A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions

Probabilistic linguistic term set (PLTS) has been proposed to tackle qualitative information efficiently in the decision-making process to achieve computing with expressions, which can be regarded as an advanced process of computing with words. The PLTS plays an important role in decision making by providing a comprehensive way for representing complex linguistic information. Owning to its usefulness and efficiency, the PLTS has attracted a lot of researchers’ attention, and fruitful research achievements regarding it has been published since it was introduced in 2016. As the probabilistic linguistic theory is still in its infancy, a survey of it contributes to understanding the previous topics and the current issues, and predicting the future research directions in this area. To implement these goals, this paper is organized by bibliometric analysis, definitions, multiple criteria decision-making methods, preference relations, and applications. Twelve future research directions related to the probabilistic linguistic decision-making theory are indicated. This paper provides some insights for researchers and practitioners who have interest in complex linguistic decision making.

[1]  Ying Li,et al.  The PROMTHEE II Method Based on Probabilistic Linguistic Information and Their Application to Decision Making , 2018, Informatica.

[2]  Hui Wang,et al.  Multi-attribute Group Decision-Making Based on the Evidential Reasoning with Different Probabilistic Linguistic Term Sets , 2019, DEStech Transactions on Computer Science and Engineering.

[3]  Zeshui Xu,et al.  Entropy Measures of Probabilistic Linguistic Term Sets , 2018, Int. J. Comput. Intell. Syst..

[4]  G. Mavrotas,et al.  Determining objective weights in multiple criteria problems: The critic method , 1995, Comput. Oper. Res..

[5]  Hong-yu Zhang,et al.  Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information , 2018 .

[6]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets for Decision Making , 2012, IEEE Transactions on Fuzzy Systems.

[7]  J. Rezaei.  Best-worst multi-criteria decision-making method , 2015 .

[8]  Peide Liu,et al.  Probabilistic linguistic TODIM approach for multiple attribute decision-making , 2017, GRC 2017.

[9]  Giovanni Abramo,et al.  Are researchers that collaborate more at the international level top performers? An investigation on the Italian university system , 2018, J. Informetrics.

[10]  Zeshui Xu,et al.  Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets , 2018, Int. J. Intell. Syst..

[11]  Zeshui Xu,et al.  ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing , 2019, Nonlinear Dynamics.

[12]  Lotfi A. Zadeh,et al.  Computing with Words - Principal Concepts and Ideas , 2012, Studies in Fuzziness and Soft Computing.

[13]  Peide Liu,et al.  Probabilistic linguistic TODIM method for selecting products through online product reviews , 2019, Inf. Sci..

[14]  Huchang Liao,et al.  An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule , 2020 .

[15]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[16]  Yongming Song,et al.  Deriving the priority weights from probabilistic linguistic preference relation with unknown probabilities , 2018, PloS one.

[17]  Gholamhossein Yari,et al.  Interval Entropy and Informative Distance , 2012, Entropy.

[18]  Peide Liu,et al.  Multi-attribute decision making method based on generalized maclaurin symmetric mean aggregation operators for probabilistic linguistic information , 2019, Comput. Ind. Eng..

[19]  Bonifacio Llamazares,et al.  An analysis of the generalized TODIM method , 2018, Eur. J. Oper. Res..

[20]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[21]  C. Spearman.  The proof and measurement of association between two things. By C. Spearman, 1904. , 1987, The American journal of psychology.

[22]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[23]  Zeshui Xu,et al.  An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations , 2018, Int. J. Mach. Learn. Cybern..

[24]  Francisco Herrera,et al.  A Sequential Selection Process in Group Decision Making with a Linguistic Assessment Approach , 1995, Inf. Sci..

[25]  Francisco Herrera,et al.  A continuous interval-valued linguistic ORESTE method for multi-criteria group decision making , 2018, Knowl. Based Syst..

[26]  Francisco Herrera,et al.  A linear programming method for multiple criteria decision making with probabilistic linguistic information , 2017, Inf. Sci..

[27]  Xiaobing Yu,et al.  Combination of Probabilistic Linguistic Term Sets and PROMETHEE to Evaluate Meteorological Disaster Risk: Case Study of Southeastern China , 2019, Sustainability.

[28]  Xiaolu Zhang,et al.  A Novel Probabilistic Linguistic Approach for Large-Scale Group Decision Making with Incomplete Weight Information , 2018, Int. J. Fuzzy Syst..

