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Abstract: The intersection of the different classes of implications is one of the most popular topics nowadays due to the large number of construction methods of these operators. In this paper, we deal with the characterization of the intersection of Yager’s implications with QL and D-implications. Some initial steps have already been made with the intersection of Yager’s implications with (S, N), R and QL-implications, however some questions remain unanswered. In particular, we solve an open problem related to the characterization of those implications that are both QL-implications and f-generated implications with f(0)<∞, fully determining the expression of the QL-implications generated by a continuous t-conorm that belong to the considered intersection. Furthermore, we perform a similar study for D-implications and finally, we study the intersection of Yager’s implications with their φ-conjugates. [Copyright &y& Elsevier]

In a group decision making problem, experts often express their opinions through the so-called preference relations. In recent years, several different definitions of preference relations depending on the framework and the nature of the problem have been introduced. These approaches vary from interval-valued fuzzy preference relations to incomplete fuzzy linguistic preference relations. In this paper, a novel definition of preference relation, the so-called subjective linguistic preference relation, is proposed. These preference relations are based on the concept of subjective evaluations, introduced in the linguistic computational model based on discrete fuzzy numbers. In this framework, the experts have more flexibility to express their opinions and the solid mathematical background of this model is a guarantee of no loss of information. Finally, an example of a multi-expert decision making problem with a hierarchical multi-granular linguistic context is analyzed to illustrate the potential of the proposed method and its advantages with respect to other methods. [ABSTRACT FROM AUTHOR]

In the last decade, several new construction methods of fuzzy implication functions from one or more given ones have been proposed. Following this line of research, in our paper some construction methods based on polynomial functions of three variables are presented. Concretely, these methods provide a (possibly new) fuzzy implication function from a given one and a quadratic polynomial function. A complete characterization of those quadratic functions adequate to obtain a fuzzy implication function through this strategy is presented. Moreover, the invariant fuzzy implication functions with respect to this method are determined. Finally, some quadratic construction methods preserving some specific additional properties are analysed. [ABSTRACT FROM AUTHOR]