Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision‐making process

Hesitant Pythagorean fuzzy (HPF) sets can easily express the uncertain information while Maclaurin symmetric mean (MSM) operator, can capture the interrelationship among the multiattributes, and are suitable for aggregating the information into a single number. By taking the advantages of both, in this paper, we extend the traditional MSM to HPF environment. For this, we develop the HPFMSM operator for aggregating the HPF information. The desirable characteristics, such as idempotency, monotonicity, and boundedness, are studied. Then, we discussed some special cases with respect to the parameter value of the HPFMSM operators and showed that it generalizes the various existing operators. Furthermore, we studied the weighted HPFMSM operator to aggregate the HPF information with different preferences to the input arguments. On the basis of these operators, we solved the multiattribute decision‐making problems with HPF information. The practicality and effectiveness of the developed approach are demonstrated through a numerical example.

[1]  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..

[2]  Harish Garg,et al.  An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making , 2018, Soft Computing.

[3]  Gagandeep Kaur,et al.  CUBIC INTUITIONISTIC FUZZY AGGREGATION OPERATORS , 2018 .

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

[5]  Guiwu Wei,et al.  Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications , 2018, Int. J. Intell. Syst..

[6]  Guiwu Wei,et al.  Dual hesitant fuzzy aggregation operators in multiple attribute decision making , 2014, J. Intell. Fuzzy Syst..

[7]  Zeshui Xu,et al.  Hesitant fuzzy information aggregation in decision making , 2011, Int. J. Approx. Reason..

[8]  Zeshui Xu,et al.  On distance and correlation measures of hesitant fuzzy information , 2011, Int. J. Intell. Syst..

[9]  Harish Garg,et al.  A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem , 2016, J. Intell. Fuzzy Syst..

[10]  K. Atanassov,et al.  Interval-Valued Intuitionistic Fuzzy Sets , 2019, Studies in Fuzziness and Soft Computing.

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

[12]  Harish Garg,et al.  A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision‐Making Processes , 2016, Int. J. Intell. Syst..

[13]  Zeshui Xu,et al.  Pythagorean fuzzy TODIM approach to multi-criteria decision making , 2016, Appl. Soft Comput..

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

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

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

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

[18]  Dejian Yu,et al.  Multi-Criteria Decision Making Based on Choquet Integral under Hesitant Fuzzy Environment , 2011 .

[19]  Harish Garg,et al.  A Novel Improved Accuracy Function for Interval Valued Pythagorean Fuzzy Sets and Its Applications in the Decision‐Making Process , 2017, Int. J. Intell. Syst..

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

[21]  Jun Ye Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making , 2014 .

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

[23]  Peide Liu,et al.  Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision-making , 2017, J. Exp. Theor. Artif. Intell..

[24]  Gagandeep Kaur,et al.  Generalized Cubic Intuitionistic Fuzzy Aggregation Operators Using t-Norm Operations and Their Applications to Group Decision-Making Process , 2018, Arabian Journal for Science and Engineering.

[25]  Zeshui Xu,et al.  Hesitant fuzzy geometric Bonferroni means , 2012, Inf. Sci..

[26]  Harish Garg,et al.  Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision‐making , 2018, Expert Syst. J. Knowl. Eng..

[27]  Harish Garg,et al.  Some methods for strategic decision‐making problems with immediate probabilities in Pythagorean fuzzy environment , 2018, Int. J. Intell. Syst..

[28]  Harish Garg,et al.  New exponential operational laws and their aggregation operators for interval‐valued Pythagorean fuzzy multicriteria decision‐making , 2018, Int. J. Intell. Syst..

[29]  Harish Garg,et al.  A Linear Programming Method Based on an Improved Score Function for Interval-Valued Pythagorean Fuzzy Numbers and Its Application to Decision-Making , 2018, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[30]  Harish Garg,et al.  Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process , 2017, Computational and Mathematical Organization Theory.

[31]  Xindong Peng,et al.  Pythagorean fuzzy set: state of the art and future directions , 2017, Artificial Intelligence Review.

[32]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy sets , 2011, Inf. Sci..

[33]  Harish Garg,et al.  A NEW IMPROVED SCORE FUNCTION OF AN INTERVAL-VALUED PYTHAGOREAN FUZZY SET BASED TOPSIS METHOD , 2017 .

[34]  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..

[35]  Xiaolu Zhang,et al.  Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods , 2016, Inf. Sci..

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

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

[38]  Harish Garg,et al.  HESITANT PYTHAGOREAN FUZZY SETS AND THEIR AGGREGATION OPERATORS IN MULTIPLE ATTRIBUTE DECISION-MAKING , 2018 .

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

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

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

[42]  Harish Garg,et al.  DISTANCE AND SIMILARITY MEASURES FOR DUAL HESITANT FUZZY SOFT SETS AND THEIR APPLICATIONS IN MULTICRITERIA DECISION MAKING PROBLEM , 2017 .

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

[44]  Na Chen,et al.  Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis , 2013 .

[45]  Harish Garg,et al.  Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process , 2018, Int. J. Intell. Syst..

[46]  Witold Pedrycz,et al.  Hesitant Fuzzy Maclaurin Symmetric Mean Operators and Its Application to Multiple-Attribute Decision Making , 2015, Int. J. Fuzzy Syst..

[47]  Guiwu Wei,et al.  Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making , 2018, Int. J. Intell. Syst..

[48]  Guiwu Wei,et al.  Hesitant fuzzy prioritized operators and their application to multiple attribute decision making , 2012, Knowl. Based Syst..