[29]  Ming Tang,et al.  Inclusion measures of probabilistic linguistic term sets and their application in classifying cities in the Economic Zone of Chengdu Plain , 2019, Appl. Soft Comput..

[30]  Peide Liu,et al.  Some Muirhead mean operators for probabilistic linguistic term sets and their applications to multiple attribute decision-making , 2018, Appl. Soft Comput..

[31]  Jin-Hsien Wang,et al.  A new version of 2-tuple fuzzy linguistic representation model for computing with words , 2006, IEEE Trans. Fuzzy Syst..

[32]  Zeshui Xu,et al.  Multi-attribute group decision-making under probabilistic uncertain linguistic environment , 2018, J. Oper. Res. Soc..

[33]  Zeshui Xu,et al.  Ordered Weighted Hesitant Fuzzy Information Fusion-Based Approach to Multiple Attribute Decision Making with Probabilistic Linguistic Term Sets , 2018, Fundam. Inform..

[34]  Zeshui Xu,et al.  Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets , 2018, Appl. Soft Comput..

[35]  Ren Zhang,et al.  Comparisons of probabilistic linguistic term sets for multi-criteria decision making , 2017, Knowl. Based Syst..

[36]  J. Paelinck.  Qualiflex: A flexible multiple-criteria method , 1978 .

[37]  Huchang Liao,et al.  Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method , 2019, Appl. Soft Comput..

[38]  Jianqiang Wang,et al.  Distance‐based multicriteria group decision‐making approach with probabilistic linguistic term sets , 2018, Expert Syst. J. Knowl. Eng..

[39]  Zeshui Xu,et al.  Venture capital group decision-making with interaction under probabilistic linguistic environment , 2018, Knowl. Based Syst..

[40]  Pei Jia Ren,et al.  A Novel Hybrid Correlation Measure for Probabilistic Linguistic Term Sets and Crisp Numbers and Its Application in Customer Relationship Management , 2019, Int. J. Inf. Technol. Decis. Mak..

[41]  Edmundas Kazimieras Zavadskas,et al.  Multi-Criteria Inventory Classification Using a New Method of Evaluation Based on Distance from Average Solution (EDAS) , 2015, Informatica.

[42]  Ren Zhang,et al.  Interval‐valued probabilistic linguistic term sets in multi‐criteria group decision making , 2018, Int. J. Intell. Syst..

[43]  Carlos A. Bana e Costa,et al.  MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) , 2011 .

[44]  Huchang Liao,et al.  Water security evaluation based on the TODIM method with probabilistic linguistic term sets , 2018, Soft Comput..

[45]  Reza Baradaran Kazemzadeh,et al.  PROMETHEE: A comprehensive literature review on methodologies and applications , 2010, Eur. J. Oper. Res..

[46]  Adjei Peter Darko,et al.  Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making , 2019, Symmetry.

[47]  Dong-Ling Xu,et al.  Evidential reasoning rule for evidence combination , 2013, Artif. Intell..

[48]  Yin-Feng Xu,et al.  Consistency and consensus measures for linguistic preference relations based on distribution assessments , 2014, Inf. Fusion.

[49]  Xiaozhan Xu,et al.  The SIR method: A superiority and inferiority ranking method for multiple criteria decision making , 2001, Eur. J. Oper. Res..

[50]  Decui Liang,et al.  Grey Relational Analysis Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Geometric Bonferroni Mean , 2017, International Journal of Fuzzy Systems.

[51]  Francisco Herrera,et al.  Probabilistic Linguistic MULTIMOORA: A Multicriteria Decision Making Method Based on the Probabilistic Linguistic Expectation Function and the Improved Borda Rule , 2018, IEEE Transactions on Fuzzy Systems.

[52]  Yongming Song,et al.  A large-scale group decision-making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection , 2019, J. Oper. Res. Soc..

[53]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Set and Its Application in Decision Making: A State-of-the-Art Survey , 2017, International Journal of Fuzzy Systems.

[54]  M. Roubens.  Preference relations on actions and criteria in multicriteria decision making , 1982 .

[55]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making , 2014, Inf. Sci..

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

[57]  Edmundas Kazimieras Zavadskas,et al.  A new additive ratio assessment (ARAS) method in multicriteria decision‐making , 2010 .

