{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T00:15:11Z","timestamp":1782951311189,"version":"3.54.5"},"reference-count":103,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,13]],"date-time":"2023-07-13T00:00:00Z","timestamp":1689206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universiti Malaysia Pahang","award":["PGRS220301"],"award-info":[{"award-number":["PGRS220301"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review.<\/jats:p>","DOI":"10.3390\/info14070400","type":"journal-article","created":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:39:41Z","timestamp":1689295181000},"page":"400","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0763-0948","authenticated-orcid":false,"given":"Nik Muhammad Farhan Hakim Nik Badrul","family":"Alam","sequence":"first","affiliation":[{"name":"Centre for Mathematical Sciences, Universiti Malaysia Pahang, Kuantan 26300, Pahang, Malaysia"},{"name":"Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA Pahang Branch, Jengka 26400, Pahang, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ku Muhammad Naim","family":"Ku Khalif","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Sciences, Universiti Malaysia Pahang, Kuantan 26300, Pahang, Malaysia"},{"name":"Centre of Excellence for Artificial Intelligence & Data Science, Universiti Malaysia Pahang, Kuantan 26300, Pahang, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nor Izzati","family":"Jaini","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Sciences, Universiti Malaysia Pahang, Kuantan 26300, Pahang, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6166-296X","authenticated-orcid":false,"given":"Alexander","family":"Gegov","sequence":"additional","affiliation":[{"name":"School of Computing, University of Portsmouth, Portsmouth PO1 3HE, UK"},{"name":"English Faculty of Engineering, Technical University of Sofia, 1756 Sofia, Bulgaria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0020-0255(75)90017-1","article-title":"The Concept of a Linguistic Variable and Its Application to Approximate Reasoning-III","volume":"9","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic Fuzzy Sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_4","first-page":"529","article-title":"Hesitant Fuzzy Sets","volume":"29","author":"Torra","year":"2010","journal-title":"Int. J. Intell. Syst."},{"key":"ref_5","first-page":"33","article-title":"Single Valued Neutrosophic Sets","volume":"3","author":"Wang","year":"2011","journal-title":"Fuzzy Sets Rough Sets Multivalued Oper. Appl."},{"key":"ref_6","unstructured":"Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability. Am. Res. Press, 1\u2013141."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Aliev, R.A. (2013). Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions, Springer.","DOI":"10.1007\/978-3-642-34895-2"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zadeh, L.A. (2009, January 10\u201312). Computing with Words and Perceptions-A Paradigm Shift. Proceedings of the 2009 IEEE International Conference on Information Reuse & Integration, Las Vegas, CA, USA.","DOI":"10.1109\/IRI.2009.5211627"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/978-1-4615-6245-0_8","article-title":"Imperfect Information: Imprecision and Uncertainty","volume":"Volume 17","author":"Smets","year":"1997","journal-title":"Uncertainty Management in Information Systems"},{"key":"ref_10","first-page":"37","article-title":"A Consistency-Driven Approach to Construction of Z-Number-Valued Pairwise Comparison Matrices","volume":"18","author":"Aliev","year":"2021","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1061\/(ASCE)CO.1943-7862.0002362","article-title":"Z-Number-Based Quantitative Expression of Activity Information in Uncertain Project Scheduling","volume":"148","author":"Liu","year":"2022","journal-title":"J. Constr. Eng. Manag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.1016\/j.ins.2011.02.022","article-title":"A Note on Z-Numbers","volume":"181","author":"Zadeh","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1142\/S0219622020300025","article-title":"A Review on Some Arithmetic Concepts of Z-Number and Its Application to Real-World