{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,24]],"date-time":"2024-09-24T04:22:22Z","timestamp":1727151742775},"reference-count":40,"publisher":"Emerald","issue":"4","license":[{"start":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T00:00:00Z","timestamp":1717459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["GS"],"published-print":{"date-parts":[[2024,9,24]]},"abstract":"Purpose<\/jats:title>The reported Kullback\u2013Leibler (K\u2013L) distance-based generalized grey target decision method (GGTDM) for mixed attributes is an asymmetric decision-making basis (DMB) that does not have the symmetric characteristic of distance in common sense, which may affect the decision-making result. To\u00a0overcome the deficiency of the asymmetric K\u2013L distance, the symmetric K\u2013L distance is investigated to act as the DMB of GGTDM for mixed attributes.<\/jats:p><\/jats:sec>Design\/methodology\/approach<\/jats:title>The decision-making steps of the proposed approach are as follows: First, all mixed attribute values are transformed into binary connection numbers, and the target centre indices of all attributes are determined. Second, all the binary connection numbers (including the target centre indices) are divided into deterministic and uncertain terms and converted into two-tuple (determinacy and uncertainty) numbers. Third, the comprehensive weighted symmetric K\u2013L distance can be computed, as can the alternative index of normalized two-tuple (deterministic degree and uncertainty degree) number and that of the target centre. Finally, the decision-making is made by the comprehensive weighted symmetric K\u2013L distance according to the rule that the smaller the value, the better the alternative.<\/jats:p><\/jats:sec>Findings<\/jats:title>The case study verifies the proposed approach with its sufficient theoretical basis for decision-making and reflects the preferences of decision-makers to address the uncertainty of an uncertain number.<\/jats:p><\/jats:sec>Originality\/value<\/jats:title>This work compares the single-direction-based K\u2013L distance to the symmetric one and uses the symmetric K\u2013L distance as the DMB of GGTDM. At the same time, different coefficients are assigned to an uncertain number\u2019s deterministic term and uncertain term in the calculation process, as this reflects the preference of the decision-maker.<\/jats:p><\/jats:sec>","DOI":"10.1108\/gs-01-2024-0001","type":"journal-article","created":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T03:32:41Z","timestamp":1717385561000},"page":"754-769","source":"Crossref","is-referenced-by-count":0,"title":["Symmetric Kullback\u2013Leibler distance based generalized grey\u00a0target decision method for\u00a0mixed attributes"],"prefix":"10.1108","volume":"14","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-2705-1241","authenticated-orcid":false,"given":"Jinshan","family":"Ma","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0009-0000-7080-1047","authenticated-orcid":false,"given":"Hongliang","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"140","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"issue":"6","key":"key2024092402102621900_ref001","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1177\/0142331219888370","article-title":"Online monitoring scheme using principal component analysis through Kullback-Leibler divergence analysis technique for fault detection","volume":"42","year":"2020","journal-title":"Transactions of the Institute of Measurement and Control"},{"issue":"2","key":"key2024092402102621900_ref002","first-page":"59","article-title":"Multi-attribute decision analysis on three-parameter interval grey number based on bellshaped possibility","volume":"34","year":"2022","journal-title":"Journal of Grey System"},{"issue":"7","key":"key2024092402102621900_ref003","first-page":"2431","article-title":"Hybrid multiple attribute recognition based on coefficient of incidence bull's-eye-distance","volume":"36","year":"2015","journal-title":"Acta Aeronautica Et Astronautica Sinica"},{"issue":"3","key":"key2024092402102621900_ref004","first-page":"115","article-title":"A review of grey target decision model","volume":"34","year":"2022","journal-title":"Journal of Grey System"},{"issue":"4","key":"key2024092402102621900_ref005","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1108\/gs-05-2022-0049","article-title":"Grey system theory in sustainable development research\u2014a literature review (2011\u22122021)","volume":"12","year":"2022","journal-title":"Grey Systems: Theory and Application"},{"issue":"3","key":"key2024092402102621900_ref006","doi-asserted-by":"publisher","first-page":"3831","DOI":"10.3233\/jifs-190602","article-title":"A dynamic grey target evaluation method with multiple reference points for new r&d institution performance","volume":"40","year":"2021","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"22","key":"key2024092402102621900_ref007","first-page":"79","article-title":"On information and sufficiency","volume":"1","year":"1951","journal-title":"The Annals of Mathematical Statistics"},{"issue":"3","key":"key2024092402102621900_ref008","first-page":"96","article-title":"Multi-attribute group grey target decision-making method