 On Possibilistic Representations of Fuzzy IntervalsLuciano Stefanini () and Maria Guerra No 1602, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini Abstract: It is well known that a fuzzy interval has two equivalent representations given in terms of the so called Left and Right sides of the membership function (LR-representation) or in terms of the Lower and Upper branches defining the endpoints of the -cuts (LU-representation). In this paper we suggest an additional representation of fuzzy intervals called ACF-representation (using an average cumulative function instead of the membership function), based on possibility theory. We illustrate how to build the new representation and we state its basic properties. The main result is that the Average Cumulative (AC) function can be uniquely defined for any fuzzy interval and it is possible to go from one representation to the others through appropriate transformations. An interesting link can be established between ACF-representation and quantile functions, with a possible statistical interpretation useful in real application. We also recommend a parametric form of the AC function. Keywords: KEYWORDS: possibility distribution; parametric representations; fuzzy intervals; quantiles; average cumulative function. (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:urb:wpaper:16_02 Access Statistics for this paper More papers in Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini Contact information at EDIRC. |
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