Ordered Continuous Means and Information

Arthur Ramer ()
Additional contact information
Arthur Ramer: University of New South Wales, Knowledge Systems Group, Computer Science

A chapter in The Ordered Weighted Averaging Operators, 1997, pp 107-119 from Springer

Abstract: Abstract Possibilistic measures of information have been characterized as a form of OWA operators on the possibility values. This correspondence can be carried on to the continuous domains and distributions. Continuous information measures have been previously discussed only once in the open literature [12], while continuous OWA’s were only hinted at in conference papers [17, 18]. This chapter presents a method of defining such functions on a continuous universe of discourse — a domain which is a measurable space of measure 1. The method is based on the concept of rearangement [5] of a function, used in lieu of sorting for the discrete possibility values. For a continuous distribution, represented by a measurable function f(x) on the domain of discourse X, first a decreasing rearrangement—f(x) on [0, μ(X)]—is constructed. Then, depending on μ(X), one of two definitions is appropriate For technical reasons the quantification of uncertainty must be in the form of information distance [6, 13] measuring the departure from the most ‘uninformed’ distribution (constant possibility 1). The final form of the information content for possibility distribution f, defined on domain X, μ(X) = 1, is given by the continuous OWA operato Relationship with the discrete OWA’s, and especially the discrete uncertainty measures, is discussed and various limit properties and approximations are established. Lastly, an investigation of continuous OWA as an integral transform is indicated.

Keywords: Function rearrangement; fuzzy set; fuzzy membership; information distance; information metric; information measure; information theory; ordered average; OWA; possibility distribution; weighted average (search for similar items in EconPapers)
Date: 1997
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-6123-1_10

Ordering information: This item can be ordered from
http://www.springer.com/9781461561231

DOI: 10.1007/978-1-4615-6123-1_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().