Exploring the use of type-2 fuzzy sets in multi-criteria decision making based on TOPSIS

Madi, Elissa; Garibaldi, Jonathan M.; Wagner, Christian

Abstract

Multi-criteria decision making (MCDM) problems are a well known category of decision making problem that has received much attention in the literature, with a key approach being the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). While TOPSIS has been developed towards the use of Type-2 Fuzzy Sets (T2FS), to date, the additional information provided by T2FSs in TOPSIS has been largely ignored since the final output, the Closeness Coefficient (CC), has remained a crisp value. In this paper, we develop an alternative approach to T2 fuzzy TOPSIS, where the final CC values adopt an interval-valued form. We show in a series of systematically designed experiments, how increasing uncertainty in the T2 membership functions affects the interval-valued CC outputs. Specifically, we highlight the complex behaviour in terms of the relationship of the uncertainty levels and the outputs, including non-symmetric and non-linear growth in the CC intervals in response to linearly growing levels of uncertainty. As the first TOPSIS approach which provides an interval-valued output to capture output uncertainty, the proposed method is designed to reduce the loss of information and to maximize the benefit of using T2FSs. The initial results indicate substantial potential in the further development and exploration of the proposed and similar approaches and the paper highlights promising next steps.

Citation

Madi, E., Garibaldi, J. M., & Wagner, C. (2017). Exploring the use of type-2 fuzzy sets in multi-criteria decision making based on TOPSIS. In 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (1-6). https://doi.org/10.1109/FUZZ-IEEE.2017.8015664

• Conference Name: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2017)
• Conference Location: Naples, Italy
• Start Date: Jul 9, 2017
• End Date: Jul 12, 2017
• Acceptance Date: Mar 14, 2017
• Online Publication Date: Aug 24, 2017
• Publication Date: 2017
• Deposit Date: Apr 26, 2017
• Publicly Available Date: Aug 24, 2017
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Pages: 1-6
• Series ISSN: 1558-4739
• Book Title: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 978-1-5090-6035-1
• DOI: https://doi.org/10.1109/FUZZ-IEEE.2017.8015664
• Public URL: https://nottingham-repository.worktribe.com/output/871940
• Publisher URL: https://ieeexplore.ieee.org/document/8015664/