Evaluation of the product quality of the online shopping platform using t-spherical fuzzy preference relations

As a generalization of Pythagorean fuzzy sets and picture fuzzy sets, spherical fuzzy sets provide decision makers more flexible space in expressing their opinions. Preference relations have received widespread acceptance as an efficient tool in representing decision makers’ preference over alternatives in the decision-making process. In this paper, some new preference relations are investigated based on the spherical fuzzy sets. Firstly, the deficiency of the existing operating laws is elaborated in detail and three cases are described to identify the accuracy of the proposed operating laws in the context of t-spherical fuzzy environment. Also, a novel score function is proposed to obtain the consistent value in ranking of the alternatives. The backbone of this research, t-spherical fuzzy preference relation, consistent t-spherical fuzzy preference relations, incomplete t-spherical fuzzy preference relations, consistent incomplete t-spherical fuzzy preference relations, and acceptable incomplete t-spherical fuzzy preference relations are established. Additionally, some ranking and selection algorithms are established using the proposed novel score function and preference relations to tackle the uncertainty in real-life decision-making problems. Finally, evaluation of the product quality of the online shopping platform problem is demonstrated to show the applicability and reliability of proposed technique.

[1]  Cengiz Kahraman,et al.  Novel similarity measures in spherical fuzzy environment and their applications , 2020, Engineering Applications of Artificial Intelligence.

[2]  Ewa Rak,et al.  An Approach Towards Decision-Making and Shortest Path Problems Based on T-Spherical Fuzzy Information , 2020, Int. J. Fuzzy Syst..

[3]  Ronald R. Yager,et al.  Two-level multi-criteria comprehensive evaluation for preference vectors in online shopping platform evaluation , 2020, J. Intell. Fuzzy Syst..

[4]  Zhou-Jing Wang,et al.  Prioritization and Aggregation of Intuitionistic Preference Relations: A Multiplicative-Transitivity-Based Transformation from Intuitionistic Judgment Data to Priority Weights , 2017 .

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

[6]  Qaisar Khan,et al.  An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets , 2019, Neural Computing and Applications.

[7]  Shouzhen Zeng,et al.  Application of Exponential Jensen Picture Fuzzy Divergence Measure in Multi-Criteria Group Decision Making , 2019, Mathematics.

[8]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[9]  Shu-Ping Wan,et al.  Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations , 2016, Knowl. Based Syst..

[10]  Lazim Abdullah,et al.  Child Development Influence Environmental Factors Determined Using Spherical Fuzzy Distance Measures , 2019, Mathematics.

[11]  Lazim Abdullah,et al.  Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems , 2019, Mathematics.

[12]  Tahir Mahmood,et al.  Spherical fuzzy Dombi aggregation operators and their application in group decision making problems , 2020, J. Ambient Intell. Humaniz. Comput..

[13]  Saleem Abdullah,et al.  Symmetric sum based aggregation operators for spherical fuzzy information: Application in multi-attribute group decision making problem , 2020, J. Intell. Fuzzy Syst..

[14]  Zeshui Xu,et al.  A survey of approaches to decision making with intuitionistic fuzzy preference relations , 2015, Knowl. Based Syst..

[15]  Muhammad Akram,et al.  Spherical Fuzzy Graphs with Application to Decision-Making , 2020 .

[16]  Saleem Abdullah,et al.  Spherical Fuzzy Logarithmic Aggregation Operators Based on Entropy and Their Application in Decision Support Systems , 2019, Entropy.

[17]  Harish Garg,et al.  Algorithm for T-Spherical Fuzzy Multi-Attribute Decision Making Based on Improved Interactive Aggregation Operators , 2018, Symmetry.

[18]  T. Saaty.  Axiomatic foundation of the analytic hierarchy process , 1986 .

[19]  Saleem Abdullah,et al.  Emergency decision support modeling for COVID‐19 based on spherical fuzzy information , 2020, Int. J. Intell. Syst..

[20]  Cengiz Kahraman,et al.  A novel spherical fuzzy analytic hierarchy process and its renewable energy application , 2020, Soft Comput..

[21]  Prasenjit Mandal,et al.  Pythagorean fuzzy preference relations and their applications in group decision‐making systems , 2019, Int. J. Intell. Syst..

[22]  Saleem Abdullah,et al.  Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms , 2019, J. Intell. Fuzzy Syst..

[23]  Poom Kumam,et al.  Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems , 2019, Symmetry.

[24]  Muhammad Arif,et al.  A New Approach to Fuzzy TOPSIS Method Based on Entropy Measure under Spherical Fuzzy Information , 2019, Entropy.

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

[26]  Tahir Mahmood,et al.  The cosine similarity measures of spherical fuzzy sets and their applications in decision making , 2019, J. Intell. Fuzzy Syst..

[27]  Fanyong Meng,et al.  An approach to incomplete multiplicative preference relations and its application in group decision making , 2015, Inf. Sci..

[28]  Tahir Mahmood,et al.  Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making , 2019, Symmetry.

[29]  Yang Yang,et al.  Some preference relations based on q ‐rung orthopair fuzzy sets , 2019, Int. J. Intell. Syst..

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

[31]  Saleem Abdullah,et al.  Spherical aggregation operators and their application in multiattribute group decision‐making , 2018, Int. J. Intell. Syst..

[32]  Saleem Abdullah,et al.  Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems , 2019, Mathematics.

[33]  Qaisar Khan,et al.  Different Approaches to Multi-Criteria Group Decision Making Problems for Picture Fuzzy Environment , 2018, Bulletin of the Brazilian Mathematical Society, New Series.

[34]  T. Mahmood,et al.  GRA method based on spherical linguistic fuzzy Choquet integral environment and its application in multi-attribute decision-making problems , 2018, Mathematical Sciences.

[35]  Tahir Mahmood,et al.  Spherical fuzzy sets and their applications in multi-attribute decision making problems , 2019, J. Intell. Fuzzy Syst..

[36]  S. Orlovsky.  Decision-making with a fuzzy preference relation , 1978 .

[37]  Peide Liu,et al.  T-Spherical Fuzzy Power Muirhead Mean Operator Based on Novel Operational Laws and Their Application in Multi-Attribute Group Decision Making , 2019, IEEE Access.

[38]  Mariana-Daniela González-Zamar,et al.  Financial Technology: Review of Trends, Approaches and Management , 2020, Mathematics.

[39]  Huayou Chen,et al.  Approaches to group decision making with intuitionistic fuzzy preference relations based on multiplicative consistency , 2016, Knowl. Based Syst..