TOPSIS Method Based on Correlation Coefficient under Pythagorean Fuzzy Soft Environment and Its Application towards Green Supply Chain Management

The correlation coefficient between two variables is an important aspect of statistics. The accuracy of assessments of correlation relies on information from a set of discourses. Data collected in statistical studies are often full of exceptions. Pythagorean fuzzy soft sets (PFSS) are a parametrized family of extended Pythagorean fuzzy sets (PFS). They comprise a generalization of intuitionistic fuzzy soft sets which may be used to accurately assess deficiencies and uncertainties in evaluations. PFSS can accommodate uncertainty more competently than intuitionistic fuzzy soft sets and are the most important strategy when dealing with fuzzy information in decision-making processes. Herein, the concept and characteristics of correlation coefficients and the weighted correlation coefficients in PFSS are discussed. We also introduce the Pythagorean fuzzy soft weighted average (PFSWA) and Pythagorean fuzzy soft weighted geometric (PFSWG) operators and discuss their desirable characteristics. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under the PFSS environment based on correlation coefficients and weighted correlation coefficients will be introduced. Through the proposed methodology, a technique for decision-making is developed. Additionally, an application of the proposed TOPSIS technique is presented for green supplier selection in green supply chain management (GSCM). The practicality, efficacy, and flexibility of the proposed approach is proved through comparative analyses, drawing upon existing studies.

[1]  Hokey Min,et al.  Green Purchasing Strategies: Trends and Implications , 1997 .

[2]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

[3]  W. Sałabun.  Assessing the 10-Year Risk of Hard Arteriosclerotic Cardiovascular Disease Events Using the Characteristic Objects Method , 2015 .

[4]  Tahir Mahmood,et al.  Entropy measure and TOPSIS method based on correlation coefficient using complex q-rung orthopair fuzzy information and its application to multi-attribute decision making , 2020, Soft Computing.

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

[6]  Robert P. Anex,et al.  The road to cooperative supply‐chain environmental management: trust and uncertainty among pro‐active firms , 2009 .

[7]  R. Handfield,et al.  ‘Green’ value chain practices in the furniture industry , 1997 .

[8]  Asis Sarkar,et al.  A TOPSIS method to evaluate the technologies , 2013 .

[9]  Zia Bashir,et al.  Hesitant Probabilistic Multiplicative Preference Relations in Group Decision Making , 2018 .

[10]  Harish Garg,et al.  TOPSIS method based on correlation coefficient for solving decision-making problems with intuitionistic fuzzy soft set information , 2020 .

[11]  Patrick T. Hester,et al.  An Analysis of Multi-Criteria Decision Making Methods , 2013 .

[12]  Xiaolu Zhang,et al.  A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making , 2016, Int. J. Intell. Syst..

[13]  Jarosław Wątróbski,et al.  Multi-criteria decision support for planning and evaluation of performance of viral marketing campaigns in social networks , 2018, PloS one.

[14]  A. Gunasekaran,et al.  Sustainable supply management: An empirical study , 2012, ECIS 2012.

[15]  Harish Garg,et al.  A robust aggregation operators for multi-criteria decision-making with intuitionistic fuzzy soft set environment , 2017 .

[16]  M. Zulqarnain,et al.  Choose Best Criteria for Decision Making Via Fuzzy Topsis Method , 2017 .

[17]  K. Lai,et al.  An Organizational Theoretic Review of Green Supply Chain Management Literature , 2011 .

[18]  Yong Yang,et al.  Some Results for Pythagorean Fuzzy Sets , 2015, Int. J. Intell. Syst..

[19]  Chen Qi.  On clustering approach to intuitionistic fuzzy sets , 2007 .

[20]  Na Li,et al.  Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making , 2020, Int. J. Intell. Syst..

[21]  Harish Garg,et al.  Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties , 2019, Computational and Applied Mathematics.

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

[23]  Andrzej Piegat,et al.  Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome , 2016, Artificial Intelligence Review.

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

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

[26]  Yafei Song,et al.  A New Method for MAGDM Based on Improved TOPSIS and a Novel Pythagorean Fuzzy Soft Entropy , 2019, Symmetry.

[27]  Xindong Peng,et al.  Pythagorean fuzzy soft MCGDM methods based on TOPSIS, VIKOR and aggregation operators , 2019, J. Intell. Fuzzy Syst..

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

[29]  Harish Garg,et al.  A robust correlation coefficient measure of dual hesitant fuzzy soft sets and their application in decision making , 2018, Eng. Appl. Artif. Intell..

[30]  C. Searcy,et al.  A comparative literature analysis of definitions for green and sustainable supply chain management , 2013 .

[31]  Zeshui Xu,et al.  Green Supplier Selection Based on Green Practices Evaluated Using Fuzzy Approaches of TOPSIS and ELECTRE with a Case Study in a Chinese Internet Company , 2020, International journal of environmental research and public health.

[32]  Muhammad Riaz,et al.  A similarity measure under Pythagorean fuzzy soft environment with applications , 2020, Computational and Applied Mathematics.

[33]  Khurrum S. Bhutta,et al.  Supplier selection problem: a comparison of the total cost of ownership and analytic hierarchy process approaches , 2002 .

