Multi-Attribute Decision-making Based on Pythagorean Fuzzy Numbers and its Application in Hotel Evaluations

This article describes a method for assessing hotel management using Pythagorean Fuzzy Numbers inside a Multi-attribute Decision-Making framework. It offers a grey relational analysis projection to deal with scenarios in which attribute values fluctuate within the Pythagorean Fuzzy Set range and attribute weights are unknown. The study developed numerous operational rules and computed the anticipated value and the Hamming distance between two Pythagorean Fuzzy Sets. The information entropy method was then utilized to calculate attribute weights, creating the Grey Relational Analysis and Grey Relational Projection methodologies. Alternatives were rated based on their proximity to the Positive Ideal Target using Grey Relational Projection values from both positive and negative ideal solutions for each alternative. The validity of this model was verified through a case study on hotel management evaluation, demonstrating its practicality and effectiveness, and Comparative Analysis involving the adjustment of criteria weight coefficients.