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 concept of a strong $n$-Connected Total Perfect $k$-connected total perfect $k$-dominating set and a weak $n$-connected total perfect $k$-dominating set in fuzzy graphs is introduced. In the current work, the triple-connected total perfect dominating set is modified to an $n$-connected total perfect $k$-dominating set $n_{ctpkD}$(G) and number $\gamma n_{ctpD}\left(G\right).$ New definitions are compared with old ones. Strong and weak $n$-connected total perfect $k$-dominating set and number of fuzzy graphs are obtained. The results of those fuzzy sets are discussed with the definitions of spanning fuzzy graphs, strong and weak arcs, dominating sets, perfect dominating sets, generalization of triple-connected total perfect dominating sets of fuzzy graphs, complete, connected, bipartite, cut node, tree, bridge and some other new notions of fuzzy graphs which are analyzed with a strong and weak $n_{ctpkD}$(G) set of fuzzy graphs. The order and size of the strong and weak $n_{ctpkD}\left(\mathrm{G}\right)$ fuzzy set are studied. Additionally, a few related theorems and statements are analyzed.