Problems","volume":"19","author":"Abdullahi","year":"2020","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"310","DOI":"10.12688\/f1000research.109709.1","article-title":"Fuzzy MCDM Models for Selection of the Tourism Development Site: The Case of Azerbaijan","volume":"11","author":"Nuriyev","year":"2022","journal-title":"F1000Research"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1617","DOI":"10.1016\/j.ins.2022.07.056","article-title":"Information Volume of Z-Number","volume":"608","author":"Xu","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TFUZZ.2021.3094657","article-title":"A Decade of the Z-Numbers","volume":"30","author":"Banerjee","year":"2022","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.30564\/jcsr.v4i2.4499","article-title":"A Review on Ranking of Z-Numbers","volume":"4","author":"Bilgin","year":"2022","journal-title":"J. Comput. Sci. Res."},{"key":"ref_18","first-page":"703","article-title":"A Method of Converting Z-Number to Classical Fuzzy Number","volume":"9","author":"Kang","year":"2012","journal-title":"J. Inf. Comput. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3232","DOI":"10.1109\/TFUZZ.2018.2816581","article-title":"Z-VIKOR Method Based on a New Comprehensive Weighted Distance Measure of Z-Number and Its Application","volume":"26","author":"Shen","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gardashova, L.A. (2019). Z-Number Based TOPSIS Method in Multi-Criteria Decision Making, Springer International Publishing.","DOI":"10.1007\/978-3-030-04164-9_10"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Aliev, R.A., Huseynov, O.H., Aliyev, R.R., and Alizadeh, A.A. (2015). The Arithmetic of Z-Numbers, World Scientific Publishing.","DOI":"10.1142\/9575"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.procs.2017.11.249","article-title":"An Introduction to the Arithmetic of Z-Numbers by Using Horizontal Membership Functions","volume":"120","author":"Aliev","year":"2017","journal-title":"Procedia Comput. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.procs.2017.11.205","article-title":"A Sum of a Large Number of Z-Numbers","volume":"120","author":"Aliev","year":"2017","journal-title":"Procedia Comput. Sci."},{"key":"ref_24","first-page":"27","article-title":"Is the Conventional Interval Arithmetic Correct ?","volume":"6","author":"Piegat","year":"2012","journal-title":"J. Theor. Appl. Comput. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1080\/16168658.2018.1509517","article-title":"A Fresh Look at Z-Numbers\u2013Relationships with Belief Functions and p-Boxes","volume":"10","author":"Dubois","year":"2018","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1007\/s40815-020-00819-8","article-title":"A New Uncertainty Measure of Discrete Z-Numbers","volume":"22","author":"Li","year":"2020","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_27","first-page":"1","article-title":"A Modified Uncertainty Measure of Z-Numbers","volume":"17","author":"Li","year":"2022","journal-title":"Int. J. Comput. Commun. Control."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2021.08.077","article-title":"Relative Entropy of Z-Numbers","volume":"581","author":"Li","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1002\/int.21995","article-title":"Generating Z-Number Based on OWA Weights Using Maximum Entropy","volume":"33","author":"Kang","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yager, R.R., and Kacprzyk, J. (1997). The Ordered Weighted Averaging Operators: Theory and Applications, Springer Science & Business Media.","DOI":"10.1007\/978-1-4615-6123-1"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"15841","DOI":"10.1007\/s00500-020-04914-8","article-title":"A Modified Method of Generating Z-Number Based on OWA Weights and Maximum Entropy","volume":"24","author":"Tian","year":"2020","journal-title":"Soft Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.procs.2016.09.363","article-title":"Z-Valued T-Norm and T-Conorm Operators-Based Aggregation of Partially Reliable Information","volume":"102","author":"Aliev","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3014387","DOI":"10.1155\/2019\/3014387","article-title":"Approach to Multicriteria Group Decision Making with Z-Numbers Based on TOPSIS and Power Aggregation Operators","volume":"2019","author":"Wang","year":"2019","journal-title":"Math. Probl. