Attribute-Object Ordered Soft Set and its Applications in Decision-Making Problems Based on Comparison of Attributes and Objects

This paper introduces a novel mathematical construct, termed the "Attribute-Object Ordered Soft Set," which addresses a fundamental challenge encountered in practical scenarios. In real-life applications, it is a common requirement to compare not only the attributes of individual objects but also the objects themselves based on their specific attributes. To effectively address this requirement, the Attribute-Object Ordered Soft Set mandates that both objects and attributes must be subjected to a systematic ordering process. This imposition of order facilitates the handling of complex decision-making problems in real-world contexts. To demonstrate the applicability and utility of this concept, the paper presents a suite of algorithmic solutions tailored to various classes of real-life decision-making challenges. These algorithms are crafted to provide effective and systematic methodologies for tackling a diverse array of decision-making problems, further enhancing the practicality and versatility of the Attribute-Object Ordered Soft Set in real-world contexts.