triangular subnorms along with standard fuzzy negation and the probabilistic sum. As the main results, this family of QL-subimplications extend related QL-implications by preserving their corresponding properties. For that, let U be the unitary interval (U = [0, 1]).Consider the subconorm S i : U 2 → U , S i (x, y) = 1 −
ABSTRACT. (S,N)-and QL-subimplications can be obtained by a distributive n-ary aggregation performed over the families T of t-subnorms and S of t-subconorms along with a fuzzy negation. Since these classes of subimplications are explicitly represented by t-subconorms and t-subnorms verifying the generalized associativity, the corresponding (S,N)-and QL-subimplicators, referred as I S,N and I S,T,N , are characterized as distributive n-ary aggregation together with related generalizations as the exchange and neutrality principles. Moreover, the classes of (S,N)-and QL-subimplicators are obtained by the median operation performed over the standard negation N S together with the families of t-subnorms and t-subconorms by considering the product t-norm T P as well as the algebraic sum S P , respectively. As the main results, the family of subimplications I S P ,N and I S P ,T P ,N extends the corresponding classes of implicators by preserving their properties, discussing dual and conjugate constructions.
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