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/3468.983429","article-title":"The Power Average Operator","volume":"31","author":"Yager","year":"2001","journal-title":"IEEE Trans. Syst. Man, Cybern. Part ASystems Humans."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.ins.2021.04.022","article-title":"Group Decision-Making Based on the Aggregation of Z-Numbers with Archimedean t-Norms and t-Conorms","volume":"569","author":"Peng","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1007\/s00500-022-07667-8","article-title":"A Multi-Criteria Group Decision-Making Method Based on OWA Aggregation Operator and Z-Numbers","volume":"27","author":"Cheng","year":"2022","journal-title":"Soft Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"105216","DOI":"10.1016\/j.knosys.2019.105216","article-title":"On the Fusion of Multiple Multi-Criteria Aggregation Functions with Focus on the Fusion of OWA Aggregations","volume":"191","author":"Yager","year":"2020","journal-title":"Knowl. Based Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1016\/j.ins.2022.12.005","article-title":"The Aggregation of Z-Numbers Based on Overlap Functions and Grouping Functions and Its Application on Group Decision-Making","volume":"623","author":"Qi","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"403","DOI":"10.11113\/mjfas.v16n4.1632","article-title":"Ordered Discrete and Continuous Z-Numbers","volume":"16","author":"Abdullahi","year":"2020","journal-title":"Malays. J. Fundam. Appl. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Sari, I.U., and Kahraman, C. (2021). Intelligent and Fuzzy Techniques: Smart and Innovative Solutions, Proceedings of the INFUS 2020. Advances in Intelligent Systems and Computing, Istanbul, Turkey, 21\u201323 July 2020, Springer.","DOI":"10.1007\/978-3-030-51156-2"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/s40747-020-00204-w","article-title":"Some Aggregation Operators of Neutrosophic Z-Numbers and Their Multicriteria Decision Making Method","volume":"7","author":"Du","year":"2021","journal-title":"Complex Intell. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"13975","DOI":"10.1007\/s00500-021-06199-x","article-title":"Similarity Measures Based on the Generalized Distance of Neutrosophic Z-Number Sets and Their Multi-Attribute Decision Making Method","volume":"25","author":"Ye","year":"2021","journal-title":"Soft Comput."},{"key":"ref_43","first-page":"57","article-title":"La Methode ELECTRE","volume":"8","author":"Roy","year":"1968","journal-title":"Rev. d\u2019Informatique et. Rech. Oper."},{"key":"ref_44","unstructured":"Gabus, A., and Fontela, E. (1972). World Problems, An Invitation to Further Thought within The Framework of DEMATEL, Battelle Geneva Research Centre."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Saaty, T.L. (1980). The Analytic Hierarchy Process, McGraw-Hill.","DOI":"10.21236\/ADA214804"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Hwang, C.-L., and Yoon, K. (1981). Multiple Attribute Decision Making, Springer.","DOI":"10.1007\/978-3-642-48318-9"},{"key":"ref_47","first-page":"85","article-title":"Promethee V: Mcdm Problems with Segmentation Constraints","volume":"30","author":"Brans","year":"1992","journal-title":"INFOR Inf. Syst. Oper. Res."},{"key":"ref_48","unstructured":"Opricovic, S. (1998). Multicriteria Optimization of Civil Engineering Systems. [Ph.D. Thesis, Faculty of Civil Engineering, University of Belgrade]."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.ejor.2007.10.046","article-title":"An Application of the TODIM Method to the Multicriteria Rental Evaluation of Residential Properties","volume":"193","author":"Gomes","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_50","first-page":"3","article-title":"Optimization of Weighted Aggregated Sum Product Assessment","volume":"122","author":"Zavadskas","year":"2012","journal-title":"Elektron. Elektrotechnika"},{"key":"ref_51","first-page":"25","article-title":"A New Combinative Distance-Based Assessment (CODAS) Method for Multi-Criteria Decision-Making","volume":"50","author":"Ghorabaee","year":"2016","journal-title":"Econ. Comput. Econ. Cybern. Stud. Res."