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Set‐based extended aggregation functions
Author(s) -
Mesiar Radko,
Kolesárová Anna,
Gómez Daniel,
Montero Javier
Publication year - 2019
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22128
Subject(s) - set (abstract data type) , set function , fuzzy set , computer science , fuzzy logic , function (biology) , set theory , characterization (materials science) , theoretical computer science , algorithm , algebra over a field , mathematics , artificial intelligence , pure mathematics , programming language , materials science , evolutionary biology , nanotechnology , biology
Abstract Inspired by the Zadeh approach to fuzzy connectives in fuzzy set theory and by some applications, we introduce and study set‐based extended functions, and in particular, set‐based extended aggregation functions. These functions reflect neither reordering nor repetition of input values, and, linking different arities, they introduce serious constraints for extended functions. A complete characterization of set‐based extended (aggregation) functions is given, and some constructions of such functions are also proposed, including several examples.