Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

AbstractIn recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy- membership and falsity-membership degree have a set of crisp values between zero and one, respectively. Then the operations of multi-valued neutrosophic numbers (MVNNs) based on Einstein operations are defined, and a comparison method for MVNNs is developed depending on the related research of HFSs and Atanassov's intuitionistic fuzzy sets (IFSs). Furthermore, the multi-valued neutrosophic power weighted average (MVNPWA) operator and the multi-valued neutrosophic power weighted geometric (MVNPWG) operator are proposed and the desirable properties of two operators are also discussed. Finally, an approach for solving MCGDM problems is explored by applying the power aggreg...

[1]  Hong-yu Zhang,et al.  New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis , 2013, Inf. Sci..

[2]  Radko Mesiar,et al.  Triangular norms. Position paper I: basic analytical and algebraic properties , 2004, Fuzzy Sets Syst..

[3]  Hong-yu Zhang,et al.  Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems , 2014, TheScientificWorldJournal.

[4]  Jianqiang Wang,et al.  Multi-criteria Group Decision-Making Method Based on Intuitionistic Interval Fuzzy Information , 2012, Group Decision and Negotiation.

[5]  Ronald R. Yager,et al.  Multiple objective decision-making using fuzzy sets , 1977 .

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

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

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

[9]  Florentin Smarandache,et al.  A unifying field in logics : neutrosophic logic : neutrosophy, neutrosophic set, neutrosophic probability , 2020 .

[10]  Jing Wang,et al.  Multicriteria Decision-Making Approach with Hesitant Interval-Valued Intuitionistic Fuzzy Sets , 2014, TheScientificWorldJournal.

[11]  B. Farhadinia,et al.  Distance and similarity measures for higher order hesitant fuzzy sets , 2014, Knowl. Based Syst..

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

[13]  Roberto Cavoretto,et al.  Two and Three Dimensional Partition of Unity Interpolation by Product-Type Functions , 2015 .

[14]  Hai Wang,et al.  Generalized hesitant fuzzy sets and their application in decision support system , 2013, Knowl. Based Syst..

[15]  Yanqing Zhang,et al.  Interval Neutrosophic Sets and Logic: Theory and Applications in Computing , 2005, ArXiv.

[16]  F. Smarandache.  A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

[17]  Vicenç Torra,et al.  Hesitant fuzzy sets , 2010, Int. J. Intell. Syst..

[18]  Peide Liu,et al.  Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean , 2014, Neural Computing and Applications.

[19]  Zeshui Xu,et al.  Projection Models for Intuitionistic Fuzzy Multiple Attribute Decision Making , 2010, Int. J. Inf. Technol. Decis. Mak..

[20]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

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

[22]  L. A. Zadeh,et al.  Fuzzy logic and approximate reasoning , 1975, Synthese.

[23]  Peide Liu,et al.  Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making , 2014 .

[24]  Witold Pedrycz,et al.  Fuzzy sets in pattern recognition: Methodology and methods , 1990, Pattern Recognit..

[25]  Jun Ye.  Single valued neutrosophic cross-entropy for multicriteria decision making problems , 2014 .

[26]  Zeshui Xu,et al.  Prioritized intuitionistic fuzzy aggregation operators , 2013, Inf. Fusion.

[27]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[28]  Umberto Rivieccio,et al.  Neutrosophic logics: Prospects and problems , 2008, Fuzzy Sets Syst..

[29]  H.-Y. Zhang,et al.  Multicriteria Decision-Making Approach Based on Atanassov's Intuitionistic Fuzzy Sets With Incomplete Certain Information on Weights , 2013, IEEE Transactions on Fuzzy Systems.

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

[31]  Hong-yu Zhang,et al.  Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems , 2016, Int. J. Syst. Sci..

[32]  Jun Ye,et al.  Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment , 2013, Int. J. Gen. Syst..

[33]  Hong-yu Zhang,et al.  Multi-criteria outranking approach with hesitant fuzzy sets , 2013, OR Spectrum.

[34]  Weihua Su,et al.  Intuitionistic fuzzy ordered weighted distance operator , 2011, Knowl. Based Syst..

[35]  Francisco Gallego Lupiáñez,et al.  Interval neutrosophic sets and topology , 2008, Kybernetes.

[36]  Tamalika Chaira,et al.  Intuitionistic fuzzy set approach for color region extraction , 2010 .

[37]  Zhiming Zhang,et al.  Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making , 2013, Inf. Sci..

[38]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[39]  F. Smarandache,et al.  Correlation Coefficient of Interval Neutrosophic Set , 2013 .

[40]  Ting-Yu Chen,et al.  An outcome-oriented approach to multicriteria decision analysis with intuitionistic fuzzy optimistic/pessimistic operators , 2010, Expert Syst. Appl..

[41]  Pinaki Majumdar,et al.  On similarity and entropy of neutrosophic sets , 2013, J. Intell. Fuzzy Syst..

[42]  Gui-Wu Wei,et al.  Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making , 2011, Expert Syst. Appl..

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

[44]  Hong-yu Zhang,et al.  outranking approach for multi-criteria decision-making problems ith simplified neutrosophic sets uan - , 2014 .

[45]  Peng Zhou,et al.  Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator , 2014, TOP.

[46]  Jun Ye,et al.  Single valued neutrosophic cross-entropy for multicriteria decision making problems , 2014 .

[47]  Xiao-hong Chen,et al.  A Multi-Criteria Decision-Making Approach based on TODIM and Choquet Integral within a Multiset Hesitant Fuzzy Environment , 2015 .

[48]  Li Zheng,et al.  A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets , 2012, Expert Syst. Appl..

[49]  Rajshekhar Sunderraman,et al.  Single Valued Neutrosophic Sets , 2010 .

[50]  Jun Ye,et al.  Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making , 2014, J. Intell. Fuzzy Syst..

[51]  Jing Wang,et al.  Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems , 2015 .

[52]  Hong-yu Zhang,et al.  Intuitionistic fuzzy multi-criteria decision-making method based on evidential reasoning , 2013, Appl. Soft Comput..