García Segador,P.Miranda Menéndez, Pedro2024-07-102024-07-102023-02García-Segador, P., & Miranda, P.. On the polytope of 3-tolerant fuzzy measures. Int. J. Uncertain. Fuzziness Knowl.-Based Syst., 2023 :31(01): 57-82.0218-48851793-641110.1142/s0218488523500058https://hdl.handle.net/20.500.14352/105917In 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.engjournal articleopen access3-interactive fuzzy measures3-tolerant fuzzy measuresOrder polytopeRandom generationEstadística matemática (Estadística)Investigación operativa (Matemáticas)1209 Estadística1207 Investigación Operativa