based on three-parameter interval grey number","volume":"32","year":"2020","journal-title":"Journal of Grey System"},{"issue":"1","key":"key2024092402102621900_ref009","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1109\/18.61115","article-title":"Divergence measures based on the Shannon entropy","volume":"37","year":"1991","journal-title":"IEEE Transactions on Information Theory"},{"issue":"5","key":"key2024092402102621900_ref010","doi-asserted-by":"publisher","first-page":"1957","DOI":"10.1016\/j.apm.2011.07.074","article-title":"The multi-attribute grey target decision method for attribute value within three-parameter interval grey number","volume":"36","year":"2012","journal-title":"Applied Mathematical Modelling"},{"key":"key2024092402102621900_ref011","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2014\/572529","article-title":"Grey target decision method for a variable target centre based on the decision maker's preferences","volume":"2014","year":"2014","journal-title":"Journal of Applied Mathematics"},{"issue":"1","key":"key2024092402102621900_ref012","doi-asserted-by":"publisher","first-page":"625","DOI":"10.3233\/jifs-17851","article-title":"Generalised grey target decision method for mixed attributes with index weights containing uncertain numbers","volume":"34","year":"2018","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"7","key":"key2024092402102621900_ref013","doi-asserted-by":"publisher","first-page":"523","DOI":"10.3390\/e20070523","article-title":"Generalized grey target decision method for mixed attributes based on Kullback-Leibler distance","volume":"20","year":"2018","journal-title":"Entropy"},{"issue":"24","key":"key2024092402102621900_ref014","doi-asserted-by":"publisher","first-page":"13449","DOI":"10.1007\/s00500-019-03883-x","article-title":"Generalised grey target decision method for mixed attributes based on the improved Gini\u2013Simpson index","volume":"23","year":"2019","journal-title":"Soft Computing"},{"issue":"2","key":"key2024092402102621900_ref015","first-page":"28","article-title":"Generalised grey target decision method with index and weight both containing mixed attribute values based on improved Gini-Simpson index","volume":"34","year":"2019","journal-title":"Statistics and Information Forum"},{"issue":"4","key":"key2024092402102621900_ref016","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1108\/dta-02-2019-0019","article-title":"Generalised grey target decision method based on the Gini\u2013Simpson index involving mixed attributes and uncertain numbers","volume":"53","year":"2019","journal-title":"Data Technologies and Applications"},{"issue":"7","key":"key2024092402102621900_ref017","first-page":"32","article-title":"Mixed -attribute generalized grey target decision-making method based on target of decision maker's preference","volume":"35","year":"2019","journal-title":"Statistics and Decision"},{"issue":"4","key":"key2024092402102621900_ref018","first-page":"64","article-title":"A determination method of objective weights for mixed attribute decisions based on symmetric k-l distances and decision makers' subjective preferences","volume":"26","year":"2023","journal-title":"Industrial Engineering Journal"},{"key":"key2024092402102621900_ref019","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2014\/763543","article-title":"Generalized grey target decision method for mixed attributes based on connection number","volume":"2014","year":"2014","journal-title":"Journal of Applied Mathematics"},{"key":"key2024092402102621900_ref020","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2014\/304202","article-title":"Fuzzy similar priority method for mixed attributes","volume":"2014","year":"2014","journal-title":"Journal of Applied Mathematics"},{"key":"key2024092402102621900_ref021","doi-asserted-by":"publisher","first-page":"162847","DOI":"10.1109\/access.2020.3020045","article-title":"Kullback-Leibler distance based generalized grey target decision method with index and weight both containing mixed attribute values","volume":"8","year":"2020","journal-title":"IEEE Access"},{"issue":"1","key":"key2024092402102621900_ref022","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1108\/gs-09-2020-0125","article-title":"A novel generalized grey target decision method with index and weight both containing mixed types of data","volume":"12","year":"2021","journal-title":"Grey Systems: Theory and Application"},{"issue":"6","key":"key2024092402102621900_ref023","doi-asserted-by":"publisher","first-page":"1121","DOI":"10.1007\/s10726-022-09794-x","article-title":"Combination generalized grey target decision method for mixed attributes based on zero-sum game theory","volume":"31","year":"2022","journal-title":"Group Decision and Negotiation"},{"issue":"2","key":"key2024092402102621900_ref024","doi-asserted-by":"publisher","first-page":"961","DOI":"10.2991\/icsem.2013.69","article-title":"The application research of coal seam co source identification based on the d-s evidence conflict","volume":"341","year":"2013","journal-title":"Applied Mechanics and Materials"},{"issue":"1","key":"key2024092402102621900_ref025","first-page":"69","article-title":"Grey target decision model based on interval grey number type panel data and its