On the Polytope of 3-Tolerant Fuzzy Measures-Reference-Cited by-同舟云学术

On the Polytope of 3-Tolerant Fuzzy Measures

Published:2023-02 Issue:01 Volume:31 Page:57-82
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:

García-Segador P.¹,Miranda P.²

Affiliation:

1. National Statistics Institute, Paseo de la Castellana, 183, 28071 Madrid, Spain

2. Interdisciplinary Mathematical Institute, Complutense University of Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain

Abstract

In this paper we study some geometrical properties of the polytope of 3-tolerant fuzzy measures. To achieve this task, we profit that this polytope is an order polytope and hence many properties can be extracted from the subjacent poset. The main result in the paper is a straightforward procedure for obtaining a random 3-tolerant fuzzy measure. We also compute the volume and obtain some other properties of this polytope. These results can be also applied by duality to the polytope of 3-intolerant measures and they can also be easily extended to other subfamilies of fuzzy measures.

Funder

Ministry of Economy and Competitiveness of Spain

Publisher

World Scientific Pub Co Pte Ltd

Subject

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

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218488523500058

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