A general framework for multi-granulation rough decision-making method under q-rung dual hesitant fuzzy environment

In the realistic decision-making (DM) process, the DM results were provided by multiple DM experts, which are more accurate than those based on one DM expert. Therefore, the multi-granulation rough set (MGRS) model is more accurate in DM problems. It is imperative to apply the idea of multi-granulation to the complex fuzzy uncertain information. By combining q-rung dual hesitant fuzzy sets (q-DHFSs) with multi-granulation rough sets (MGRSs) over two universes, we propose a q-rung dual hesitant fuzzy multi-granulation rough set (q-RDHFMGRS) over two universes, and prove some of their basic properties. Then, based on this model, we propose a new multi-attribute DM algorithm. Finally, we validate the practicability and validity of the algorithm through an example of medical diagnosis.

[1]  Zeshui Xu,et al.  Dual Hesitant Fuzzy Sets , 2012, J. Appl. Math..

[2]  Xiaomin Zhu,et al.  Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making , 2019, J. Intell. Fuzzy Syst..

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

[4]  Asad Ali,et al.  Pythagorean Fuzzy Weighted Averaging Aggregation Operator and its Application to Decision Making Theory , 2017 .

[5]  Jie Wang,et al.  Some q‐rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization , 2018, Int. J. Intell. Syst..

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

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

[8]  M. Tadi,et al.  Optimal infinite-dimensional estimator and compensator for a Timoshenko beam , 1994 .

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

[10]  Guiwu Wei,et al.  Dual hesitant pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making , 2017 .

[11]  Runtong Zhang,et al.  Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making , 2019, Soft Comput..

[12]  Harish Garg,et al.  Novel neutrality operation–based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis , 2019, Int. J. Intell. Syst..

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

[14]  Haoyang Wu,et al.  An Interval Type-2 Fuzzy Rough Set Model for Attribute Reduction , 2009, IEEE Transactions on Fuzzy Systems.

[15]  Harish Garg,et al.  Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision‐making process , 2018, Int. J. Intell. Syst..

[16]  Lan Shu,et al.  Hesitant fuzzy rough set over two universes and its application in decision making , 2017, Soft Comput..

[17]  Zeshui Xu,et al.  Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators , 2018, Complex..

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

[19]  Shu-Ping Wan,et al.  Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees , 2017, Knowledge and Information Systems.

[20]  Manish Aggarwal,et al.  Probabilistic Variable Precision Fuzzy Rough Sets , 2016, IEEE Transactions on Fuzzy Systems.

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

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

[23]  Harish Garg,et al.  Exponential operation and aggregation operator for q‐rung orthopair fuzzy set and their decision‐making method with a new score function , 2018, Int. J. Intell. Syst..

[24]  Jianming Zhan,et al.  Covering-based intuitionistic fuzzy rough sets and applications in multi-attribute decision-making , 2018, Artificial Intelligence Review.

[25]  S. K. Wong,et al.  A NON-NUMERIC APPROACH TO UNCERTAIN REASONING , 1995 .

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

[27]  Lan Shu,et al.  Dual Hesitant Fuzzy Soft Set and Its Properties , 2016 .

[28]  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..

[29]  Harish Garg,et al.  Dual Hesitant Fuzzy Soft Aggregation Operators and Their Application in Decision-Making , 2018, Cognitive Computation.

[30]  Wei-Zhi Wu,et al.  Intuitionistic Fuzzy Rough Set-Based Granular Structures and Attribute Subset Selection , 2019, IEEE Transactions on Fuzzy Systems.

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

[32]  Harish Garg,et al.  Interval-Valued $q$ -Rung Orthopair 2-Tuple Linguistic Aggregation Operators and Their Applications to Decision Making Process , 2019, IEEE Access.

[33]  Muhammad Sajjad Ali Khan,et al.  Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making , 2018, Granular Computing.

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

[35]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[36]  Shyi-Ming Chen,et al.  Multiple-Attribute Group Decision-Making Based on q-Rung Orthopair Fuzzy Power Maclaurin Symmetric Mean Operators , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[37]  Peng Wang,et al.  Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making , 2018, Int. J. Intell. Syst..

[38]  Yong Yang,et al.  Pythagorean Fuzzy Choquet Integral Based MABAC Method for Multiple Attribute Group Decision Making , 2016, Int. J. Intell. Syst..

[39]  Peide Liu,et al.  Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making , 2018, Int. J. Intell. Syst..

[40]  Harish Garg,et al.  Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process , 2020, J. Ambient Intell. Humaniz. Comput..

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

[42]  Jianming Zhan,et al.  Two types of coverings based multigranulation rough fuzzy sets and applications to decision making , 2018, Artificial Intelligence Review.

[43]  Huafei Sun,et al.  Cubic Pythagorean fuzzy sets and their application to multi-attribute decision making with unknown weight information , 2019, J. Intell. Fuzzy Syst..

[44]  Muhammad Sajjad Ali Khan,et al.  Pythagorean hesitant fuzzy sets and their application to group decision making with incomplete weight information , 2017, J. Intell. Fuzzy Syst..

[45]  Hong-yu Zhang,et al.  The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making , 2015, Int. J. Syst. Sci..

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

[47]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[48]  Luis Alberto Rodríguez-Picón,et al.  MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making , 2018, Complex..

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

[50]  Zeshui Xu,et al.  The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets , 2017, Appl. Soft Comput..

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

[52]  Gui-Wu Wei,et al.  Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making , 2017, Int. J. Knowl. Based Intell. Eng. Syst..

[53]  Runtong Zhang,et al.  Some q-rung orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making , 2018 .

[54]  Wei-Zhi Wu,et al.  Granulation selection and decision making with multigranulation rough set over two universes , 2018, Int. J. Mach. Learn. Cybern..

[55]  J. Goguen.  L-fuzzy sets , 1967 .

[56]  Ronald R. Yager,et al.  Generalized Orthopair Fuzzy Sets , 2017, IEEE Transactions on Fuzzy Systems.

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

[58]  Vicenç Torra,et al.  On hesitant fuzzy sets and decision , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[59]  Jun Wang,et al.  Some q-Rung Dual Hesitant Fuzzy Heronian Mean Operators with Their Application to Multiple Attribute Group Decision-Making , 2018, Symmetry.