Pythagorean Fuzzy Multigranulation Rough Set over Two Universes and Its Applications in Merger and Acquisition

Pythagorean fuzzy set, an extension form of intuitionistic fuzzy set, which owns many advantages for dealing with uncertainties, and it has been developed to deal with various complex decision‐making problems. Furthermore, based on lower and upper approximations induced by multiple binary relations, the multigranulation rough set has become one of the most promising directions in rough set theory. To combine the two ideas and explore the practical decision‐making problems, we develop a new multigranulation rough set model, called Pythagorean fuzzy multigranulation rough set over two universes. In the framework of our study, we introduce the models of Pythagorean fuzzy rough set over two universes and Pythagorean fuzzy multigranulation rough set over two universes, respectively. Both the definition and basic properties are explored. Finally, we give a general algorithm, which is applied to a decision‐making problem in merger and acquisition, and the effectiveness of the algorithm is demonstrated by a numerical example.

[1]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy logics as tools for evaluation of Data Mining processes , 2015, Knowl. Based Syst..

[2]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[3]  Salvatore Greco,et al.  Rough approximation by dominance relations , 2002, Int. J. Intell. Syst..

[4]  Wei Guo,et al.  The Fuzzy Decision-Making Model Based on Rough Set of the M&A of Resource-Typed Enterprises , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

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

[6]  S. Pal,et al.  Image enhancement using fuzzy set , 1980 .

[7]  Ya-Qing Bi,et al.  New Proofs of Some q-Summation and q-Transformation Formulas , 2014, TheScientificWorldJournal.

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

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

[10]  Donald H. Kraft,et al.  Fuzzy Set Techniques in Information Retrieval , 1999 .

[11]  Yuhua Qian,et al.  NMGRS: Neighborhood-based multigranulation rough sets , 2012, Int. J. Approx. Reason..

[12]  Atanu Chaudhuri,et al.  Project network-oriented materials management policy for complex projects: a Fuzzy Set Theoretic approach , 2015 .

[13]  Guoyin Wang,et al.  Rough Sets, Fuzzy Sets, Data Mining and Granular Computing , 2011, Lecture Notes in Computer Science.

[14]  Zhongzhi Shi,et al.  APPLICATIONS OF INCLUSION DEGREE IN ROUGH SET THEORY , 2002 .

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

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

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

[18]  Kwangsoo Kim,et al.  Identification and evaluation of corporations for merger and acquisition strategies using patent information and text mining , 2013, Scientometrics.

[19]  Jiye Liang,et al.  Rough Set Approximation Based on Dynamic Granulation , 2005, RSFDGrC.

[20]  Xiangping Kang,et al.  Rough set model based on formal concept analysis , 2013, Inf. Sci..

[21]  Caihui Liu,et al.  Covering Rough Set Model Based on Multi-granulations , 2011, RSFDGrC.

[22]  Y. Yao,et al.  A NON-NUMERIC APPROACH TO UNCERTAIN REASONING , 1995 .

[23]  Chen Xiang,et al.  Coal Mine Enterprises Merger & Acquisition Efficiency Prediction Based on Support Vector Machine , 2010, WKDD.

[24]  Chung-Tsen Tsao,et al.  Applying a fuzzy multiple criteria decision-making approach to the M&A due diligence , 2009, Expert Syst. Appl..

[25]  Janusz Kacprzyk,et al.  Intuitionistic Fuzzy Decision Tree: A New Classifier , 2014, IEEE Conf. on Intelligent Systems.

[26]  James P. Walsh,et al.  Doing a deal: Merger and acquisition negotiations and their impact upon target company top management turnover , 1989 .

[27]  Jiye Liang,et al.  Incomplete Multigranulation Rough Set , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[28]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[29]  Jiye,et al.  Pessimistic Rough Decision , 2010 .

[30]  Luke Georghiou,et al.  Integrating technology into merger and acquisition decision making , 1998 .

[31]  Gleb Beliakov,et al.  Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs , 2014, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[32]  Zongben Xu,et al.  Rough Set Models on Two universes , 2004, Int. J. Gen. Syst..

[33]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[34]  Tian Liang,et al.  The Study on the Multi-object Fuzzy Decision-Making of the M&A of Resource –Typed Enterprises Based on Rough Sets , 2012 .

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

[36]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[37]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[38]  DEYU LI,et al.  On Knowledge Reduction In Inconsistent Decision Information Systems , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[39]  M. R. Seikh,et al.  Matrix Games with Intuitionistic Fuzzy Pay-offs , 2015 .

[40]  Myeong-gu Seo,et al.  Understanding the Human Side of Merger and Acquisition , 2005 .

[41]  Debi Prasanna Acharjya,et al.  Algebraic Properties of Rough Set on Two Universal Sets based on Multigranulation , 2014, Int. J. Rough Sets Data Anal..

[42]  Jiye Liang,et al.  International Journal of Approximate Reasoning Multigranulation Decision-theoretic Rough Sets , 2022 .

[43]  Witold Pedrycz,et al.  Positive approximation: An accelerator for attribute reduction in rough set theory , 2010, Artif. Intell..

[44]  Xizhao Wang,et al.  On the generalization of fuzzy rough sets , 2005, IEEE Transactions on Fuzzy Systems.

[45]  Vicenç Torra,et al.  Hesitant fuzzy sets , 2010, Int. J. Intell. Syst..

[46]  Yiyu Yao,et al.  MGRS: A multi-granulation rough set , 2010, Inf. Sci..

[47]  Ronald R. Yager,et al.  Suggesting Recommendations Using Pythagorean Fuzzy Sets illustrated Using Netflix Movie Data , 2014, IPMU.

[48]  Ronald R. Yager,et al.  Pythagorean fuzzy subsets , 2013, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).

[49]  Shuqun Luo,et al.  Rough Atanassov's Intuitionistic Fuzzy Sets Model over Two Universes and Its Applications , 2014, TheScientificWorldJournal.

[50]  Bingzhen Sun,et al.  Fuzzy rough set model on two different universes and its application , 2011 .

[51]  Ramon E. Moore,et al.  Interval analysis and fuzzy set theory , 2003, Fuzzy Sets Syst..

[52]  Zeshui Xu,et al.  Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets , 2014, Int. J. Intell. Syst..

[53]  Jiye Liang,et al.  International Journal of Approximate Reasoning an Efficient Rough Feature Selection Algorithm with a Multi-granulation View , 2022 .

[54]  Ronald R. Yager,et al.  Pythagorean Membership Grades in Multicriteria Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

[55]  H. Zimmermann,et al.  Fuzzy Set Theory and Its Applications , 1993 .

[56]  Wei Wei,et al.  A comparative study of rough sets for hybrid data , 2012, Inf. Sci..

[57]  Ronald R. Yager,et al.  Pythagorean Membership Grades, Complex Numbers, and Decision Making , 2013, Int. J. Intell. Syst..

[58]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..