Abstract
In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets (T2FSs) as provided by Singh (Frontiers of Computer Science, 2014, 8(5), 741–752), are incorrect by a counterexample. Further, these propositions have been corrected in the present manuscript by giving a correct relation between the T2FSs and validate it with a numerical example.
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References
Singh P. Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems. Frontiers of Computer Science, 2014, 8(5): 741–752
Mendel J M, John R I B. Type-2 fuzzcsactions on Fuzzy Systems, 2002, 10(2): 117–127
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The authors are thankful to the Editor-in-Chief and the anonymous reviewers for their suggestions and helpful comments in revising the paper.
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Sukhveer Singh is a PhD candidate at Thapar University, Patiala, India. He received his master degree in mathematics in 2012 and M.Tech degree in computer science in 2014. His research interests include uncertainty theory, type-2 fuzzy sets, and multi criteria decision making.
Harish Garg is an assistant professor at Thapar University, Patiala, India. He received the PhD degree in applied mathematics with specialization of reliability theory and soft computing techniques, from Indian Institute of Technology Roorkee, India in 2013 and the MS degree in mathematics from Punjabi University, Patiala, India in 2008. His research interests are in the field of computational intelligence, multi-criteria decision making problems, reliability theory, optimization techniques, various nature inspired algorithms (e.g., genetic algorithms, swarm optimization), fuzzy and intuitionistic fuzzy set theory, and expert systems. Application areas include a wide range of industrial and structural engineering design problems. Garg has authored/co-authored over 110 technical papers published in refereed international journals including Applied Soft Computing, Experts Systems with Applications, Journal of Intelligent and Fuzzy Systems, Journal of Manufacturing Systems, etc. He has published six book chapters. He also severs as an editorial board member of various international journals. He is listed in International Who’s Who of Professionals, Marquis Who’s Who in the World, and Marquis Who’s Who in Science and Engineering. In 2016, Dr. Garg was awarded an outstanding reviewer for the journal Applied Soft Computing (ASOC), Elsevier.
Pushpinder Singh received the PhD degree in the School of Mathematics and Computer Applications from Thapar University, Patiala, India. He worked as a post-doctoral fellow with the Department of Computer Science at Palacky University, Olomouc, Czech Republic. Currently, he is working as an assistant professor at Lovely Professional University, India. His research interests include fuzzy similarity measures, group decision making problems, etc.
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Singh, S., Garg, H. Comments on “Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems”. Front. Comput. Sci. 12, 396–400 (2018). https://doi.org/10.1007/s11704-016-6292-x
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DOI: https://doi.org/10.1007/s11704-016-6292-x