Thick Fuzzy Sets (TFSs) and Their Potential Use in Uncertain Fuzzy Computations and Modeling

Reda Boukezzoula (1) , Luc Jaulin (2, 3) , Benoît Desrochers (2, 3) , Didier Coquin (1)

1 LISTIC - Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance
2 Lab-STICC_ROBEX - Equipe ROBotics for EXploration
3 ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne

This paper aims at proposing the concept of thick fuzzy sets (TFSs). A TFS is based on the joint use of thick sets (TSs) and -cuts concepts. A TFS is represented by a family of nested TSs. A TS is an uncertain set, which is represented by a pair of crisp sets (CSs). These CSs characterize the upper and lower bounds of the TS. Therefore, a TS can be regarded as an interval of CSs. In this framework, as a type-1 fuzzy set (T1FS) is regarded as a family of nested CSs, a TFS can be represented by a family of nested TSs. Furthermore, according to the vertical dimension, a TFS can be regarded as an interval with T1FS bounds. The potentialities of the TFS concept have been validated using application examples where a real-world application for modeling the zone explored by an underwater robot is given.

Mots clés: Type-1 fuzzy sets (T1FSs); Type-2 fuzzy sets (T2FSs); Crisp sets (CSs); Thick sets (TSs); Thick fuzzy sets (TFSs); Underwater robot

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Reda Boukezzoula, Luc Jaulin, Benoît Desrochers, Didier Coquin. Thick Fuzzy Sets (TFSs) and Their Potential Use in Uncertain Fuzzy Computations and Modeling. IEEE Transactions on Fuzzy Systems, 2021, 29 (11), pp.3334 - 3348. ⟨10.1109/tfuzz.2020.3018550⟩. ⟨hal-03128908⟩