Abstract
Recently, there has been great interest on single valued neutrosophic hesitant fuzzy set theory. When compared single valued neutrosophic set, it is more convenient for real life situations. But even in this case, there is still missing data for some decision problems. Probabilistic single valued neutrosophic hesitant fuzzy sets (PSVNHFSs) are defined to solve this problem. Even though it contains more information, it needs some improvements. In this paper, the modified PSVNHFS is defined and some improvements in the theory of PSVNHFS are proposed. Also, we improve some algebraic properties of this set theory and define a distance operator for PSVNHFSs. Then we introduce two aggregation operators called probabilistic single valued neutrosophic hesitant fuzzy weighted arithmetic average (PSVNHFWA) operator and probabilistic single valued neutrosophic hesitant fuzzy weighted geometric average (PSVNHFWG) operator related to algebraic properties presented in this paper. Also, we extend the MABAC method under the probabilistic single valued neutrosophic hesitant fuzzy set theory. Finally, we give an illustrative example to demonstrate the stability and reliability of the proposed theory.
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References
Abdel-Basset M, Mohamed M (2018) The role of single valued neutrosophic sets and rough sets in smart city: imperfect and incomplete information systems. Measurement 124:47–55
Abdel-Basset M, Mohamed M, Sangaiah AK (2018) Neutrosophic AHP-Delphi Group decision making model based on trapezoidal neutrosophic numbers. J Ambient Intell Human Comput 9(5):1427–1443
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96
Atanassov KT (1999) Interval valued intuitionistic fuzzy sets. In: Intuitionistic fuzzy sets. Physica, Heidelberg, pp. 139–177
Aydoğdu A (2015) On similarity and entropy of single valued neutrosophic sets. Gen Math Notes 29:67–74
Benayoun R, Roy B, Sussman B (1969) ELECTRE: une méthode pour guider le choix en présence de points de vue multiples. Rev Franaise Informat Recherche Opérationnelle 3:31–56
Biswas T, Das M (2018) Selection of hybrid vehicle for green environment using multi-attributive border approximation area comparison method. Management Science Letters 8(2):121–130
Biswas P, Pramanik S, Giri BC (2016) TOPSIS method for multi-criteria group decision-making under simplified neutrosophic environment. Neural Comput Appl 27(3):727–737
Božanić DI, Pamučar DS, Karović SM (2016) Application the MABAC method in support of decision-making on the use of force in a defensive operation. Tehnika 71(1):129–136
Broumi S, Smarandache F (2013) Correlation coefficient of interval neutrosophic set. Appl Mech Mater 436:511–517
Garg H (2017) Some new biparametric distance measures on single-valued neutrosophic sets with applications to pattern recognition and medical diagnosis. Information 8(4):162
Garg H (2018) Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. Appl Intell 48(8):2199–2213
Garg H, Nancy J (2018) Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making. Ambient Intell Human Comput 9(6):1975–1997
Huang HL (2016) New distance measure of single-valued neutrosophic sets and its application. Int J Intell Syst 31(10):1021–1032
Hwang CL, Yoon K (1981) Methods for multiple attribute decision making. In: Multiple attribute decision making. Springer, Berlin, Heidelberg, pp 58–191
Ji P, Zhang H-Y, Wang J-Q (2018) Selecting an outsourcing provider based on the combined MABAC– ELECTRE method using single-valued neutrosophic linguistic sets. Comput Ind Eng 120:429–441
Kumar P, Singh RK, Sinha P (2016) Optimal site selection for a hospital using a fuzzy extended ELECTRE approach. J Manag Anal 3(2):115–135
Li J, Wang JQ (2017) Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cognit Comput 9(5):611–625
Liang RX, He SS, Wang JQ, Chen K, Li L (2019a) An extended MABAC method for multi-criteria group decision-making problems based on correlative inputs of intuitionistic fuzzy information. Comput Appl Math 38(3):112
Liang W, Zhao G, Wu H, Dai B (2019b) Risk assessment of rockburst via an extended MABAC method under fuzzy environment. Tunn Undergr Space Technol 83:533–544
Liu HC (2019) FMEA Using IVIFSs and MABAC method and its application to radiation therapy. In: Improved FMEA methods for proactive healthcare risk analysis. Springer, Singapore, pp 125–150
Liu P, Zhang L (2017a) An extended multiple criteria decision making method based on neutrosophic hesitant fuzzy information. J Intell Fuzzy Syst 32(6):4403–4413
Liu P, Zhang L (2017b) Multiple criteria decision making method based on neutrosophic hesitant fuzzy Heronian mean aggregation operators. J Intell Fuzzy Syst 32(1):303–319
Liu P, Zhang L, Liu X, Wang P (2016) Multi-valued neutrosophic number Bonferroni mean operators with their applications in multiple attribute group decision making. Int J Inf Technol Decis Making 15(05):1181–1210
Luo SZ, Liang WZ (2019) Optimization of roadway support schemes with likelihood-based MABAC method. Appl Soft Comput 80:80–92
Majchrzycka A, Poniszewska-Maranda A (2018) Control operation flow for mobile access control with the use of MABAC model. In: Kosiuczenko P, Madeyski L (eds) Towards a synergistic combination of research and practice in software engineering. Springer International Publishing, Cham, pp 179–192
Mareschal B, Vincke JP (1984) PROMETHEE a new family of outranking methods in multi criteria analysis. Brans J Proc Oper Res 84:477–490
Meng F, Wang N, Xu Y (2019) Interval neutrosophic preference relations and their application in virtual enterprise partner selection. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-019-01178-5
Mishra AR, Chandel A, Motwani D (2018) Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets. Granul Comput 2018:1–21
