IDEMPOTENT UNINORMS ON FINITE ORDINAL SCALES-Reference-Cited by-同舟云学术

IDEMPOTENT UNINORMS ON FINITE ORDINAL SCALES

Published:2009-02 Issue:01 Volume:17 Page:1-14
ISSN:0218-4885
Container-title:International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
language:en
Short-container-title:Int. J. Unc. Fuzz. Knowl. Based Syst.

Author:

DE BAETS BERNARD¹,FODOR JÁNOS²,RUIZ-AGUILERA DANIEL³,TORRENS JOAN³

Affiliation:

1. Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium

2. John von Neumann Faculty of Informatics, Budapest Tech, Bécsi út 96/b, H-1034 Budapest, Hungary

3. Dept. of Mathematics and Computer Science, University of the Balearic Islands, Cra. de Valldemossa, Km. 7, 5, 07122 Palma de Mallorca, Spain

Abstract

In this paper we characterize all idempotent uninorms defined on a finite ordinal scale. It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set of scale elements not smaller than the neutral element, and vice versa. Based on this one-to-one correspondence, the total number of discrete idempotent uninorms on a finite ordinal scale of n + 1 elements is equal to 2n.

Publisher

World Scientific Pub Co Pte Lt

Subject

Artificial Intelligence,Information Systems,Control and Systems Engineering,Software

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021848850900570X

Reference19 articles.

1. Triangular norms on product lattices

2. Smooth associative operations on finite ordinal scales

3. t-Operators and uninorms on a finite totally ordered set

4. On bisymmetric operators on a finite chain

5. On left and right uninorms on a finite chain

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