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.

In this paper, the concepts of neutrosophic complex graph, complete neutrosophic complex graph, strong neutrosophic complex graph, balanced neutrosophic complex graph and strictly balanced neutrosophic complex graph are introduced. Some of the interesting properties and related examples are established.

TOPSIS (technique for order preference by similarity to ideal solution) is a mathematical approach employed in the context of multi-criteria decision-making. Its primary purpose is to establish a ranking among various alternatives by taking into consideration multiple attributes or criteria. This method utilizes distance metrics to gauge the nearness of each alternative to both the ideal and anti-ideal solutions. Ultimately, its goal is to facilitate the identification of the most optimal alternative. In this era of uncertainty, many parents grapple with myriad uncertainties when it comes to selecting the right educational institution for their children. This chapter provides an initial glimpse into the neutrosophic pythagorean plithogenic hypersoft set (N_pphs) along with its fundamental definition. Additionally, an algorithm has been devised for the TOPSIS methodology, accompanied by a practical numerical illustration. This is intended to assist parents in making an informed decision when choosing the most suitable school for their children with their set of criteria.

The new concepts of a neutrosophic Gδ set and neutrosophic Gδ-α-locally closed sets are introduced. Also, a neutrosophic εGδ-α-locally quasi neighborhood, neutrosophic Gδ-α-locally continuous function, neutrosophic Gδ-α-local T2 space, neutrosophic Gδ-α-local Urysohn space, neutrosophic Gδ-α-local connected space, and neutrosophic Gδ-α-local compact space are discussed and some interesting properties are established.