Aggregation of implication functions
نویسندگان
چکیده
This paper deals with the problem of the aggregation of implication functions. After characterizing those binary operations which merge two implication functions into a new implication function, we study some aspects of the aggregated implication functions in terms of the two given ones. In particular, we are interested in aggregation processes such that properties of the implication functions are preserved.
منابع مشابه
SUPER- AND SUB-ADDITIVE ENVELOPES OF AGGREGATION FUNCTIONS: INTERPLAY BETWEEN LOCAL AND GLOBAL PROPERTIES, AND APPROXIMATION
Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {it Fuzzy Sets and Systems} {bf 291} (2016), 40--53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with ...
متن کاملON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES
Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...
متن کاملContinuity of super- and sub-additive transformations of continuous functions
We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.
متن کاملSuper- and sub-additive transformations of aggregation functions from the point of view of approximation
The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.
متن کاملBelief Aggregation in Fuzzy Framework
We explore how belief aggregation in the fuzzy framework can be molded into an optimization problem which helps avoid paradoxical outcomes without the fear of indecision. We further illustrate that depending on the choice of t -norm and fuzzy implication, we can find aggregation functions that produce collectively rational outcome without compromising on systematicity.
متن کامل