[58]  Zeshui Xu,et al.  Probabilistic Linguistic Analytic Hierarchy Process and Its Application on the Performance Assessment of Xiongan New Area , 2018, Int. J. Inf. Technol. Decis. Mak..

[59]  Zeshui Xu,et al.  Expected consistency-based emergency decision making with incomplete probabilistic linguistic preference relations , 2019, Knowl. Based Syst..

[60]  Zeshui Xu,et al.  An overview of probabilistic-based expressions for qualitative decision-making: techniques, comparisons and developments , 2018, International Journal of Machine Learning and Cybernetics.

[61]  Michel Beuthe,et al.  Comparative analysis of UTA multicriteria methods , 2001, Eur. J. Oper. Res..

[62]  K. S. Ravichandran,et al.  Probabilistic Linguistic Preference Relation-Based Decision Framework for Multi-Attribute Group Decision Making , 2018, Symmetry.

[63]  Mei Hong,et al.  Generalized analytic network process , 2015, Eur. J. Oper. Res..

[64]  Zeshui Xu,et al.  A projection method for multiple attribute group decision making with probabilistic linguistic term sets , 2018, Int. J. Mach. Learn. Cybern..

[65]  Chen Jin,et al.  Uncertain Probabilistic Linguistic Term Sets in Group Decision Making , 2019, International Journal of Fuzzy Systems.

[66]  Isis Truck,et al.  A new proposal to deal with hesitant linguistic expressions on preference assessments , 2018, Inf. Fusion.

[67]  Boquan Li,et al.  Operators and comparisons of probabilistic linguistic term sets , 2019, Int. J. Intell. Syst..

[68]  W. Y. Xie,et al.  Dual probabilistic linguistic term set and its application on multi-criteria group decision making problems , 2017, 2017 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM).

[69]  Zeshui Xu,et al.  Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information , 2016, Appl. Soft Comput..

[70]  T. Tanino.  Fuzzy preference orderings in group decision making , 1984 .

[71]  Huchang Liao,et al.  An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making , 2018, Inf. Fusion.

[72]  Zeshui Xu,et al.  Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets , 2016, Inf. Sci..

[73]  Ju-Xiang Wang,et al.  A MAGDM Algorithm with Multi-Granular Probabilistic Linguistic Information , 2019, Symmetry.

[74]  Jawad Ali,et al.  Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making , 2018, Symmetry.

[75]  Francisco Herrera,et al.  Interval MULTIMOORA Method Integrating Interval Borda Rule and Interval Best–Worst-Method-Based Weighting Model: Case Study on Hybrid Vehicle Engine Selection , 2020, IEEE Transactions on Cybernetics.

[76]  Hong-yu Zhang,et al.  A Novel Selection Model of Surgical Treatments for Early Gastric Cancer Patients Based on Heterogeneous Multicriteria Group Decision-Making , 2018, Symmetry.

[77]  Xiaolu Zhang,et al.  A probabilistic linguistic-based deviation method for multi-expert qualitative decision making with aspirations , 2020, Appl. Soft Comput..

[78]  Allan D. Shocker,et al.  Linear programming techniques for multidimensional analysis of preferences , 1973 .

[79]  Bernard Roy,et al.  Classement et choix en présence de points de vue multiples , 1968 .

[80]  Meng Zhao,et al.  An Approach to Consensus Measure Based on Possibility Degrees of PLTSs in Group Decision Making , 2018, Int. J. Fuzzy Syst..

[81]  Xiaolu Zhang,et al.  Probabilistic Linguistic VIKOR Method to Evaluate Green Supply Chain Initiatives , 2017 .

[82]  Cheng Zhang,et al.  An Integrated Method with PROMETHEE and Conflict Analysis for Qualitative and Quantitative Decision-Making: Case Study of Site Selection for Wind Power Plants , 2019, Cognitive Computation.

[83]  Zeshui Xu,et al.  Probabilistic linguistic term sets in multi-attribute group decision making , 2016, Inf. Sci..

[84]  PingHua Zhang,et al.  Assessment of Service Quality in Wireless Sensor Networks with Probabilistic Linguistic Term Sets , 2017, Int. J. Online Eng..

[85]  Edmundas Kazimieras Zavadskas,et al.  Selection of rational dispute resolution method by applying new step‐wise weight assessment ratio analysis (Swara) , 2010 .

[86]  Gwo-Hshiung Tzeng,et al.  Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS , 2004, Eur. J. Oper. Res..

