A Novel Pythagorean Fuzzy Stepwise Weight Assessment Ratio Analysis Approach for Group Decision-Making Under Heterogeneous Information Conditions

A central challenge in complex group decision-making is how to integrate heterogeneous types of information. Experts differ in background and experience, which leads to variation in their understanding of assessment attributes and in the forms of information they provide. Such information may include fuzzy semantic information, fuzzy semantic interval information, and uncertain information, increasing the complexity of the decision process. Traditional approaches commonly employ fuzzy set (FS) and intuitionistic fuzzy set (IFS) models to address group decision-making problems involving human cognitive judgments. These models constrain the sum of the membership degree (MD) and the non-membership degree (non-MD) to be equal to 1 and less than or equal to 1, respectively. However, when assessment information is insufficient, the MD and non-membership degree provided by experts may exceed this constraint. In addition, the score function (SF) and accuracy function (AF) used in FS and IFS do not account for indeterminacy, making them unsuitable for handling incomplete and hesitation information. To overcome these limitations, this study proposes a Pythagorean fuzzy stepwise weight assessment ratio analysis-based method and introduces a new score function (NSF) and a new accuracy function (NAF) within the Pythagorean fuzzy set framework for complex group decision-making. An illustrative case on raw material vendor selection for shipbuilding enterprises is used to validate the effectiveness of the proposed method. The results demonstrate that the method produces more reasonable and accurate vendor ranking outcomes.