Next Article in Journal
Existence and Nonexistence of Solutions to p-Laplacian Problems on Unbounded Domains
Next Article in Special Issue
New Concepts of Picture Fuzzy Graphs with Application
Previous Article in Journal
Hermite-Hadamard Type Inequalities for Interval (h1, h2)-Convex Functions
Previous Article in Special Issue
p-Regularity and p-Regular Modification in ⊤-Convergence Spaces
Article

Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets

Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(5), 437; https://doi.org/10.3390/math7050437
Received: 4 April 2019 / Revised: 30 April 2019 / Accepted: 10 May 2019 / Published: 17 May 2019
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
This paper analyzes the counterintuitive behaviors of adopted twelve distance-based similarity measures between intuitionistic fuzzy sets. Among these distance-based similarity measures, the largest number of components of the distance in the similarity measure is four. We propose six general counterintuitive test problems to analyze their counterintuitive behaviors. The results indicate that all the distance-based similarity measures have some counterintuitive test problems. Furthermore, for the largest number of components of the distance-based similarity measure, four types of counterintuitive examples exist. Therefore, the counterintuitive behaviors are inevitable for the distance-based similarity measures between intuitionistic fuzzy sets. View Full-Text
Keywords: intuitionistic fuzzy set; similarity; counterintuitive intuitionistic fuzzy set; similarity; counterintuitive
MDPI and ACS Style

Tang, H.-C.; Yang, S.-T. Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets. Mathematics 2019, 7, 437. https://doi.org/10.3390/math7050437

AMA Style

Tang H-C, Yang S-T. Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets. Mathematics. 2019; 7(5):437. https://doi.org/10.3390/math7050437

Chicago/Turabian Style

Tang, Hui-Chin, and Shen-Tai Yang. 2019. "Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets" Mathematics 7, no. 5: 437. https://doi.org/10.3390/math7050437

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop