Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

Abstract

In multiple attribute decision-making (MADM), to better denote complicated preference information of decision-makers (DMs), picture fuzzy set (PFS) as an expansion of intuitionistic fuzzy set (IFS) has become a powerful tool in the recent years. Meanwhile, to remove the impact of abnormal data and capture the correlations among attributes in MADM issue, we propose the power improved generalized Heronian mean (PIGHM) operators in this paper, which have the merits of both power average (PA) operator and improved generalized Heronian mean (IGHM) operator. Additionally, Hamacher operations as a generalization of Algebraic operations and Einstein operations demonstrate good smooth approximate. Motivated by these, the main purpose is to explore PIGHM operators utilizing Hamacher operations to cope with MADM issue with picture fuzzy information. First, we introduce the Hamacher operations, the normalized hamming distance, and similarity measure of picture fuzzy numbers (PHNs). Second, based on these, two new picture fuzzy aggregating operators (AOs), the picture fuzzy Hamacher weighted power improved generalized Heronian mean (PFHWPIGHM) operator and the picture fuzzy Hamacher weighted geometric power improved generalized Heronian mean (PFHWGPIGHM) operator, are put forward, and some properties and special instances of proposed AOs are also investigated. Third, a new MADM model in terms of the PIGHM AOs is developed. Eventually, a practical MADM example, together with sensitivity analysis and comparative analysis, is conducted to verify the credibility and superiority of the new MADM model.