Some Cosine Similarity Measures and Distance Measures between Complex q-Rung Orthopair Fuzzy Sets and Their Applications

Authors

Peide Liu^{1, *,} , Zeeshan Ali², Tahir Mahmood^2,

¹School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250015, China

²Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

^*Corresponding author. Email: peide.liu@gmail.com

DOI

10.2991/ijcis.d.210528.002How to use a DOI?

Keywords

Complex q-rung orthopair fuzzy sets; Cosine similarity measures; Cosine distance measures; Technique for an order of preference by similarity to ideal solution

Abstract

As a modification of the q-rung orthopair fuzzy sets (QROFSs), complex QROFSs (CQROFSs) can describe the inaccurate information by complex-valued truth grades with an additional term, named as phase term. Cosine similarity measures (CSMs) and distance measures (DMs) are important tools to verify the grades of discrimination between the two sets. In this manuscript, we develop some CSMs and DMs for CQROFSs. Firstly, the CSMs and Euclidean DMs (EDMs) for CQROFSs and their properties are investigated. Because the CSMs do not keep the axiom of similarity measure (SM), we investigate a technique to develop other SMs based on CQROFSs, and they meet the axiom of the SMs. Moreover, we propose a cosine DM (CDM) based on CQROFSs by considering the interrelationship among the SMs and DMs, then we propose an extended TOPSIS method to solve the multi-attribute decision-making problems. Finally, we provide some sensible examples to demonstrate the practicality and efficiency of the suggested procedure, at the same time, the graphical representations of the developed measures are also utilized in this manuscript.

Copyright

© 2021 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Peide Liu
AU  - Zeeshan Ali
AU  - Tahir Mahmood
PY  - 2021
DA  - 2021/06/10
TI  - Some Cosine Similarity Measures and Distance Measures between Complex q-Rung Orthopair Fuzzy Sets and Their Applications
JO  - International Journal of Computational Intelligence Systems
SP  - 1653
EP  - 1671
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210528.002
DO  - 10.2991/ijcis.d.210528.002
ID  - Liu2021
ER  -