Approaches to multi-attribute decision-making based on picture fuzzy Aczel–Alsina average aggregation operators

• Published in: Computational & applied mathematics Vol. 41; no. 1
• Main Author: Senapati, Tapan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2022; Springer Nature B.V
• Subjects: Accumulation; Agglomeration; Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Decision making; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Multiplication; Operators; Aczel–Alsina operations; Picture fuzzy Aczel–Alsina average aggregation operators; PFNs; MADM
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-021-01742-w

Picture fuzzy numbers (PFNs) are extremely reasonable to be utilized for delineating dubious or fuzzy data. In this article, we introduce the aggregation strategies of PFNs with assistance from Aczel–Alsina operations. We initially broaden the Aczel–Alsina t-norm and t-conorm to picture fuzzy (PF) situations and present a few new operations of PFNs; for example, Aczel–Alsina sum, Aczel–Alsina product, Aczel–Alsina scalar multiplication, and Aczel–Alsina exponentiation, in view of which we build up a few new PF aggregation operators; for instance, the PF Aczel–Alsina weighted average (PFAAWA) operator, PF Aczel–Alsina order weighted average (PFAAOWA) operator, and PF Aczel–Alsina hybrid average (PFAAHA) operator. We further build up various characteristics of those operators, keep several exceptional instances among themselves, and investigate the connections among such operators. Besides, we apply such operators to build up a methodology for managing multiple attribute decision-making (MADM) with PF data. A numerical example is stated to delineate the reasonableness, the viability of the created operators, and the approach. A comparative analysis is additionally introduced.