{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T13:57:05Z","timestamp":1780581425562,"version":"3.54.1"},"reference-count":44,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,4]],"date-time":"2018-07-04T00:00:00Z","timestamp":1530662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates an intuitionistic fuzzy multiple attribute decision-making method based on weighted induced distance and its application to investment selection. Specifically, an intuitionistic fuzzy weighted induced ordered weighted averaging operator is proposed to eliminate the drawbacks of existing methods by extending the functions of the order-induced variables. The main advantage of the proposed operator is its dual roles of the order-inducing variables that can simultaneously induce arguments and moderate associated weights. A further extension of the proposed operator is its adaptation towards measuring intuitionistic fuzzy information more effectively. In addition, a multiple attribute decision-making model based on the proposed distance operators is proposed. Finally, the practicability and validity of the proposed model are illustrated by using a numerical example related to investment selection.<\/jats:p>","DOI":"10.3390\/sym10070261","type":"journal-article","created":{"date-parts":[[2018,7,4]],"date-time":"2018-07-04T12:23:02Z","timestamp":1530706982000},"page":"261","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Intuitionistic Fuzzy Multiple Attribute Decision-Making Model Based on Weighted Induced Distance Measure and Its Application to Investment Selection"],"prefix":"10.3390","volume":"10","author":[{"given":"Zhengmao","family":"Li","sequence":"first","affiliation":[{"name":"School of Finance, Zhejiang Gongshang University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dechao","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Computer and Information, Zhejiang Wanli University, Ningbo 315100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shouzhen","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Business, Ningbo University, Ningbo 315211, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,4]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"3653","DOI":"10.3233\/IFS-162111","article-title":"Visualization and quantitative research on intuitionistic fuzzy studies","volume":"30","author":"Yu","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.asoc.2015.03.027","article-title":"Researching the development of Atanassov intuitionistic fuzzy set: Using a citation network analysis","volume":"32","author":"Yu","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_4","first-page":"1073","article-title":"Supplier evaluation and selection in fuzzy environments: A review of MADM approaches","volume":"30","author":"Mehdi","year":"2017","journal-title":"Econ. Res. Ekon. Istra\u017e."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.ins.2017.10.045","article-title":"An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation","volume":"428","author":"Shen","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.knosys.2015.06.011","article-title":"A distance measure between intuitionistic fuzzy belief functions","volume":"86","author":"Song","year":"2015","journal-title":"Knowl.-Based Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.ins.2013.04.040","article-title":"New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets","volume":"245","author":"Zhang","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1016\/j.patrec.2004.06.006","article-title":"Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance","volume":"25","author":"Hung","year":"2004","journal-title":"Pattern Recognit. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1016\/j.knosys.2011.05.013","article-title":"Intuitionistic fuzzy ordered weighted distance operator","volume":"24","author":"Zeng","year":"2011","journal-title":"Knowl.-Based Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1108\/K-04-2015-0093","article-title":"TOPSIS method for intuitionistic fuzzy multiple-criteria decision making and its application to investment selection","volume":"45","author":"Zeng","year":"2016","journal-title":"Kybernetes"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.cie.2010.09.017","article-title":"Decision making with distance measures and induced aggregation operators","volume":"60","author":"Casanovas","year":"2011","journal-title":"Comput. Ind. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"11","DOI":"10.3233\/JIFS-141219","article-title":"Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making","volume":"32","author":"Zeng","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_13","first-page":"123","article-title":"A new Minkowski distance based on induced aggregation operators","volume":"4","author":"Casanovas","year":"2011","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1080\/01969722.2016.1206767","article-title":"Decision making in reinsurance with induced OWA operators and Minkowski distances","volume":"47","author":"Casanovas","year":"2016","journal-title":"Cybern. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7603","DOI":"10.1016\/j.eswa.2010.12.103","article-title":"Induced aggregation operators in the Euclidean distance and its application in financial decision making","volume":"38","author":"Casanovas","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1142\/S0219622013500296","article-title":"Extended induced ordered weighted averaging distance operators and their application to group decision-making","volume":"12","author":"Zeng","year":"2013","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"431","DOI":"10.3846\/20294913.2013.821686","article-title":"Uncertain group decision-making with induced aggregation operators and Euclidean distance","volume":"19","author":"Su","year":"2013","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"127","DOI":"10.3233\/IFS-120720","article-title":"Fuzzy decision making with induced heavy aggregation operators and distance measures","volume":"26","author":"Zeng","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1016\/j.jcss.2014.03.004","article-title":"A method based on induced aggregation operators and distance measures to multiple attribute decision making under 2-tuple linguistic environment","volume":"80","author":"Li","year":"2014","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1002\/int.21648","article-title":"Fuzzy linguistic induced euclidean OWA distance operator and its application in group linguistic decision making","volume":"29","author":"Xian","year":"2014","journal-title":"Int. J. Intell. