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- Title
INTERVAL-VALUED REPRESENTABILITY OF QUALITATIVE DATA:: THE CONTINUOUS CASE.
- Authors
BOSI, GIANNI; CAMPIÓN, MARIA JESÚS; CANDEAL, JUAN CARLOS; INDURÁIN, ESTEBAN
- Abstract
In the framework of the representability of ordinal qualitative data by means of interval-valued correspondences, we study interval orders defined on a nonempty set X. We analyse the continuous case, that corresponds to a set endowed with a topology that furnishes an idea of continuity, so that it becomes natural to ask for the existence of quantifications based on interval-valued mappings from the set of data into the real numbers under preservation of order and topology. In the present paper we solve a continuous representability problem for interval orders. We furnish a characterization of the representability of an interval order through a pair of continuous real-valued functions so that each element in X has associated in a continuous manner a characteristic interval or equivalently a symmetric triangular fuzzy number.
- Subjects
ELECTRONIC data processing; INFORMATION storage &; retrieval systems; FUZZY numbers; SET-valued maps; MATHEMATICAL mappings; SET theory
- Publication
International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, 2007, Vol 15, Issue 3, p299
- ISSN
0218-4885
- Publication type
Article
- DOI
10.1142/S0218488507004698