[34]  Tabasam Rashid,et al.  A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique , 2020, Symmetry.

[35]  Harish Garg,et al.  Entropy and distance measures of Pythagorean fuzzy soft sets and their applications , 2019, J. Intell. Fuzzy Syst..

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

[37]  S. A. R. Khan,et al.  Research on the Measuring Performance of Green Supply Chain Management: In the Perspective of China , 2016 .

[38]  Izabela Ewa Nielsen,et al.  Comparative analysis of government incentives and game structures on single and two-period green supply chain , 2019, Journal of Cleaner Production.

[39]  Muhammad Riaz,et al.  q-Rung Orthopair Fuzzy Prioritized Aggregation Operators and Their Application Towards Green Supplier Chain Management , 2020, Symmetry.

[40]  Harish Garg,et al.  New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications , 2018, Int. J. Intell. Syst..

[41]  P. Rao.  Greening the supply chain: a new initiative in South East Asia , 2002 .

[42]  Izabela Ewa Nielsen,et al.  Is It a Strategic Move to Subsidized Consumers Instead of the Manufacturer? , 2019, IEEE Access.

[43]  Dmytro Matsypura,et al.  Supply chain networks with corporate social responsibility through integrated environmental decision-making , 2009 .

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

[45]  Cengiz Kahraman,et al.  Fuzzy multi-criteria evaluation of industrial robotic systems , 2007, Comput. Ind. Eng..

[46]  Xiao Long Xin,et al.  Extension of TOPSIS method under intuitionistic fuzzy hypersoft environment based on correlation coefficient and aggregation operators to solve decision making problem , 2021, AIMS Mathematics.

[47]  A. R. Roy,et al.  Soft set theory , 2003 .

[48]  Ramesh Chandra Rath.  An Impact of Green Marketing on Practices of Supply Chain Management in Asia: Emerging Economic Opportunities and Challenges , 2013 .

[49]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[50]  Animesh Biswas,et al.  An Integrated TOPSIS Approach to MADM with Interval-Valued Intuitionistic Fuzzy Settings , 2018 .

[51]  Wojciech Sałabun,et al.  A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management , 2020, Energies.

[52]  Harish Garg,et al.  Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set , 2019, Journal of Ambient Intelligence and Humanized Computing.

[53]  S. Saha,et al.  Game-Theoretic Analysis to Examine How Government Subsidy Policies Affect a Closed-Loop Supply Chain Decision , 2019, Applied Sciences.

[54]  Samir K. Srivastava,et al.  Green Supply-Chain Management: A State-of-the-Art Literature Review , 2007 .

[55]  Harish Garg,et al.  Generalized Maclaurin symmetric mean aggregation operators based on Archimedean t-norm of the intuitionistic fuzzy soft set information , 2020, Artificial Intelligence Review.

[56]  Artur Karczmarczyk,et al.  Using the COMET Method in the Sustainable City Transport Problem: an Empirical Study of the Electric Powered Cars , 2018, KES.

[57]  Drakoulis Martakos,et al.  Customer evaluation for order acceptance using a novel class of fuzzy methods based on TOPSIS , 2009, Expert Syst. Appl..

[58]  A. Y. Yayla,et al.  Fuzzy TOPSIS Method in Supplier Selection and Application in the Garment Industry , 2012 .

[59]  E. Zavadskas,et al.  Multiple criteria decision making (MCDM) methods in economics: an overview , 2011 .

[60]  Harish Garg,et al.  Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making , 2017, Applied Intelligence.

[61]  Haidong Zhang,et al.  Possibility Pythagorean fuzzy soft set and its application , 2019, J. Intell. Fuzzy Syst..

[62]  Felix T.S. Chan,et al.  Analysis of flexible decision strategies for sustainability-focused green product recovery system , 2013 .

[63]  A. Young,et al.  Sustainable Supply Network Management , 2001 .

[64]  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..

[65]  Pavel V. Sevastjanov,et al.  An approach to generalization of fuzzy TOPSIS method , 2013, Inf. Sci..

[66]  Paul R. Murphy,et al.  Green logistics strategies: An analysis of usage patterns , 2000 .

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

[68]  Zeshui Xu,et al.  Clustering algorithm for intuitionistic fuzzy sets , 2008, Inf. Sci..

[69]  Ting-Yu Chen,et al.  An Integrated Multicriteria Group Decision-Making Approach for Green Supplier Selection Under Pythagorean Fuzzy Scenarios , 2020, IEEE Access.

[70]  Wojciech Salabun,et al.  Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods , 2020, Symmetry.

[71]  Charbel José Chiappetta Jabbour,et al.  Selecting green suppliers based on GSCM practices: Using fuzzy TOPSIS applied to a Brazilian electronics company , 2014, Eur. J. Oper. Res..

[72]  Zeshui Xu,et al.  Symmetric Pythagorean Fuzzy Weighted Geometric/Averaging Operators and Their Application in Multicriteria Decision‐Making Problems , 2016, Int. J. Intell. Syst..

[73]  Xizhao Wang,et al.  An On-line Multi-CBR Agent Dispatching Algorithm , 2006, Soft Comput..

[74]  Kannan Govindan,et al.  Application of fuzzy VIKOR for evaluation of green supply chain management practices , 2015 .