A Method for Fuzzy Soft Sets in Decision Making Based on Grey Relational Analysis and D-S Theory of Evidence: Application to Medical Diagnosis

A method based on grey relational analysis and D-S theory of evidence is proposed for fuzzy soft sets in decision making. Firstly, grey relational analysis is used to calculate grey mean relational degrees and determine uncertain degrees of parameters. Then based on uncertain degrees, suitable mass functions of different independent alternatives with different parameters can be constructed. Next, D-S rule of evidence combination is applied to aggregate these alternatives into a collective alternative. Finally, these alternatives are ranked and the best alternative(s) are obtained. Moreover, the effectiveness and feasibility of this method are demonstrated by comparing with the mean potentiality approach and giving an application to medical diagnosis.

[1]  Pabitra Kumar Maji,et al.  FUZZY SOFT SETS , 2001 .

[2]  Naim Çag ˘ man,et al.  Soft set theory and uni-int decision making , 2010 .

[3]  Shyamal Kumar Mondal,et al.  A balanced solution of a fuzzy soft set based decision making problem in medical science , 2012, Appl. Soft Comput..

[4]  Desheng Dash Wu,et al.  The method of grey related analysis to multiple attribute decision making problems with interval numbers , 2005, Math. Comput. Model..

[5]  Gui-Wu Wei,et al.  Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making , 2011, Expert Syst. Appl..

[6]  Athar Kharal,et al.  On Fuzzy Soft Sets , 2009, Adv. Fuzzy Syst..

[7]  Richard W. Jones,et al.  A framework for intelligent medical diagnosis using the theory of evidence , 2002, Knowl. Based Syst..

[8]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[9]  A. R. Roy,et al.  An application of soft sets in a decision making problem , 2002 .

[10]  Bo-Suk Yang,et al.  Application of Dempster–Shafer theory in fault diagnosis of induction motors using vibration and current signals , 2006 .

[11]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[12]  Tsau Young Lin,et al.  Combination of interval-valued fuzzy set and soft set , 2009, Comput. Math. Appl..

[13]  D. Molodtsov.  Soft set theory—First results , 1999 .

[14]  Young Bae Jun,et al.  Soft BCK/BCI-algebras , 2008, Comput. Math. Appl..

[15]  Wei-Zhi Wu,et al.  Knowledge reduction in random information systems via Dempster-Shafer theory of evidence , 2005, Inf. Sci..

[16]  Liqun Gao,et al.  Letter to the editor: Comment on A fuzzy soft set theoretic approach to decision making problems , 2009 .

[17]  Feng Feng,et al.  Soft subsets and soft product operations , 2013, Inf. Sci..

[18]  Yong Tang,et al.  An adjustable approach to intuitionistic fuzzy soft sets based decision making , 2011 .

[19]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[20]  Young Bae Jun,et al.  Fuzzy soft set theory applied to BCK/BCI-algebras , 2010, Comput. Math. Appl..

[21]  Eric C. C. Tsang,et al.  The parameterization reduction of soft sets and its applications , 2005 .

[22]  Feng Feng,et al.  Generalized uni-int decision making schemes based on choice value soft sets , 2012, Eur. J. Oper. Res..

[23]  Young Bae Jun,et al.  Soft semirings , 2008, Comput. Math. Appl..

[24]  Shanlin Yang,et al.  CSMC: A combination strategy for multi-class classification based on multiple association rules , 2008, Knowl. Based Syst..

[25]  Chyi Hwang,et al.  An FFT-based algorithm for 2D power series expansions , 1999 .

[26]  A. R. Roy,et al.  A fuzzy soft set theoretic approach to decision making problems , 2007 .

[27]  Zhi Kong,et al.  Application of fuzzy soft set in decision making problems based on grey theory , 2011, J. Comput. Appl. Math..

[28]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[29]  Naim Çagman,et al.  Soft matrix theory and its decision making , 2010, Comput. Math. Appl..

[30]  Young Bae Jun,et al.  An adjustable approach to fuzzy soft set based decision making , 2010, J. Comput. Appl. Math..

[31]  Li Peng,et al.  Interval-valued Intuitionistic Fuzzy Numbers Decision-making Method Based on Grey Incidence Analysis and D-S Theory of Evidence , 2011 .

[32]  Desheng Dash Wu,et al.  Supplier selection in a fuzzy group setting: A method using grey related analysis and Dempster-Shafer theory , 2009, Expert Syst. Appl..

[33]  Naim Çagman,et al.  Soft set theory and uni-int decision making , 2010, Eur. J. Oper. Res..

[34]  Kun-Li Wen,et al.  Applying Grey Relational Analysis and Grey Decision-Making to evaluate the relationship between company attributes and its financial performance - A case study of venture capital enterprises in Taiwan , 2007, Decis. Support Syst..

[35]  Young Bae Jun,et al.  Applications of soft sets in ideal theory of BCK/BCI-algebras , 2008, Inf. Sci..

[36]  Ju Wang,et al.  Extending soft sets with description logics , 2010, Comput. Math. Appl..