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"B-141","DOI":"10.1287\/mnsc.17.4.B141","article-title":"Decision-Making in a Fuzzy Environment","volume":"17","author":"Bellman","year":"1970","journal-title":"Manage. Sci."},{"key":"ref_53","first-page":"2807","article-title":"Decision Making Using Z-Numbers under Uncertain Environment","volume":"8","author":"Kang","year":"2012","journal-title":"J. Comput. Inf. Syst."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1080\/10798587.2014.901650","article-title":"Expected Utility Based Decision Making Under Z-Information","volume":"20","author":"Zeinalova","year":"2014","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"364512","DOI":"10.1155\/2015\/364512","article-title":"Expected Utility Based Decision Making under Z-Information and Its Application","volume":"2015","author":"Aliev","year":"2015","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1080\/18756891.2016.1150003","article-title":"Interactive TOPSIS Based Group Decision Making Methodology Using Z-Numbers","volume":"9","author":"Yaakob","year":"2016","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.procs.2016.09.387","article-title":"Z-Number-Based Alloy Selection Problem","volume":"102","author":"Babanli","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.ins.2014.08.024","article-title":"The Arithmetic of Discrete Z-Numbers","volume":"290","author":"Aliev","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"791","DOI":"10.3233\/JIFS-161973","article-title":"Hybrid Fuzzy MCDM Model for Z-Numbers Using Intuitive Vectorial Cntroid","volume":"33","author":"Gegov","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Forghani, A., Sadjadi, S.J., and Moghadam, B.F. (2018). A Supplier Selection Model in Pharmaceutical Supply Chain Using PCA, Z-TOPSIS and MILP: A Case Study. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0201604"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"739","DOI":"10.3846\/20294913.2016.1261375","article-title":"A Multi-Criteria Decision Making for Renewable Energy Selection Using Z-Numbers in Uncertain Environment","volume":"24","author":"Chatterjee","year":"2018","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1016\/j.fss.2005.11.006","article-title":"On the Centroids of Fuzzy Numbers","volume":"157","author":"Wang","year":"2006","journal-title":"Fuzzy Sets Syst."},{"key":"ref_63","first-page":"88","article-title":"A Z-Number Valued Analytical Hierarchy Process","volume":"2018","author":"Zeinalova","year":"2018","journal-title":"Chem. Technol. Control Manag."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1631\/FITEE.1700434","article-title":"TODIM and TOPSIS with Z-Numbers","volume":"20","author":"Krohling","year":"2019","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1109\/TFUZZ.2016.2612303","article-title":"Approximate Reasoning on a Basis of Z-Number-Valued If-Then Rules","volume":"25","author":"Aliev","year":"2017","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.3233\/JIFS-182733","article-title":"CODAS Method Using Z-Fuzzy Numbers","volume":"38","author":"Kahraman","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1007\/s12652-019-01228-y","article-title":"Environmental Assessment under Uncertainty Using Dempster\u2013Shafer Theory and Z-Numbers","volume":"11","author":"Kang","year":"2020","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1007\/s12652-019-01251-z","article-title":"li Multi-Criteria PROMETHEE Method Based on Possibility Degree with Z-Numbers under Uncertain Linguistic Environment","volume":"11","author":"Qiao","year":"2020","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.3233\/JIFS-16139","article-title":"Ranking Z-Numbers with an Improved Ranking Method for Generalized Fuzzy Numbers","volume":"32","author":"Jiang","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Mahmoodi, A.H., Sadjadi, S.J., Sadi-Nezhad, S., Soltani, R., and Sobhani, F.M. (2020). Linguistic Z-Number Weighted Averaging Operators and Their Application to Portfolio Selection Problem. