A Novel Approach Based on Sine Trigonometric Picture Fuzzy Aggregation Operators and Their Application in Decision Support System

Saleem Abdullah,Ronnason Chinram,Saifullah Khan,Muhammad Qiyas

doi:10.1155/2021/8819517

Saleem Abdullah, Ronnason Chinram + Show 2 more

Open Access

https://doi.org/10.1155/2021/8819517

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Abstract

Picture fuzzy sets (PFSs) are one of the fundamental concepts for addressing uncertainties in decision problems, and they can address more uncertainties compared to the existing structures of fuzzy sets; thus, their implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the decision-maker over the multiple parameters. Taking this feature and the significances of the PFSs into consideration, the main objective of the article is to describe some reliable sine trigonometric laws STLs for PFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the picture fuzzy numbers. Also, we characterized the desirable properties of the proposed operators. Then, we presented a group decision-making strategy to address the multiple attribute group decision-making (MAGDM) problem using the developed aggregation operators and demonstrated this with a practical example. To show the superiority and the validity of the proposed aggregation operations, we compared them with the existing methods and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.

Highlights

Multiple attribute group decision-making (MAGDM) method is one of the most relevant and evolving topics explaining how to choose the finest alternative with community of decision-makers (DMs) with some attributes.ere are two relevant tasks in this system. e first is to define the context in which the values of the various parameters are effectively calculated, while the second is to summarize the information described
Some more generalized functional aggregation operators are presented with the help of the defined sine trigonometric operational laws (STOLs) for PFNs, and many basic relations between the developed AOs are discussed; a novel MAGDM technique depending on the developed operators to solve the group decision-making problems is presented
We have described a number of aggregation operators in this portion of the article on the basis of sine trigonometric operational laws (STOLs)

Summary

Introduction

Multiple attribute group decision-making (MAGDM) method is one of the most relevant and evolving topics explaining how to choose the finest alternative with community of decision-makers (DMs) with some attributes. Wang et al [37] introduced a similarity measure of q-ROFSs. Wei et al [38] developed bidirectional projection method for PFSs. Ashraf et al [39,40,41] developed the idea of different approaches to MAGDM problems, picture fuzzy linguistic sets and exponential Jensen PF divergence measure, respectively. Some more generalized functional aggregation operators are presented with the help of the defined sine trigonometric operational laws (STOLs) for PFNs, and many basic relations between the developed AOs are discussed; a novel MAGDM technique depending on the developed operators to solve the group decision-making problems is presented. (4) A novel MAGDM method based on the proposed operators to solve the group decision-making problems is presented.

Preliminaries

Sine Trigonometric Aggregation Operators

Fundamental Properties of the Proposed Aggregation Operators

Illustrative Example

Comparative Analysis

Conclusion