Soft Covering Based Rough Sets and Their Application

Abstract

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty.

A comparative study for medical diagnosis of prostate cancer

“…Method 1. In [25], we give a multi-criteria group decision making method using soft covering approximations at Feng's method [9]. This method can be summarized as follows:…”

“…Definition 12. [25] Let S = (U,C G ) be a soft covering approximation space. For a set X ⊆ U, the soft covering lower and upper approximations are respectively defined as…”

“…Yüksel et al [25] used soft covering approximations at Feng's method and they presented an example in medicine which aims to obtain the optimal choice for applying biopsy to the patients with prostate cancer risk.…”

“…In this study, we apply Chen's method to a medicine problem calculating the risk of prostate cancer and we compare the obtained results with an other method's results given by us [25]. For this process, it is used as laboratory data, prostate specific antigen (PSA), free prostate specific antigen (fPSA), prostate volume (PV) and age of the patient.…”

Leukemia Image Segmentation Using a Hybrid Histogram-Based Soft Covering Rough K-Means Clustering Algorithm

“…Maji et al [9] improved Molodtsov's idea by introducing several operations in soft set theory. In [10], the researcher investigated a soft covering-based rough set as a new kind of soft rough set. This method is a combination of a covering soft set and rough set.…”