Enhancing Expert Decision-Making for Wastewater Treatment Plants with Seidel Laplacian Energy and Cosine Similarity Measure in Intuitionistic Fuzzy Graphs

Abstract

Abstract Wastewater treatment facilities’ main goal is to protect the public and environment from the hazardous and poisonous materials found in wastewater. Water treatment facilities were developed to speed up the natural process of cleansing water. A novel cosine similarity measure across intuitionistic fuzzy graphs has been proven to be more effective than certain present ones in group decision-making issues using example verification. This paper provides a unique approach for calculating expert-certified, well-known scores by finding the ambiguous information of intuitionistic fuzzy preference relations as well as the regular cosine similarity grades from one separable intuitionistic fuzzy preference relation to another. The new technique considers both "objective" and "subjective" information provided by experts. Using intuitionistic fuzzy preference relations, we provide workable techniques for judging experts’ eligible reputational ratings. This can be used to raise or decrease the relevance of the stated criteria in an evaluation that takes into account several competing elements. We give a solution to a decisional problem by using two effective methods: the newly constructed cosine similarity measure and the Seidel Laplacian energy (SLe+) of an intuitionistic fuzzy graph. Finally, two working procedures and circumstances are offered to show the effectiveness and superiority of the proposed techniques.

Keywords

• Seidel Laplacian energy
• Intuitionistic fuzzy graph
• Intuitionistic fuzzy adjacency matrix
• Cosine similarity measure