On the Concept of Meaningfulness in Constrained Type-2 Fuzzy Sets

D'Alterio, Pasquale; Garibaldi, Jonathan M.; John, Robert

Abstract

Constrained type-2 fuzzy sets have been proposed as a tool to model type-2 fuzzy sets starting from a type-1 generator set with uncertainty. This constrained representation only defines as acceptable the embedded sets that have the same shape as the generator set in order to process only membership functions that are considered "meaningful" when using fuzzy operators such as centroid defuzzification. However, the idea of "meaningfulness" has never been clearly defined; at the same time there are some contexts in which a given concept (e.g. medium height) can be reasonably represented by multiple shapes, such as triangular and Gaussian. The aim of this paper is both to formally define the idea of meaningfulness of shapes and to extend the formal definitions of constrained interval type-2 fuzzy sets in order to allow the presence of multiple shapes among the acceptable embedded sets.

Citation

D'Alterio, P., Garibaldi, J. M., & John, R. (2019). On the Concept of Meaningfulness in Constrained Type-2 Fuzzy Sets. In 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)https://doi.org/10.1109/FUZZ-IEEE.2019.8858942

• Conference Name: International Conference on Fuzzy Systems (FUZZ-IEEE 2019)
• Conference Location: New Orleans, LA, USA
• Start Date: Jun 23, 2019
• End Date: Jun 26, 2019
• Acceptance Date: Mar 7, 2019
• Online Publication Date: Oct 10, 2019
• Publication Date: Jun 26, 2019
• Deposit Date: Apr 3, 2019
• Publicly Available Date: Apr 3, 2019
• Publisher: Institute of Electrical and Electronics Engineers
• Book Title: 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 9781538617281
• DOI: https://doi.org/10.1109/FUZZ-IEEE.2019.8858942
• Public URL: https://nottingham-repository.worktribe.com/output/1735064
• Publisher URL: https://ieeexplore.ieee.org/document/8858942
• Related Public URLs: https://attend.ieee.org/fuzzieee-2019/
• Additional Information: © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.