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Join and Meet Operations for Type-2 Fuzzy Sets with Nonconvex Secondary Memberships

Ruiz, G and Hagras, H and Pomares, H and Rojas, I and Bustince, H (2016) 'Join and Meet Operations for Type-2 Fuzzy Sets with Nonconvex Secondary Memberships.' IEEE Transactions on Fuzzy Systems, 24 (4). 1000 - 1008. ISSN 1063-6706

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Abstract

© 2015 IEEE. In this paper, we will present two theorems for the join and meet operations for general type-2 fuzzy sets with arbitrary secondary memberships, which can be nonconvex and/or nonnormal type-1 fuzzy sets. These results will be used to derive the join and meet operations of the more general descriptions of interval type-2 fuzzy sets presented in a paper by Bustince Sola et al. ('Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: Towards a wider view on their relationship,' IEEE Trans. Fuzzy Syst., vol. 23, pp. 1876-1882, 2015), where the secondary grades can be nonconvex. Hence, this study will help to explore the potential of type-2 fuzzy logic systems which use the general forms of interval type-2 fuzzy sets which are not equivalent to interval-valued fuzzy sets. Several examples for both general type-2 and the more general forms of interval type-2 fuzzy sets are presented.

Item Type: Article
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Hani Hagras
Date Deposited: 23 Oct 2015 10:55
Last Modified: 23 Jan 2019 00:17
URI: http://repository.essex.ac.uk/id/eprint/15346

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