Medical Diagnosis Based on Single-Valued Neutrosophic Probabilistic Rough Multisets over Two Universes

In real-world diagnostic procedures, due to the limitation of human cognitive competence, a medical expert may not conveniently use some crisp numbers to express the diagnostic information, and plenty of research has indicated that generalized fuzzy numbers play a significant role in describing complex diagnostic information. To deal with medical diagnosis problems based on generalized fuzzy sets (FSs), the notion of single-valued neutrosophic multisets (SVNMs) is firstly used to express the diagnostic information in this article. Then the model of probabilistic rough sets (PRSs) over two universes is applied to analyze SVNMs, and the concepts of single-valued neutrosophic rough multisets (SVNRMs) over two universes and probabilistic rough single-valued neutrosophic multisets (PRSVNMs) over two universes are introduced. Based on SVNRMs over two universes and PRSVNMs over two universes, single-valued neutrosophic probabilistic rough multisets (SVNPRMs) over two universes are further established. Next, a three-way decisions model by virtue of SVNPRMs over two universes in the context of medical diagnosis is constructed. Finally, a practical case study along with a comparative study are carried out to reveal the accuracy and reliability of the constructed three-way decisions model.

[1]  R. Yager.  ON THE THEORY OF BAGS , 1986 .

[2]  Bingzhen Sun,et al.  Multigranulation rough set theory over two universes , 2015, J. Intell. Fuzzy Syst..

[3]  Chao Zhang,et al.  Pythagorean Fuzzy Multigranulation Rough Set over Two Universes and Its Applications in Merger and Acquisition , 2016, Int. J. Intell. Syst..

[4]  S. Karthikeyan,et al.  An ensemble design of intrusion detection system for handling uncertainty using Neutrosophic Logic Classifier , 2012, Knowl. Based Syst..

[5]  D. K. Mak,et al.  A Fuzzy Probabilistic Method for Medical Diagnosis , 2015, Journal of Medical Systems.

[6]  Florentin Smarandache.  Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic , 2003, EUSFLAT Conf..

[7]  F. Smarandache,et al.  Relations on neutrosophic multi sets with properties , 2015, 1506.04025.

[8]  André Rogatko,et al.  A neutrosophic description logic , 2006, 2006 IEEE International Conference on Granular Computing.

[9]  Florentin Smarandache,et al.  An Extension of Neutrosophic AHP-SWOT Analysis for Strategic Planning and Decision-Making , 2018, Symmetry.

[10]  Florentin Smarandache,et al.  Single valued neutrosophic graphs: Degree, order and size , 2016, 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[11]  Muhammad Akram,et al.  A New Multi-Attribute Decision-Making Method Based on m-Polar Fuzzy Soft Rough Sets , 2017, Symmetry.

[12]  F. Smarandache.  A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

[13]  Le Hoang Son,et al.  Intuitionistic fuzzy recommender systems: An effective tool for medical diagnosis , 2015, Knowl. Based Syst..

[14]  Deyu Li,et al.  An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis , 2017 .

[15]  Jiye Liang,et al.  Hesitant fuzzy linguistic rough set over two universes model and its applications , 2018, Int. J. Mach. Learn. Cybern..

[16]  Juan Lu,et al.  Granular Structure of Type-2 Fuzzy Rough Sets over Two Universes , 2017, Symmetry.

[17]  Zdzisław Pawlak,et al.  Can Bayesian confirmation measures be useful for rough set decision rules? , 2004, Eng. Appl. Artif. Intell..

[18]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[19]  Kyung-Soo Han,et al.  A fuzzy medical diagnosis based on quantiles of diagnostic measures , 2016, J. Intell. Fuzzy Syst..

[20]  Chao Zhang,et al.  A Dual Hesitant Fuzzy Multigranulation Rough Set over Two-Universe Model for Medical Diagnoses , 2015, Comput. Math. Methods Medicine.

[21]  Yiyu Yao,et al.  Two Bayesian approaches to rough sets , 2016, Eur. J. Oper. Res..

[22]  Yuhua Qian,et al.  Multigranulation fuzzy rough set over two universes and its application to decision making , 2017, Knowl. Based Syst..

[23]  Bingzhen Sun,et al.  A fuzzy rough set approach to emergency material demand prediction over two universes , 2013 .

