An Innovative Method for Attribute Reduction: Weighted Attribute Concepts for Probabilistic Analysis of Decision Attributes

Abstract

Attribute reduction, a seminal aspect of data analysis, primarily hinges on the indiscernibility matrix. Previous studies have explored the weight of an attribute via various methods, yet achieving optimal reduction remains elusive. This study proposes a novel approach to optimal reduction, leveraging the concept of weighted attributes based on the probability values of core and non-core elements. This approach scrutinizes the accuracy of both core and non-core attributes, thereby enhancing our comprehension of the object's attributes. The weighted attribute concept is derived in light of entropy information and the indiscernibility matrix. A discernibility matrix aids in ascertaining the reduct, whereas entropy information facilitates the analysis of the weight of uncertain data. By deploying decision attributes, we derive the core and its corresponding probabilistic value, establishing an algebraic structure as an ordered pair of objects with associated weight concepts. This structure further enables the investigation of the consistency set and the join (meet) irreducible set employing weighted attribute concepts. Ultimately, optimal reduction is determined by the weight of non-core elements, allowing a comprehensive analysis of the information system and procurement of its essential attributes for decision-making. The proposed concept of weighted attributes is elucidated using a biological dataset.