A LATTICE STRUCTURE OF Z-SOFT COVERING BASED ROUGH SET AND ITS APPLICATION

A LATTICE STRUCTURE OF Z-SOFT COVERING BASED ROUGH SET AND ITS APPLICATION

S. Pavithra, A. Manimaran

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Abstract

The aim of this paper is to construct the lattice structure for Z-soft covering based rough set. First, we de ne an equivalence relation R0 on a universal set to obtain the equivalence classes induced by Z-soft covering-based rough set. Also, we de ne a relation RS on the family of Z-soft covering-based rough set (TS) to show that the relation RS is a poset on TS. Second, we de ne two operations join _ and meet ^ on TS. Using these two operations, we prove that every pair of elements of RS has a least upper bound and a greatest lower bound and as a result, TS is a lattice. Finally, we develop a novel Multiple Attribute Group Decision Making (MAGDM) model using Z-soft covering based rough set in medical diagnosis to determine the patients at high risk of chronic kidney disease using the collected data from the UCI Machine Learning Repository.

Keywords

Soft set, Rough set, Soft covering based rough set, Lattice.