Mohanty M, Shankar R (2019) A hierarchical analytical model for performance management of integrated logistics. J Manag Anal 6(2):173–208
Ocampo LA (2016) Fuzzy analytic network process (FANP) approach in formulating infrastructural decisions of sustainable manufacturing strategy. J Manag Anal 3(3):266–284
Opricovic S, Tzeng GH (2002) Multi-criteria planning of post-earthquake sustainable reconstruction. Comput Aided Civ Infrastruct Eng 17(3):211–220
Pamučar D, Božanić D (2019) Selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic MABAC model. Oper Res Eng Sci Theory Appl 2(2):55–71
Pamučar D, Ćirović G (2015) The selection of transport and handling resources in logistics centers using multi-attributive border approximation area comparison (MABAC). Expert Syst Appl 42(6):3016–3028
Peng X, Dai J (2017) Hesitant fuzzy soft decision making methods based on WASPAS, MABAC and COPRAS with combined weights. J Intell Fuzzy Syst 33(2):1313–1325
Peng X, Dai J (2018) Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function. Neural Comput Appl 29(10):939–954
Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346
Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2016) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci 47(10):2342–2358
Peng X, Dai J, Yuan H (2017) Interval-valued fuzzy soft decision making methods based on MABAC, similarity measure and EDAS. Fund Inf 152(4):373–396
Peng HG, Zhang HY, Wang JQ (2018) Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems. Neural Comput Appl 30(2):563–583
Şahin R, Karabacak M (2015) A multi attribute decision making method based on inclusion measure for interval neutrosophic sets. Int J Eng Appl Sci 2:2
Şahin R, Küçük A (2015) Subsethood measure for single valued neutrosophic sets. J Intell Fuzzy Syst 29(2):525–530
Şahin R, Liu P (2016) Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information. Neural Comput Appl 27(7):2017–2029
Şahin R, Liu P (2017a) Possibility-induced simplified neutrosophic aggregation operators and their application to multi-criteria group decision-making. J Exp Theor Artif Intell 29(4):769–785
Şahin R, Liu P (2017b) Some approaches to multi criteria decision making based on exponential operations of simplified neutrosophic numbers. J Intell Fuzzy Syst 32(3):2083–2099
Shao S, Zhang X, Li Y, Bo C (2018) Probabilistic single-valued (interval) neutrosophic hesitant fuzzy set and its application in multi-attribute decision making. Symmetry 10(9):419
Sharma SK, Chanda U (2017) Developing a Bayesian belief network model for prediction of R&D project success. J Manag Anal 4(3):321–344
Smarandache F (1998) Neutrosophy: neutrosophic probability, set and logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, p 105
Tian Z, Wang J, Wang J, Zhang H (2017) Simplified neutrosophic linguistic multi-criteria group decisionmaking approach to green product development. Group Decis Negot 26:597–627
Torra V (2010) Hesitant fuzzy sets. J Intell Fuzzy Syst 25(6):529–539
Turksen I (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20:191–210
Viriyasitavat W (2016) Multi-criteria selection for services selection in service workflow. J Ind Inf Integr 1:20–25
Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: theory and applications in computing: Theory and applications in computing Hexis, Phoenix
Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413
Wang Y, Ji W, Chaudhry SS (2014) A hybrid approach for the evaluation of supermarket food safety. J Manag Anal 1(2):156–167
Wei G, Zhang Z (2019) Some single-valued neutrosophic Bonferroni power aggregation operators in multiple attribute decision making. J Ambient Intell Human Comput 10(3):863–882
Wu W, Li Y, Ni Z, Jin F, Zhu X (2018) Probabilistic interval-valued hesitant fuzzy information aggregation operators and their application to multi-attribute decision making. Algorithms 11(8):120
Xu LD (1990) Linguistic approach to the multi-criteria ranking problem. Int J Syst Sci 21(9):1773–1782
Xu LD (1998) A fuzzy multiobjective programming algorithm in decision support systems. Ann Oper Res 12:315–320. https://doi.org/10.1007/BF02186373
Xue YX, You JX, Lai XD, Liu HC (2016) An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information. Appl Soft Comput 38:703–713
Ye J (2014a) A multi-criteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466
Ye J (2014b) Similarity measures between interval neutrosophic sets and their applications in multi-criteria decision-making. J Intell Fuzzy Syst 26(1):165–172
Ye J (2014c) Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int J Fuzzy Syst 16(2):204–211
Ye J (2015) Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment. J Intell Syst 24(1):23–36
Ye J, Zhang QS (2014) Single valued neutrosophic similarity measures for multiple attribute decision making. Neutrosophic Sets Syst 2:48–54
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zandieh M, Aslani B (2019) A hybrid MCDM approach for order distribution in a multiple-supplier supply chain: a case study. J Ind Inf Integr 16:100104
Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision making problems. Sci Word J, 2014, p 645953
Zhang HY, Ji P, Wang JQ, Chen XH (2015) An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. Int J Comput Intell Syst 8(6):1027–1043
Zhang S, Xu Z, He Y (2017) Operations and integrations of probabilistic hesitant fuzzy information in decision making. Inf Fusion 38:1–11
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Şahin, R., Altun, F. Decision making with MABAC method under probabilistic single-valued neutrosophic hesitant fuzzy environment. J Ambient Intell Human Comput 11, 4195–4212 (2020). https://doi.org/10.1007/s12652-020-01699-4
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DOI: https://doi.org/10.1007/s12652-020-01699-4