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0227307"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/978-3-030-35249-3_10","article-title":"Solution of Zadeh\u2019s \u201cFast Way\u201d Problem under z-Information","volume":"1095 AISC","author":"Aliyev","year":"2020","journal-title":"Adv. Intell. Syst. Comput."},{"key":"ref_72","unstructured":"Jabbarova, K., and Alizadeh, A.V. (2021). Advances in Intelligent Systems and Computing, Springer."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.ins.2022.03.049","article-title":"Country Selection Problem for Business Venturing in Z-Information Environment","volume":"597","author":"Aliev","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/978-3-030-92127-9_10","article-title":"Z+ \u2212 Number Based Alternatives Selection in Investment Problem","volume":"362 LNNS","author":"Ahmadov","year":"2022","journal-title":"Lect. Notes Netw. Syst."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/978-3-030-92127-9_42","article-title":"Using Z-Number-Based Information in Personnel Selection Problem","volume":"Volume 362 LNNS","author":"Gardashova","year":"2022","journal-title":"Lecture Notes in Networks and Systems"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1007\/s40747-020-00239-z","article-title":"Prioritization of Public Services for Digitalization Using Fuzzy Z-AHP and Fuzzy Z-WASPAS","volume":"7","author":"Sergi","year":"2021","journal-title":"Complex Intell. Syst."},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Liu, Q., Chen, J., Wang, W., and Qin, Q. (2021). Conceptual Design Evaluation Considering Confidence Based on Z-AHP-TOPSIS Method. Appl. Sci., 11.","DOI":"10.3390\/app11167400"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"103158","DOI":"10.1016\/j.ergon.2021.103158","article-title":"A Hybrid Evaluation Method for Human Error Probability by Using Extended DEMATEL with Z-Numbers: A Case of Cargo Loading Operation","volume":"84","author":"Wang","year":"2021","journal-title":"Int. J. Ind. Ergon."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"117369","DOI":"10.1016\/j.eswa.2022.117369","article-title":"An Integrated Multicriteria Group Decision Making Methodology for Property Concealment Risk Assessment under Z-Number Environment","volume":"205","author":"Hu","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.ins.2022.10.081","article-title":"Z-Number Dominance, Support and Opposition Relations for Multi-Criteria Decision-Making","volume":"621","author":"Peng","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_81","unstructured":"Azman, W.N.A.W., Zamri, N., and Abas, S.S. (2022). Lecture Notes in Networks and Systems, Springer."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"13333","DOI":"10.1007\/s00500-022-07487-w","article-title":"Novel Multi-Attribute Decision-Making Method Based on Z-Number Grey Relational Degree","volume":"26","author":"Li","year":"2022","journal-title":"Soft Comput."},{"key":"ref_83","first-page":"6405","article-title":"A Z-Number Based Multi-Attribute Decision-Making Algorithm for Hydro-Environmental System Management","volume":"3","author":"Nourani","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1109\/TFUZZ.2022.3191359","article-title":"Pythagorean Fuzzy Sets to Solve Z-Numbers in Decision-Making Model","volume":"31","author":"Jia","year":"2022","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_85","unstructured":"Zamri, N., Ahmad, F., Rose, A.N.M., and Makhtar, M. (2017). Recent Advances on Soft Computing and Data Mining, Proceedings of the International Conference on Soft Computing and Data Mining, Bandung, Indonesia, 18\u201320 August 2016, Springer."},{"key":"ref_86","first-page":"149","article-title":"A Fuzzy TOPSIS with Z-Numbers Method for Assessment on Memorandum of Understanding at University","volume":"7","author":"Awajan","year":"2018","journal-title":"Int. J. Eng. Technol."},{"key":"ref_87","unstructured":"Khalif, K.M.N.K., Bakar, A.S.A., and Gegov, A. (2019). Applying Fuzzy Logic for the Digital Economy and Society, Springer."