NTMSCI 7, No. 1, 102-112 (2019) 102 New Trends in Mathematical Sciences http://dx.doi.org/10.20852/ntmsci.2019.347 A comparative study for medical diagnosis of prostate cancer Naime Demirtas ¸ (Tozlu) 1 , Tugba Han Dizman (Simsekler) 2 , Bijan Davvaz 3 and Saziye Yuksel 4 1 Mersin University, Department of Mathematics, Mersin, Turkey 2 Gaziantep University, Department of Mathematics Education, Gaziantep, Turkey 3 Yazd University, Department of Mathematics, Yazd, Iran 4 Selcuk University, Department of Mathematics, Konya, Turkey Received: 4 September 2018, Accepted: 17 January 2019 Published online: 29 March 2019. Abstract: In recent years great attention has been paid to studies on artiﬁcial intelligence since it can be applied easily to several areas like medical diagnosis, engineering and economics, among others. In this paper we present an example in medicine which aims to ﬁnd the patients with high prostate cancer risk using a multi-criteria decision making method. Also we compare this method with another method which we studied before. We discuss which method is more convenient. Our datas are prostate speciﬁc antigen (PSA), free prostate speciﬁc antigen (fPSA), prostate volume (PV) and age factors of 78 patients from Selcuk University Meram Medicine Faculty. Keywords: Uncertainty modelling, multi-criteria decision making, prostate cancer, Fuzzy TOPSIS, soft covering approximations. 1 Introduction We can not solve the problems by using mathematical tools generally in the social life since in mathematics the concepts are precise and not subjective. Some theories were developed to eliminate this lack of vagueness such as fuzzy set theory [28] and rough set theory [17]. But all of these theories have their own difﬁculties. Soft set theory [15] is introduced by Molodtsov as a new approach to the vagueness and based on parametrization operation. It is shown that this new theory is free from some difﬁcultness seen most useful theories of fuzzy set and rough set. In a short time the theory gave rise to many researchers and applications. Since soft set is more general concept than fuzzy set, the researchers lean to solve the problems by soft sets. Chen [5] extended the concept of TOPSIS (Technique for order performance by similarity to ideal solution) [10] to develop a methodology for solving multi-person multi-criteria decision making problems in fuzzy environment. De et al. [6] studied Sanchez’s [20, 21] method of medical diagnosis using an intuitionistic fuzzy set. Feng [9] discussed soft set based group decision making in 2011. This study can be seen as a ﬁrst attempt toward the possible application of soft rough approximations in multi-criteria group decision making under vagueness. C ¸elik and Yamak [4] applied fuzzy soft set theory through well-known Sanchez’s approach for medical diagnosis using fuzzy arithmetic operations. In [27], soft set theory was introduced into grey system theory to solve multi-attribute decision making problems in which evaluation attribute sets are different and evaluation decision making values are interval grey numbers. Y¨ uksel 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. Prostate cancer is the second most common cause of cancer death among men in most industrialized countries. It depends on various factors as family’s cancer history, age, ethnic background, and the level of prostate speciﬁc antigen (PSA) in the blood. Since PSA is a substance produced by the prostate, it is very important factor to an initial diagnosis c  2019 BISKA Bilisim Technology ∗ Corresponding author e-mail: tsimsekler@gantep.edu.tr