{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T20:13:16Z","timestamp":1785528796834,"version":"3.56.0"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T00:00:00Z","timestamp":1670976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["72001214"],"award-info":[{"award-number":["72001214"]}]},{"name":"Natural Science Foundation of China","award":["62106283"],"award-info":[{"award-number":["62106283"]}]},{"name":"Natural Science Foundation of China","award":["72071209"],"award-info":[{"award-number":["72071209"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Existing missile defense target threat assessment methods ignore the target timing and battlefield changes, leading to low assessment accuracy. In order to overcome this problem, a dynamic multi-time fusion target threat assessment method is proposed. In this method, a new interval valued intuitionistic fuzzy weighted averaging operator is proposed to effectively aggregate multi-source uncertain information; an interval-valued intuitionistic fuzzy entropy based on a cosine function (IVIFECF) is designed to determine the target attribute weight; an improved interval-valued intuitionistic fuzzy number distance measurement model is constructed to improve the discrimination of assessment results. Specifically, first of all, we define new interval-valued intuitionistic fuzzy operation rules based on algebraic operations. We use these rules to provide a new model of interval-valued intuitionistic fuzzy weighted arithmetic averaging (IVIFWAA) and geometric averaging (IVIFWGA) operators, and prove a number of algebraic properties of these operators. Then, considering the subjective and objective weights of the incoming target, a comprehensive weight model of target attributes based on IVIFECF is proposed, and the Poisson distribution method is used to solve the time series weights to process multi-time situation information. On this basis, the IVIFWAA and IVIFWGA operators are used to aggregate the decision information from multiple times and multiple decision makers. Finally, based on the improved TOPSIS method, the interval-valued intuitionistic fuzzy numbers are ordered, and the weighted multi-time fusion target threat assessment result is obtained. Simulation results of comparison show that the proposed method can effectively improve the reliability and accuracy of target threat assessment in missile defense.<\/jats:p>","DOI":"10.3390\/e24121825","type":"journal-article","created":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T01:52:30Z","timestamp":1671069150000},"page":"1825","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["A New Model of Interval-Valued Intuitionistic Fuzzy Weighted Operators and Their Application in Dynamic Fusion Target Threat Assessment"],"prefix":"10.3390","volume":"24","author":[{"given":"Chengli","family":"Fan","sequence":"first","affiliation":[{"name":"Air Defense and Antimissile College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiang","family":"Fu","sequence":"additional","affiliation":[{"name":"Air Defense and Antimissile College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0962-0671","authenticated-orcid":false,"given":"Yafei","family":"Song","sequence":"additional","affiliation":[{"name":"Air Defense and Antimissile College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingqi","family":"Lu","sequence":"additional","affiliation":[{"name":"Air Defense and Antimissile College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Li","sequence":"additional","affiliation":[{"name":"Air Defense and Antimissile College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaowen","family":"Zhu","sequence":"additional","affiliation":[{"name":"Air Defense and Antimissile College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5349","DOI":"10.1007\/s10462-021-10119-8","article-title":"Group decision-making with Fermatean fuzzy soft expert knowledge","volume":"55","author":"Akram","year":"2022","journal-title":"Artif. Intell. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1057\/s41274-017-0182-y","article-title":"Multi-attribute group decision-making under probabilistic uncertain linguistic environment","volume":"60","author":"Lin","year":"2018","journal-title":"Oper. Res. Soc."},{"key":"ref_3","first-page":"1300","article-title":"Threat assessment method of warships formation air defense based on DBN under the condition of small sample data missing","volume":"41","author":"Sun","year":"2019","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_4","first-page":"54","article-title":"The application of the hybrid interval rough weighted Power-Heronian operator in multi-criteria decision making","volume":"3","year":"2020","journal-title":"Oper. Res. Eng. Sci. Theory Appl."},{"key":"ref_5","first-page":"1322","article-title":"Combination of temporal evidence sources based on intuitionistic fuzzy sets","volume":"42","author":"Song","year":"2016","journal-title":"Acta. Auto. Sin."},{"key":"ref_6","first-page":"2805","article-title":"Techniques for threat assessment based on intuitionistic fuzzy reasoning","volume":"29","author":"Lei","year":"2007","journal-title":"J. Electron. Inform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4127","DOI":"10.3233\/JIFS-169972","article-title":"Air multi-target threat assessment method based on improved GGIFSS","volume":"36","author":"Qiang","year":"2019","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_8","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":"Inform. Contr."},{"key":"ref_9","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 Set. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"44","DOI":"10.31181\/rme200101044p","article-title":"Normalized weighted geometric Dombi Bonferroni mean operator with interval grey numbers: Application in multicriteria decision making","volume":"1","author":"Pamucar","year":"2020","journal-title":"Rep. Mech. Eng."