application","volume":"30","year":"2018","journal-title":"Journal of Grey System"},{"issue":"1","key":"key2024092402102621900_ref026","doi-asserted-by":"publisher","first-page":"35","DOI":"10.5391\/ijfis.2020.20.1.35","article-title":"Order v entropy and cross entropy of uncertain variables for portfolio selection","volume":"20","year":"2020","journal-title":"International Journal of Fuzzy Logic and Intelligent Systems"},{"key":"key2024092402102621900_ref027","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1016\/j.ins.2017.07.016","article-title":"Semi-supervised cross-entropy clustering with information bottleneck constraint","volume":"421","year":"2017","journal-title":"Information Sciences"},{"issue":"3","key":"key2024092402102621900_ref028","first-page":"291","article-title":"The decision-making model of harden grey target based on interval number with preference information on alternatives","volume":"21","year":"2009","journal-title":"Journal of Grey System"},{"key":"key2024092402102621900_ref029","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2019\/1739835","article-title":"Extended research on grey target decisions for a variable target centre based on decision maker preferences","volume":"2019","year":"2019","journal-title":"Mathematical Problems in Engineering"},{"issue":"3","key":"key2024092402102621900_ref030","doi-asserted-by":"publisher","first-page":"3883","DOI":"10.3233\/jifs-18818","article-title":"Uncertain multiplicative linguistic soft sets and their application to group decision making","volume":"35","year":"2018","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"10","key":"key2024092402102621900_ref031","doi-asserted-by":"publisher","first-page":"533","DOI":"10.3390\/e19100533","article-title":"Cross entropy method based hybridization of dynamic group optimization algorithm","volume":"19","year":"2017","journal-title":"Entropy"},{"issue":"7","key":"key2024092402102621900_ref032","doi-asserted-by":"publisher","first-page":"3797","DOI":"10.1109\/tit.2014.2320500","article-title":"R\u00e9nyi divergence and Kullback-Leibler divergence","volume":"60","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"key2024092402102621900_ref033","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1108\/gs-04-2017-0010","article-title":"Grey target decision-making model of interval grey number based on cone volume","volume":"7","year":"2017","journal-title":"Grey Systems: Theory and Application"},{"issue":"4","key":"key2024092402102621900_ref034","first-page":"77","article-title":"Grey target group decision model based on expected intervals of experts","volume":"32","year":"2020","journal-title":"Journal of Grey System"},{"issue":"1","key":"key2024092402102621900_ref035","doi-asserted-by":"publisher","first-page":"361","DOI":"10.24200\/sci.2016.3840","article-title":"A novel grey target decision-making model based on cobweb area and its application for choosing the software development pattern","volume":"23","year":"2016","journal-title":"Scientia Iranica"},{"issue":"4","key":"key2024092402102621900_ref036","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1108\/gs-08-2021-0134","article-title":"Multilayer grey situation group decision-making model based on cooperative game","volume":"12","year":"2022","journal-title":"Grey Systems-Theory and Application"},{"issue":"1","key":"key2024092402102621900_ref037","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1108\/gs-08-2023-0072","article-title":"Dynamic multi-attribute grey target group decision model based on quantum-like Bayesian networks","volume":"14","year":"2024","journal-title":"Grey Systems-Theory and Application"},{"issue":"6","key":"key2024092402102621900_ref038","first-page":"476","article-title":"The theoretical basis and basic algorithm of binary connection a+bi and its application in AI","volume":"3","year":"2008","journal-title":"CAA I Transactions on Intelligent Systems"},{"issue":"1","key":"key2024092402102621900_ref039","first-page":"41","article-title":"Decision making algorithm based on set par analysis for use when facing multiple uncertain in attributes","volume":"5","year":"2010","journal-title":"CAA I Transactions on Intelligent Systems"},{"key":"key2024092402102621900_ref040","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2020\/8930387","article-title":"A grey target group decision method with dual hesitant fuzzy information considering decision-maker\u2019s loss aversion","volume":"2020","year":"2020","journal-title":"Scientific Programming"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-01-2024-0001\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-01-2024-0001\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,24]],"date-time":"2024-09-24T02:10:42Z","timestamp":1727143842000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-01-2024-0001\/full\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,4]]},"references-count":40,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,6,4]]},"published-print":{"date-parts":[[2024,9,24]]}},"alternative-id":["10.1108\/GS-01-2024-0001"],"URL":"https:\/\/doi.org\/10.1108\/gs-01-2024-0001","relation":{},"ISSN":["2043-9377"],"issn-type":[{"type":"print","value":"2043-9377"}],"subject":[],"published":{"date-parts":[[2024,6,4]]}}}