[87]  Xin He,et al.  Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making , 2017, Symmetry.

[88]  Ming-Lang Tseng,et al.  Decision-making model for sustainable supply chain finance under uncertainties , 2018, International Journal of Production Economics.

[89]  Lisheng Jiang,et al.  Mixed fuzzy least absolute regression analysis with quantitative and probabilistic linguistic information , 2020, Fuzzy Sets Syst..

[90]  L. R. Dice.  Measures of the Amount of Ecologic Association Between Species , 1945 .

[91]  Alessandro Laio,et al.  Clustering by fast search and find of density peaks , 2014, Science.

[92]  Zeshui Xu,et al.  Severity assessment of chronic obstructive pulmonary disease based on hesitant fuzzy linguistic COPRAS method , 2018, Appl. Soft Comput..

[93]  Zeshui Xu,et al.  An ordinal consistency-based group decision making process with probabilistic linguistic preference relation , 2018, Inf. Sci..

[94]  Huchang Liao,et al.  Bibliometric analysis for highly cited papers in operations research and management science from 2008 to 2017 based on Essential Science Indicators , 2019, Omega.

[95]  Zeshui Xu,et al.  A consensus process for group decision making with probabilistic linguistic preference relations , 2017, Inf. Sci..

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

[97]  Zeshui Xu,et al.  Probabilistic Linguistic Distance Measures and Their Applications in Multi-criteria Group Decision Making , 2018 .

[98]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[99]  Ludo Waltman,et al.  Software survey: VOSviewer, a computer program for bibliometric mapping , 2009, Scientometrics.

[100]  Zeshui Xu,et al.  Consistency-based risk assessment with probabilistic linguistic preference relation , 2016, Appl. Soft Comput..

[101]  Yucheng Dong,et al.  Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions , 2015, Knowl. Based Syst..

[102]  Francisco Herrera,et al.  An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges , 2019, Inf. Fusion.

[103]  Lin Li,et al.  Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations , 2019, J. Oper. Res. Soc..

[104]  Huchang Liao,et al.  A consensus-based probabilistic linguistic gained and lost dominance score method , 2019, Eur. J. Oper. Res..

[105]  Deyi Li,et al.  A new cognitive model: Cloud model , 2009 .

[106]  Jianjun Zhu,et al.  A Probabilistic Linguistic Group Decision-Making Method From a Reliability Perspective Based on Evidential Reasoning , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[107]  Qi Liu,et al.  Probabilistic linguistic QUALIFLEX approach with possibility degree comparison , 2019, J. Intell. Fuzzy Syst..

[108]  P. Jaccard.  THE DISTRIBUTION OF THE FLORA IN THE ALPINE ZONE.1 , 1912 .

[109]  Jean-Claude Vansnick.  On the problem of weights in multiple criteria decision making (the noncompensatory approach) , 1986 .

[110]  Zeshui Xu,et al.  A new approach to deal with consistency and consensus issues for hesitant fuzzy linguistic preference relations , 2019, Appl. Soft Comput..

[111]  Sui-Zhi Luo,et al.  Evaluation of Cleaner Production for Gold Mines Employing a Hybrid Multi-Criteria Decision Making Approach , 2018, Sustainability.

[112]  Xiuming Chen,et al.  A MAGDM Model with Multi-Granular Probabilistic Linguistic Power , 2018, 2018 5th International Conference on Information Science and Control Engineering (ICISCE).

[113]  Ali Gazni,et al.  Investigating different types of research collaboration and citation impact: a case study of Harvard University’s publications , 2011, Scientometrics.

[114]  Jianqiang Wang,et al.  Personalized restaurant recommendation method combining group correlations and customer preferences , 2018, Inf. Sci..

[115]  Zeshui Xu,et al.  Incomplete linguistic preference relations and their fusion , 2006, Inf. Fusion.

[116]  Huchang Liao,et al.  DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making , 2020, Omega.

[117]  Zeshui Xu,et al.  Therapeutic Schedule Evaluation for Brain-Metastasized Non-Small Cell Lung Cancer with A Probabilistic Linguistic ELECTRE II Method , 2018, International journal of environmental research and public health.

[118]  Yi Yang,et al.  Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making , 2016, Inf. Sci..

[119]  S. Si,et al.  DEMATEL Technique: A Systematic Review of the State-of-the-Art Literature on Methodologies and Applications , 2018 .