Extension of Einstein geometric operators to multi-attribute decision making under q-rung orthopair fuzzy information

Aggregation operators are mathematical functions and essential tools of unifying the several inputs into single valuable output. The purpose of this paper is to analyze the aggregation operators (AOs) under the q-rung orthopair fuzzy environment with the help of Einstein norms operations. This paper presents AOs, namely, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG), q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG), generalized q-rung orthopair fuzzy Einstein weighted geometric (Gq-ROFEWG), generalized q-rung orthopair fuzzy Einstein ordered weighted geometric (Gq-ROFEOWG) operators. Some properties of these operators are explained. An algorithmic model to deal with multi-attribute decision making problems in q-rung orthopair fuzzy(q-ROF) environment using generalized q-ROF Einstein weighted geometric operator is established. These operators can remunerate for the possible asymmetric roles of the attributes that represent the problem. At the end, to prove the validity and feasibility of the proposed model, we give applications for the selection of location of thermal power station and selection of best cardiac surgeon. The comparison analysis with other existing operators shows the reliability of our work.

[1]  Ghous Ali,et al.  Group decision-making approach under multi (Q, N)-soft multi granulation rough model , 2019, Granular Computing.

[2]  Runtong Zhang,et al.  Some Partitioned Maclaurin Symmetric Mean Based on q-Rung Orthopair Fuzzy Information for Dealing with Multi-Attribute Group Decision Making , 2018, Symmetry.

[3]  Jianping Chen,et al.  A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making , 2016, Int. J. Inf. Technol. Decis. Mak..

[4]  Shyi-Ming Chen,et al.  Fuzzy Forecasting Based on Two-Factors Second-Order Fuzzy-Trend Logical Relationship Groups and the Probabilities of Trends of Fuzzy Logical Relationships , 2015, IEEE Transactions on Cybernetics.

[5]  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..

[6]  Weize Wang,et al.  Intuitionistic fuzzy geometric aggregation operators based on einstein operations , 2011, Int. J. Intell. Syst..

[7]  Weize Wang,et al.  Intuitionistic Fuzzy Information Aggregation Using Einstein Operations , 2012, IEEE Transactions on Fuzzy Systems.

[8]  Rehan Ahmed,et al.  Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making , 2017, J. Intell. Fuzzy Syst..

[9]  Muhammad Akram,et al.  A hybrid decision-making model under q-rung orthopair fuzzy Yager aggregation operators , 2020, Granular Computing.

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

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

[12]  PengXindong,et al.  Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators , 2016 .

[13]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

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

[15]  Guiwu Wei,et al.  Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making , 2017, J. Intell. Fuzzy Syst..

[16]  Saleem Abdullah,et al.  Pythagorean Fuzzy Dombi Aggregation Operators and Their Application in Decision Support System , 2019, Symmetry.

[17]  Madhumangal Pal,et al.  Some Dombi aggregation of Q‐rung orthopair fuzzy numbers in multiple‐attribute decision making , 2019, Int. J. Intell. Syst..

[18]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[19]  Muhammad Akram,et al.  Novel hybrid decision-making methods based on mF rough information , 2018, Granular Computing.

[20]  Muhammad Akram,et al.  Complex fuzzy ordered weighted quadratic averaging operators , 2020 .

[21]  Muhammad Akram,et al.  Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information , 2019, Soft Computing.

[22]  Shyi-Ming Chen,et al.  Fuzzy multiple attributes group decision-making based on fuzzy preference relations , 2011, Expert Syst. Appl..

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

[24]  Yanbing Ju,et al.  Some Aggregation Operators Based on Einstein Operations under Interval-Valued Dual Hesitant Fuzzy Setting and Their Application , 2014 .

[25]  Jeng-Shyang Pan,et al.  Weighted Fuzzy Interpolative Reasoning Based on Weighted Increment Transformation and Weighted Ratio Transformation Techniques , 2009, IEEE Transactions on Fuzzy Systems.

[26]  Wieslaw A. Dudek,et al.  Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision‐making , 2019, Int. J. Intell. Syst..

[27]  Guiwu Wei,et al.  Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making , 2010, Appl. Soft Comput..

[28]  Fuad E. Alsaadi,et al.  Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making , 2017, J. Intell. Fuzzy Syst..

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

[30]  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.

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

[32]  Harish Garg,et al.  Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets , 2020, Inf. Sci..

[33]  Shyi-Ming Chen,et al.  Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making , 2018, J. Oper. Res. Soc..

[34]  GargHarish.  A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making , 2016 .

[35]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[36]  Gulfam Shahzadi,et al.  Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators , 2020, Mathematics.

[37]  Harish Garg,et al.  Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process , 2017, Int. J. Intell. Syst..

[38]  Xindong Peng,et al.  Fundamental Properties of Pythagorean Fuzzy Aggregation Operators , 2016, Fundam. Informaticae.

[39]  Muhammad Akram,et al.  Hybrid models for decision-making based on rough Pythagorean fuzzy bipolar soft information , 2018, Granular Computing.

[40]  Yong Yang,et al.  Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators , 2016, Int. J. Intell. Syst..

[41]  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..

[42]  Muhammad Akram,et al.  Group decision‐making based on pythagorean fuzzy TOPSIS method , 2019, Int. J. Intell. Syst..

[43]  Shyi-Ming Chen,et al.  Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators , 2016, Inf. Sci..

[44]  Muhammad Akram,et al.  A hybrid decision-making framework using rough mF bipolar soft environment , 2020, Granular Computing.

[45]  Yumei Wang,et al.  Multiple attribute decision making based on q-rung orthopair fuzzy generalized Maclaurin symmetic mean operators , 2020, Inf. Sci..

[46]  Harish Garg,et al.  Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process , 2019, Artificial Intelligence Review.

[47]  R. Yager.  Aggregation operators and fuzzy systems modeling , 1994 .

[48]  Muhammad Akram,et al.  Decision-making approach based on Pythagorean Dombi fuzzy soft graphs , 2020, Granular Computing.

[49]  Shyi-Ming Chen,et al.  Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values , 2016, Inf. Sci..

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

[51]  Alexander Gegov,et al.  Confidence levels q‐rung orthopair fuzzy aggregation operators and its applications to MCDM problems , 2019, Int. J. Intell. Syst..

[52]  Gui-Wu Wei,et al.  Pythagorean fuzzy power aggregation operators in multiple attribute decision making , 2018, Int. J. Intell. Syst..

[53]  Harish Garg,et al.  A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making , 2016, Int. J. Intell. Syst..

[54]  Guiwu Wei,et al.  Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in Multiple Attribute Decision Making , 2018, Int. J. Intell. Syst..