Cosine and cotangent similarity measures for intuitionistic fuzzy hypersoft sets with application in MADM problem

Muhammad Naveed Jafar; Muhammad Saeed; Ayesha Saeed; Aleen Ijaz; Mobeen Ashraf; Fahd Jarad

doi:10.1016/j.heliyon.2024.e27886

Cosine and cotangent similarity measures for intuitionistic fuzzy hypersoft sets with application in MADM problem

Heliyon. 2024 Mar 21;10(7):e27886. doi: 10.1016/j.heliyon.2024.e27886. eCollection 2024 Apr 15.

Authors

Muhammad Naveed Jafar¹, Muhammad Saeed¹, Ayesha Saeed¹, Aleen Ijaz¹, Mobeen Ashraf¹, Fahd Jarad^{2

3}

Affiliations

¹ Department of Mathematics, University of Management and Technology, 54000, Lahore, Pakistan.
² Department of Mathematics, Çankaya University, Etimesgut, 06790, Ankara, Turkey.
³ Department of Medical Research, China Medical University, Taichung, 40402, Taiwan.

Abstract

Intuitionistic fuzzy hypersoft sets (IFHSSs) are a novel model that is projected to address the limitations of Intuitionistic fuzzy soft sets (IFSSs) regarding the entitlement of a multi-argument domain for the approximation of parameters under consideration. It is more flexible and reliable as it considers the further classification of parameters into their relevant parametric valued sets. In this paper, we proposed some trigonometric (cosine and cotangent) similarity measures and their weighted trigonometric similarity measures (SMs). Trigonometric Similarity measures (SMs) for intuitionistic fuzzy hypersoft sets (IFHSSs) are significantly implied to check the similarity measures and help to determine the similarity between different factors. Also, in order to evaluate the validity of the significant study and apply the results to a daily life problem. We use them to solve problems involving the selection of renewable energy sources. According to several technical contributing factors, the analysis identifies the ideal location for the implementation of the energy production units. Future case studies with many features and additional bifurcation along with multiple decision-makers can use the suggested methodologies. Also, several existing structures, such as fuzzy, Pythagorean fuzzy, Neutrosophic theories, etc., can be utilized with the suggested method.

Keywords: Cosine; Cotangent; Hypersoft sets (HSSs); Intuitionistic fuzzy hypersoft sets (IFH0SSs); Multi-attribute decision making (MADM); Similarity measures (SMs); Soft sets (Ss).