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Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems

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Abstract

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of different proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable properties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Limitations of existing ranking methods have been studied. Further for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.

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Authors and Affiliations

  1. Department of Computer Science, Palacky University, Olomouc, CZ-77146, Czech Republic

    Pushpinder Singh

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  1. Pushpinder Singh
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Correspondence to Pushpinder Singh.

Additional information

Pushpinder Singh received the Ph.D. degree in the School of Mathematics and Computer Applications from Thapar University Patiala, India. He is currently working as post doctoral fellow with the Department of Computer Science at Palacky University, Olomouc, Czech Republic. His research interests include fuzzy similarity measures, group decision making problems etc.

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Singh, P. Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems. Front. Comput. Sci. 8, 741–752 (2014). https://doi.org/10.1007/s11704-014-3323-3

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  • DOI: https://doi.org/10.1007/s11704-014-3323-3

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