Abstract
In decision-making process, decision-makers may make different decisions because of their different experiences and knowledge. The abnormal preference value given by the biased decision-maker (the value that is too large or too small in the original data) may affect the decision result. To make the decision fair and objective, this paper combines the advantages of the power average (PA) operator and the Bonferroni mean (BM) operator to define the generalized fuzzy soft power Bonferroni mean (GFSPBM) operator and the generalized fuzzy soft weighted power Bonferroni mean (GFSWPBM) operator. The new operator not only considers the overall balance between data and information but also considers the possible interrelationships between attributes. The excellent properties and special cases of these ensemble operators are studied. On this basis, the idea of the bidirectional projection method based on the GFSWPBM operator is introduced, and a multi-attribute decision-making method, with a correlation between attributes, is proposed. The decision method proposed in this paper is applied to a software selection problem and compared to the existing methods to verify the effectiveness and feasibility of the proposed method.
Highlights
This paper proposes the generalized fuzzy soft power Bonferroni mean (GFSPBM) operator and the generalized fuzzy soft weighted power Bonferroni mean (GFSWPBM) operator by combining the advantages of the power average (PA) operator and BM operator
Considering that the PA operator can determine attribute weights according to the support relationship between attributes, thereby reducing the influence of biased decision makers’ abnormal preference values on the decision results, while the BM operator can consider the degree of correlation between different attributes; according to the characteristics of PA operator and BM operator, this chapter combines the two operators and extends it to the generalized fuzzy soft set environment, and proposes a PBM operator based on generalized fuzzy variables
To better show the advantages of the method proposed in this paper, the following further compares and analyzes with the existing methods, and selects the GFSSWBM
Summary
Scholars have studied various forms of operator (such as the power average (PA) [13] operator, the Bonferroni mean (BM) [14] operator and the power Bonferroni mean (PBM) [15] operator) to carry out corresponding operations on different opinions in order to obtain as accurate a decision scheme as possible. These operators effectively integrate the information of individual DMs. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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