Ambiguities in the X-ray Analysis of Crystal Structure Based on Neutrosophic Fuzzy Rough Aczel-Alsina Aggregation Operators and Their Application in Decision-Making

Abstract

X-ray cystography, frequently mentioned as X-ray crystal analysis, is a valuable and useful technique used to evaluate the three-dimensional atomic structure of crystalline materials. The major theme of this article is to derive the novel theory of neutrosophic fuzzy rough (NFR) information and its valuable operational laws. Furthermore, we evaluate the Aczel-Alsina operational laws based on the NFR information. Furthermore, we derive the NFR Aczel-Alsina weighted averaging (NFRAAWA) operator, NFR Aczel-Alsina ordered weighted averaging (NFRAAOWA) operator, and NFR Aczel-Alsina hybrid averaging (NFRAAHA) operator. Some suitable properties for the above operators are also invented in detail. Additionally, to find the major principle of the X-ray analysis of crystal structure, we illustrate the procedure of multi-attribute decision-making (MADM) techniques based on the invented operators for NSs. Finally, we draw a comparative analysis between the proposed operators and some prevailing techniques to evaluate the supremacy and validity of the derived operators.