Conic aggregation functions

• Published in: Fuzzy sets and systems Vol. 167; no. 1; pp. 3 - 20
• Main Authors: Jwaid, T., De Baets, B., Kalická, J., Mesiar, R.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 30.03.2011; Elsevier
• Subjects: Agglomeration; Aggregation function; Applied sciences; Boundaries; Circuit properties; Computer science; control theory; systems; Conic function; Conics; Copula; Digital circuits; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Fuzzy set theory; Information, signal and communications theory; Mathematical analysis; Mathematical methods; Mathematics; Measure and integration; Miscellaneous; Quasi-copula; Sciences and techniques of general use; T-norm; Telecommunications and information theory; Theoretical computing; Zero-set; Quasi-copula; T-norm; Copula; Zero-set; Aggregation function; Conic function; Fuzzy system; Necessary and sufficient condition; Information processing; Fuzzy set
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2010.07.004

Inspired by the notion of conic t-norms, we introduce conic aggregation functions. Such aggregation functions are completely characterized by their zero-set. Special classes of binary conic aggregation functions such as conic quasi-copulas and conic copulas are considered. We provide the necessary and sufficient conditions on the boundary curve of the zero-set of a conic aggregation function to obtain a conic (quasi-) copula and conclude that the class of conic copulas is a proper subclass of the class of conic quasi-copulas. Moreover, we characterize the class of singular conic copulas. We investigate some aggregations of conic (quasi-) copulas. Some examples are also provided.