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Xiao, Z.Q. (2014, January 9\u201310). Application of Z-Numbers in Multi-Criteria Decision Making. Proceedings of the 2014 International Conference on Informative and Cybernetics for Computational Social Systems (ICCSS), Qingdao, China.","DOI":"10.1109\/ICCSS.2014.6961822"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"030003","DOI":"10.1063\/1.5121040","article-title":"Integrating Fuzzy AHP and Z-TOPSIS for Supplier Selection in an Automotive Manufacturing Company","volume":"2138","author":"Ahmad","year":"2019","journal-title":"AIP Conf. Proc."},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Zamri, N., and Ibrahim, A.K.Y. (2019, January 19\u201321). A Combined of Fuzzy TOPSIS with Z-Number and Alpha-Cut for Decision Making Problems. Advances in Visual Informatics. Proceedings of the 6th International Visual Informatics Conference, IVIC 2019, Bangi, Malaysia.","DOI":"10.1007\/978-3-030-34032-2_23"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"4285","DOI":"10.3233\/JIFS-200318","article-title":"A GMCDM Approach with Linguistic Z-Numbers Based on TOPSIS and Choquet Integral Considering Risk Preference","volume":"39","author":"Tao","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/18756891.2015.1017371","article-title":"Multi-Layer Decision Methodology for Ranking Z-Numbers","volume":"8","author":"Gegov","year":"2015","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"040049","DOI":"10.1063\/1.4995881","article-title":"Ordering of Z-Numbers","volume":"1870","author":"Mohamad","year":"2017","journal-title":"AIP Conf. Proc."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1007\/s10489-017-1001-5","article-title":"Total Utility of Z-Number","volume":"48","author":"Kang","year":"2018","journal-title":"Appl. Intell."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1080\/10798587.2017.1367146","article-title":"New Multi-Layer Method for z-Number Ranking Using Hyperbolic Tangent Function and Convex Combination","volume":"24","author":"Ezadi","year":"2018","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1002\/int.21987","article-title":"Two New Methods for Ranking of Z-Numbers Based on Sigmoid Function and Sign Method","volume":"33","author":"Ezadi","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1002\/int.22301","article-title":"Ranking of Z-Numbers Based on Value and Ambiguity at Levels of Decision Making","volume":"36","author":"Chutia","year":"2020","journal-title":"Int. J. Intell. Syst."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0165-0114(96)00144-3","article-title":"On a Canonical Representation of Fuzzy Numbers","volume":"93","author":"Delgado","year":"1998","journal-title":"Fuzzy Sets Syst."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1016\/j.asoc.2016.09.013","article-title":"A New Method of Ranking Parametric Form of Fuzzy Numbers Using Value and Ambiguity","volume":"52","author":"Chutia","year":"2017","journal-title":"Appl. Soft Comput. J."},{"key":"ref_100","doi-asserted-by":"crossref","unstructured":"Farzam, M., Kermani, M.A., Allahviranloo, T., and Belaghi, M.J.S. (2021). Progress in Intelligent Decision Science. IDS 2020. Advances in Intelligent Systems and Computing, Springer.","DOI":"10.1007\/978-3-030-66501-2"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"305","DOI":"10.21123\/bsj.2023.8428","article-title":"Momentum Ranking Function of Z-Numbers and Its Application to Game Theory","volume":"20","author":"Parameswari","year":"2023","journal-title":"Baghdad Sci. J."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1016\/0898-1221(88)90124-1","article-title":"Comparison of Fuzzy Numbers Based on the Probability Measure of Fuzzy Events","volume":"15","author":"Lee","year":"1988","journal-title":"Comput. Math. Appl."},{"key":"ref_103","unstructured":"Ng, P.S., Ignatius, J., Goh, M., Rahman, A., and Zhang, F. (2018). Fuzzy Analytic Hierarchy Process, Taylor & Francis."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/14\/7\/400\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:12:06Z","timestamp":1760127126000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/14\/7\/400"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,13]]},"references-count":103,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["info14070400"],"URL":"https:\/\/doi.org\/10.3390\/info14070400","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,13]]}}}