[24]  S. Samanta,et al.  Single valued neutrosophic multisets , 2015 .

[25]  Yiyu Yao,et al.  Three-way decisions with probabilistic rough sets , 2010, Inf. Sci..

[26]  Mumtaz Ali,et al.  A Novel Clustering Algorithm in a Neutrosophic Recommender System for Medical Diagnosis , 2017, Cognitive Computation.

[27]  Dominik Slezak,et al.  The investigation of the Bayesian rough set model , 2005, Int. J. Approx. Reason..

[28]  Jun Ye,et al.  Dice Similarity Measure between Single Valued Neutrosophic Multisets and Its Application in Medical Diagnosis , 2015 .

[29]  Florentin Smarandache,et al.  Complex neutrosophic set , 2016, Neural Computing and Applications.

[30]  Florentin Smarandache,et al.  n-Valued Refined Neutrosophic Logic and Its Applications to Physics , 2013, ArXiv.

[31]  Yiyu Yao,et al.  Three-Way Decisions and Cognitive Computing , 2016, Cognitive Computation.

[32]  Chao Zhang,et al.  Steam turbine fault diagnosis based on single-valued neutrosophic multigranulation rough sets over two universes , 2016, J. Intell. Fuzzy Syst..

[33]  Yanqing Zhang,et al.  Interval Neutrosophic Sets and Logic: Theory and Applications in Computing , 2005, ArXiv.

[34]  Edmundas Kazimieras Zavadskas,et al.  The Selection of Wagons for the Internal Transport of a Logistics Company: A Novel Approach Based on Rough BWM and Rough SAW Methods , 2017, Symmetry.

[35]  Haiyan Zhao,et al.  An approach to emergency decision making based on decision-theoretic rough set over two universes , 2016, Soft Comput..

[36]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[37]  Arun Kumar Sangaiah,et al.  Merger and Acquisition Target Selection Based on Interval Neutrosophic Multigranulation Rough Sets over Two Universes , 2017, Symmetry.

[38]  Shouyang Wang,et al.  Fuzzy probabilistic rough set model on two universes and its applications , 2013, Int. J. Approx. Reason..

[39]  Peide Liu,et al.  Linguistic Neutrosophic Generalized Partitioned Bonferroni Mean Operators and Their Application to Multi-Attribute Group Decision Making , 2018, Symmetry.

[40]  Yiyu Yao,et al.  A Decision Theoretic Framework for Approximating Concepts , 1992, Int. J. Man Mach. Stud..

[41]  Xiaohong Zhang,et al.  Single-Valued Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators for Multi-Attribute Decision Making , 2018, Symmetry.

[42]  Chao Zhang,et al.  Multigranulation rough set model in hesitant fuzzy information systems and its application in person-job fit , 2017, Int. J. Mach. Learn. Cybern..

[43]  Xiaohong Zhang,et al.  New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets , 2018, Symmetry.

[44]  S. K. Wong,et al.  Comparison of the probabilistic approximate classification and the fuzzy set model , 1987 .

[45]  Francisco Herrera,et al.  A Historical Account of Types of Fuzzy Sets and Their Relationships , 2016, IEEE Transactions on Fuzzy Systems.

[46]  Z. Bo.  Variable precision rough sets model based on(α,τ) limited similarity relation , 2009 .

[47]  Qiang Li,et al.  A Dual Hesitant Fuzzy Rough Pattern Recognition Approach Based on Deviation Theories and Its Application in Urban Traffic Modes Recognition , 2017, Symmetry.

[48]  F. Smarandache,et al.  An Introduction to Bipolar Single Valued Neutrosophic Graph Theory , 2016 .

[49]  Xia Xiao,et al.  Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes , 2017, Int. J. Approx. Reason..

[50]  Jun Ye,et al.  Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making , 2017, Symmetry.

[51]  Jun Ye,et al.  Medical Diagnosis Using Distance-Based Similarity Measures of Single Valued Neutrosophic Multisets , 2015 .

[52]  Bingzhen Sun,et al.  Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision‐making , 2015, Expert Syst. J. Knowl. Eng..

[53]  Jun Ye,et al.  The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making , 2018, Symmetry.

[54]  Yan-Ling Liu,et al.  A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application , 2017, Symmetry.