Concave type-2 fuzzy sets: properties and operations

Authors:
Hooman Tahayori;Andrea G. B. Tettamanzi;Giovanni Degli Antoni;Andrea Visconti;Masoomeh Moharrer
Affiliations:
Universita degli Studi di Milano, Dipartimento di Scienze dell’Informazione, Via Comelico 39/41, 20135, Milan, Italy;Universita degli Studi di Milano, Dipartimento di Tecnologie dell’Informazione, Via Bramante 65, 26013, Crema, Italy;Universita degli Studi di Milano, Dipartimento di Scienze dell’Informazione, Via Comelico 39/41, 20135, Milan, Italy;Universita degli Studi di Milano, Dipartimento di Informatica e Comunicazione, Via Comelico 39/41, 20135, Milan, Italy;Politecnico di Milano, Dipartimento di Ingegneria Gestionale, Via Giuseppe Colombo 40, 20133, Milan, Italy
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2010

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Abstract

In this article, concave type-2 fuzzy sets are investigated. The calculation of union and intersection of concave type-2 fuzzy sets using the min t-norm and the max t-conorm are explored and it is proved that the set of concave type-2 fuzzy sets is closed under those operations. It is also shown that the set of LR-normal concave type-2 fuzzy sets forms a commutative semiring under join and meet.