Bipolar semicopulas

Salvatore Greco; Radko Mesiar; Fabio Rindone

doi:10.1016/j.fss.2014.10.011

Bipolar semicopulas

Salvatore Greco, Radko Mesiar, Fabio Rindone

Centre of Operational Research and Decision Analysis

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Abstract

The concept of semicopula plays a fundamental role in the aggregation theory on interval [0, 1]. Semicopulas are applied, for example, in the definition of universal integrals. We present an extension of the notion of semicopula to the case of symmetric bipolar interval [−1, 1]. We call this extension bipolar semicopula. The last definition can be used to obtain a simplified definition of the bipolar universal integral. Moreover, bipolar semicopulas allow for an extension of theory of quasi-copulas to the interval [−1, 1].

Original language	English
Pages (from-to)	141-148
Journal	Fuzzy Sets and Systems
Volume	268
Early online date	18 Oct 2014
DOIs	https://doi.org/10.1016/j.fss.2014.10.011
Publication status	Published - 1 Jun 2015

Keywords

Semicopula
Bipolar semicopula
Bipolar universal integrals

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10.1016/j.fss.2014.10.011

GRECO_2015_cright_FSS_Bipolar SemicopulasAccepted author manuscript (Post-print), 107 KBLicence: CC BY-NC-ND

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title = "Bipolar semicopulas",

abstract = "The concept of semicopula plays a fundamental role in the aggregation theory on interval [0, 1]. Semicopulas are applied, for example, in the definition of universal integrals. We present an extension of the notion of semicopula to the case of symmetric bipolar interval [−1, 1]. We call this extension bipolar semicopula. The last definition can be used to obtain a simplified definition of the bipolar universal integral. Moreover, bipolar semicopulas allow for an extension of theory of quasi-copulas to the interval [−1, 1].",

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AU - Mesiar, Radko

AU - Rindone, Fabio

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N2 - The concept of semicopula plays a fundamental role in the aggregation theory on interval [0, 1]. Semicopulas are applied, for example, in the definition of universal integrals. We present an extension of the notion of semicopula to the case of symmetric bipolar interval [−1, 1]. We call this extension bipolar semicopula. The last definition can be used to obtain a simplified definition of the bipolar universal integral. Moreover, bipolar semicopulas allow for an extension of theory of quasi-copulas to the interval [−1, 1].

AB - The concept of semicopula plays a fundamental role in the aggregation theory on interval [0, 1]. Semicopulas are applied, for example, in the definition of universal integrals. We present an extension of the notion of semicopula to the case of symmetric bipolar interval [−1, 1]. We call this extension bipolar semicopula. The last definition can be used to obtain a simplified definition of the bipolar universal integral. Moreover, bipolar semicopulas allow for an extension of theory of quasi-copulas to the interval [−1, 1].

KW - Semicopula

KW - Bipolar semicopula

KW - Bipolar universal integrals

U2 - 10.1016/j.fss.2014.10.011

DO - 10.1016/j.fss.2014.10.011

M3 - Article

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VL - 268

SP - 141

EP - 148

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

ER -

Bipolar semicopulas

Abstract

Keywords

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