Generalized bipolar product and sum

Salvatore Greco; Radko Mesiar; Fabio Rindone

doi:10.1007/s10700-015-9217-5

Generalized bipolar product and sum

Salvatore Greco, Radko Mesiar, Fabio Rindone

Centre for Operational Research & Logistics

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Abstract

Aggregation functions on [0, 1] with annihilator 0 can be seen as a generalized product on [0, 1]. We study the generalized product on the bipolar scale [−1, 1], stressing the axiomatic point of view ( compare also [9]). Based on newly introduced bipolar properties, such as the bipolar increasingness, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product are introduced and studied. A special stress is put on bipolar semicopulas, bipolar quasi-copulas and bipolar copulas. Inspired by the truncated sum on [−1, 1] we introduce also the class of generalized bipolar sums, which differ from uninorms due to the non-associativity.

Original language	English
Pages (from-to)	21-31
Journal	Fuzzy Optimization and Decision Making
Volume	15
Issue number	1
Early online date	23 Apr 2015
DOIs	https://doi.org/10.1007/s10700-015-9217-5
Publication status	Published - 1 Mar 2016

Keywords

Aggregation function
bipolar copula
bipolar scale
bipolar semicopula
symmetric minimum

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10.1007/s10700-015-9217-5

GRECO_2014_cright_FODM_Generalized bipolar product and sum
The final publication is available at Springer via http://link.springer.com/article/10.1007/s10700-015-9217-5.
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Generalized bipolar product and sum

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Keywords

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