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1080\/01969722.2015.1012889","article-title":"Uncertain induced heavy aggregation distance operator and its application to decision making","volume":"46","author":"Su","year":"2015","journal-title":"Cybern. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s10044-014-0397-3","article-title":"Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making","volume":"19","author":"Xian","year":"2016","journal-title":"Pattern Anal. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1002\/int.21874","article-title":"A novel intuitionistic fuzzy induced ordered weighted Euclidean distance operator and its application for group decision making","volume":"32","author":"Xue","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","article-title":"Intuitionistic fuzzy aggregation operators","volume":"15","author":"Xu","year":"2007","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1109\/21.87068","article-title":"On ordered weighted averaging aggregation operators in multi-criteria decision making","volume":"18","author":"Yager","year":"1988","journal-title":"IEEE Trans. Syst. Man Cybern. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/3477.752789","article-title":"Induced ordered weighted averaging operators","volume":"29","author":"Yager","year":"1999","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1002\/int.21693","article-title":"A New Family of Induced OWA Operators","volume":"30","author":"Aggarwal","year":"2015","journal-title":"Int. J. Intell. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1002\/int.21886","article-title":"Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach","volume":"32","author":"Zeng","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.asoc.2016.11.024","article-title":"Distance measures, weighted averages, OWA operators and Bonferroni means","volume":"50","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"969","DOI":"10.3846\/20294913.2016.1216472","article-title":"A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making","volume":"24","author":"Zeng","year":"2018","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_31","first-page":"3205","article-title":"A novel method based on induced aggregation operator for classroom teaching quality evaluation with probabilistic and Pythagorean fuzzy information","volume":"14","author":"Zeng","year":"2018","journal-title":"Eurasia J. Math. Sci. Technol. Educ."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"11560","DOI":"10.1016\/j.eswa.2011.03.034","article-title":"A unified model between the weighted average and the induced OWA operator","volume":"38","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"839","DOI":"10.2298\/CSIS130109046S","article-title":"Induced intuitionistic fuzzy ordered weighted averaging\u2014Weighted average operator and its application to business decision-making","volume":"11","author":"Zeng","year":"2014","journal-title":"Comput. Sci. Inf. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"901","DOI":"10.3233\/IFS-131048","article-title":"Entrepreneurial fuzzy group decision-making under complex environments","volume":"27","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1002\/int.21716","article-title":"The ordered weighted average in the variance and the covariance","volume":"30","author":"Sarabia","year":"2015","journal-title":"Int. J. Intell. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1002\/int.21953","article-title":"A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making","volume":"33","author":"Zeng","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1080\/0951192X.2016.1187299","article-title":"A Decision Investment Model to Design Manufacturing Systems based on a genetic algorithm and Monte-Carlo simulation","volume":"30","author":"Renna","year":"2017","journal-title":"Int. J. Comput. Integr. Manuf."},{"key":"ref_38","first-page":"439","article-title":"A novel hybrid method for non-traditional machining process selection using factor relationship and multi-attributive border approximation method","volume":"15","author":"Chatterjee","year":"2017","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_39","first-page":"97","article-title":"Application of the performance selection index method for solving machining MCDM problems","volume":"15","author":"Petkovic","year":"2017","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"121","DOI":"10.31181\/dmame1801121r","article-title":"A rough strength relational DEMATEL model for analysing the key success factors of hospital service quality","volume":"1","author":"Roy","year":"2018","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"82","DOI":"10.31181\/dmame180182v","article-title":"A rough multicriteria approach for evaluation of the supplier criteria in automotive industry","volume":"1","author":"Fazlollahtabar","year":"2018","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1002\/int.21676","article-title":"Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets","volume":"29","author":"Zhang","year":"2014","journal-title":"Int. J. Intell. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ye, J. (2017). Multiple attribute decision-making method using correlation coefficients of normal Neutrosophic sets. Symmetry, 9.","DOI":"10.3390\/sym9060080"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Wang, J., Wei, G.W., and Wei, Y. (2018). Models for green supplier selection with some 2-tuple linguistic Neutrosophic number Bonferroni mean operators. Symmetry, 10.","DOI":"10.3390\/sym10050131"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/7\/261\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:11:18Z","timestamp":1760195478000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/7\/261"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,4]]},"references-count":44,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["sym10070261"],"URL":"https:\/\/doi.org\/10.3390\/sym10070261","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,4]]}}}