T. Yogashanthi, Shakeela Sathish, and K. Ganesan. International Journal of Fuzzy Logic and Intelligent Systems 2023;23:34-43. https://doi.org/10.5391/IJFIS.2023.23.1.34

The formal concept of lattice plays a vital role in knowledge discovery. Reduction of the attribute has many applications in machine learning technology and data mining fields. In this paper, we introduce an object ranking concept to define a consistency set and the reduction of the attributes by structural features. An incomplete information system works on the three-way concepts using the SE-ISI Context. The granular was emphasized with join (meet) irreducible sets using the object ranking concepts. A dual operator is defined based on the object ranking concepts and its properties and conditions are verified. Hence, this elaborates on the four kinds of reduction of the attributes. The ordered pairs give the knowledge of the attributes that deal with the interval set of both the approximation of rough set theory concerning the objects. Therefore, the relationship between four kinds of reduction of the attribute was appropriate to access the consistency set using the object ranking concepts by some of the theorems and examples.

The discernibility matrix acts as an efficient tool to determine decision-making problems. The discernibility matrix enhances both the logical and theoretical knowledge of an information system. Also, it evaluated the boolean function for enhancing its relevant properties. In this paper, a granular lattice has been discussed to define a consistent set, based on object-oriented concepts. An ordered pair of attributes and objects was constructed to determine the granular lattice using indiscernibility relation. We have introduced two sets, namely the maximum and minimum sets to analyze the indiscernibility object. The indiscernibility object investigates the upper approximation space and extended its effectiveness towards maximum and minimum sets. Furthermore, the properties of the maximum set and minimum set are classified using the granularity concept. An equivalency condition is framed by the maximum set and its results are examined with the help of some theorems and lemma.