Group Decision Making Based on Power Heronian Aggregation Operators Under Linguistic Neutrosophic Environment

The power average (PA) operator can overcome some effects of awkward data given by predispose decision makers, and Heronian mean (HM) operator can consider the interrelationship of the aggregated arguments. In order to take the full use of these two kinds of operators, in this article, we combined the PA operator with HM operator and extended them to process linguistic neutrosophic information, and presented the linguistic neutrosophic power Heronian aggregation operator, linguistic neutrosophic power weight Heronian aggregation operator. Further, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose new technique based on these operators for multiple attribute group decision making. Finally, an illustrative example was given to illustrate the effectiveness and advantages of the developed method by comparing with the existing method.

[1]  Peide Liu,et al.  Multiple attribute group decision making methods based on some normal neutrosophic number Heronian Mean operators , 2017, J. Intell. Fuzzy Syst..

[2]  Jun Ye,et al.  Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment , 2014, J. Intell. Syst..

[3]  Ronald R. Yager,et al.  The power average operator , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[4]  Huayou Chen,et al.  A New Interval-valued 2-Tuple Linguistic Bonferroni Mean Operator and Its Application to Multiattribute Group Decision Making , 2017, Int. J. Fuzzy Syst..

[5]  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..

[6]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[7]  Peng Wang,et al.  Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making , 2017, Int. J. Inf. Technol. Decis. Mak..

[8]  Peide Liu,et al.  An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic Variable , 2016, Complex..

[9]  Jian-qiang Wang,et al.  A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety , 2018, Int. J. Mach. Learn. Cybern..

[10]  José M. Merigó,et al.  Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making , 2018, Appl. Soft Comput..

[11]  Gleb Beliakov,et al.  Aggregation Functions: A Guide for Practitioners , 2007, Studies in Fuzziness and Soft Computing.

[12]  Peide Liu,et al.  The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making , 2015, Neural Computing and Applications.

[13]  Zheng Pei,et al.  An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers , 2015, Int. J. Comput. Intell. Syst..

[14]  Hong-yu Zhang,et al.  Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems , 2014, Inf. Sci..

[15]  Jun Ye,et al.  A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets , 2014, J. Intell. Fuzzy Syst..

[16]  Huayou Chen,et al.  Hesitant Fuzzy Power Bonferroni Means and Their Application to Multiple Attribute Decision Making , 2015, IEEE Transactions on Fuzzy Systems.

[17]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[18]  Jun Ye,et al.  Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods , 2017, Inf..

[19]  Jun Ye,et al.  Multiple Attribute Group Decision-Making Method Based on Linguistic Neutrosophic Numbers , 2017, Symmetry.

[20]  Jun Ye,et al.  Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses , 2015, Artif. Intell. Medicine.

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

[22]  Zhang-peng Tian,et al.  A multihesitant fuzzy linguistic multicriteria decision-making approach for logistics outsourcing with incomplete weight information , 2018, Int. Trans. Oper. Res..

[23]  Shyi-Ming Chen,et al.  Group Decision Making Based on Heronian Aggregation Operators of Intuitionistic Fuzzy Numbers , 2017, IEEE Transactions on Cybernetics.

[24]  José M. Merigó,et al.  Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making , 2013, Inf. Sci..

[25]  Hong-yu Zhang,et al.  An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multi-criteria Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..

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

[27]  Xi Liu,et al.  Multiattribute Group Decision Making Methods Based on Linguistic Intuitionistic Fuzzy Power Bonferroni Mean Operators , 2017, Complex..

[28]  Jun Ye,et al.  Interval Neutrosophic Multiple Attribute Decision-Making Method with Credibility Information , 2016, International Journal of Fuzzy Systems.

[29]  Peide Liu,et al.  Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators , 2014, Appl. Soft Comput..

[30]  Peide Liu,et al.  Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators , 2017, Comput. Ind. Eng..

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

[32]  Zeshui Xu,et al.  Power-Geometric Operators and Their Use in Group Decision Making , 2010, IEEE Transactions on Fuzzy Systems.

[33]  Jian-qiang Wang,et al.  Cross-Entropy and Prioritized Aggregation Operator with Simplified Neutrosophic Sets and Their Application in Multi-Criteria Decision-Making Problems , 2016, International Journal of Fuzzy Systems.

[34]  Shyi-Ming Chen,et al.  Multiattribute group decision making based on intuitionistic 2-tuple linguistic information , 2018, Inf. Sci..

[35]  Peide Liu,et al.  Some Hamacher Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

[36]  Dejian Yu,et al.  Intuitionistic fuzzy geometric Heronian mean aggregation operators , 2013, Appl. Soft Comput..

[37]  Chunhe Xie,et al.  A New Interval Numbers Power Average Operator in Multiple Attribute Decision Making , 2017, Int. J. Intell. Syst..

[38]  Hong-Yu Zhang,et al.  LINGUISTIC NEUTROSOPHIC SETS AND THEIR APPLICATION IN MULTICRITERIA DECISION-MAKING PROBLEMS , 2017 .

[39]  Peide Liu,et al.  Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making , 2017, J. Intell. Fuzzy Syst..

[40]  He Huang,et al.  Solving reverse emergence with quantum PSO application to image processing , 2018, Soft Comput..

[41]  Yubao Chen,et al.  Some Single Valued Neutrosophic Number Heronian Mean Operators and Their Application in Multiple Attribute Group Decision Making , 2016, Informatica.

[42]  Liquan Xiao,et al.  On the Shoulders of Giants: Incremental Influence Maximization in Evolving Social Networks , 2015, Complex..

[43]  Zeshui Xu,et al.  Generalized Hesitant Fuzzy Harmonic Mean Operators and Their Applications in Group Decision Making , 2015, International Journal of Fuzzy Systems.

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

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

[46]  Jing Wang,et al.  Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..