},{"key":"ref_11","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 assessment","volume":"428","author":"Shen","year":"2018","journal-title":"Inform. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.knosys.2016.01.017","article-title":"Approaches to group decision making with intuitionistic fuzzy preference relations based on multiplicative consistency","volume":"97","author":"Jin","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1007\/s12204-019-2098-y","article-title":"Multi-criteria decision making based on correlation coefficient of triangular intuitionistic fuzzy numbers","volume":"24","author":"Wu","year":"2019","journal-title":"J. Shanghai Jiaotong Univ. (Sci.)"},{"key":"ref_14","first-page":"161","article-title":"Multi-attribute index processing method of target threat assessment in ground combat","volume":"47","author":"Kong","year":"2021","journal-title":"Acta. Auto. Sin."},{"key":"ref_15","first-page":"2509","article-title":"Threat assessment method with uncertain attribute weight based on intuitionistic fuzzy multi-attribute decision","volume":"42","author":"Wang","year":"2014","journal-title":"Acta. Electron."},{"key":"ref_16","first-page":"108","article-title":"Air target threat assessment based on intuitionistic fuzzy analytic hierarchy process","volume":"41","author":"Xiao","year":"2019","journal-title":"J. Detec. Contr."},{"key":"ref_17","first-page":"697","article-title":"Evaluating and sequencing of air target threat based on lFE and dynamic intuitionistic fuzzy sets","volume":"36","author":"Zhang","year":"2014","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103276","DOI":"10.1016\/j.engappai.2019.103276","article-title":"A novel target threat assessment method based on three-way decisions under intuitionistic fuzzy multi-attribute decision making environment","volume":"87","author":"Gao","year":"2020","journal-title":"Eng. Appl. Artif. Intel."},{"key":"ref_19","first-page":"1","article-title":"Hybridizations of Archimedean copula and generalized MSM operators and their applications in interactive decision-making with q-rung probabilistic dual hesitant fuzzy environment","volume":"11","author":"Anusha","year":"2022","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1016\/j.fss.2006.12.018","article-title":"Subsethood, entropy, and cardinality for interval-valued fuzzy sets-An algebraic Derivation","volume":"158","author":"Vlachos","year":"2007","journal-title":"Fuzzy Set. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3864","DOI":"10.1016\/j.apm.2010.03.025","article-title":"Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets","volume":"34","author":"Ye","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Chen, C.H. (2020). A Novel Multi-Criteria Decision-Making Model for Building Material Supplier Selection Based on Entropy-AHP Weighted TOPSIS. Entropy, 22.","DOI":"10.3390\/e22020259"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","article-title":"Interval valued intuitionistic fuzzy sets","volume":"31","author":"Atanassov","year":"1989","journal-title":"Fuzzy. Set. Syst."},{"key":"ref_24","first-page":"215","article-title":"Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making","volume":"22","author":"Xu","year":"2007","journal-title":"J. Control Decis."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/TFUZZ.2012.2189405","article-title":"Intuitionistic fuzzy information aggregation using Einstein operations","volume":"20","author":"Wang","year":"2012","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13353","DOI":"10.1007\/s00500-021-06181-7","article-title":"New aggregation operators on group-based generalized intuitionistic fuzzy soft sets","volume":"25","author":"Hayat","year":"2021","journal-title":"Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lourenzutti (2017). R.; Krohling. R.A.; Reformat, M.Z. Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction. Inform. Sci., 408, 41\u201369.","DOI":"10.1016\/j.ins.2017.04.037"},{"key":"ref_28","first-page":"2014","article-title":"Ranking method of interval-valued intuitionistic fuzzy numbers based on TOPSIS","volume":"30","author":"Tan","year":"2015","journal-title":"J. Control Decis."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6333","DOI":"10.1016\/j.eswa.2010.11.108","article-title":"An approach to aggregating interval numbers into interval-valued intuitionistic fuzzy information for group decision making","volume":"38","author":"Yue","year":"2011","journal-title":"Expert. Syst. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.ijar.2007.08.008","article-title":"Dynamic intuitionistic fuzzy multi-attribute decision-making","volume":"48","author":"Xu","year":"2008","journal-title":"Int. J. Approx. Reason."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.eswa.2017.03.066","article-title":"Developing dynamic intuitionistic normal fuzzy aggregation operators for multi-attribute decision-making with time sequence preference","volume":"82","author":"Yang","year":"2017","journal-title":"Expert. Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"301","DOI":"10.21629\/JSEE.2017.02.12","article-title":"Modeling and applying credible interval intuitionistic fuzzy reciprocal preference relations in group decision making","volume":"28","author":"Zhou","year":"2017","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_33","first-page":"850","article-title":"Dynamic multi-attribute decision-making method with interval-valued intuitionistic fuzzy power weighted operators","volume":"41","author":"Chen","year":"2019","journal-title":"Syst. Eng. Electron."},{"key":"ref_34","first-page":"811","article-title":"Intuitionistic fuzzy set threat assessment based on improved TOPSIS and multiple times fusion","volume":"34","author":"Zhang","year":"2019","journal-title":"J. Control Decis."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1825\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:41:18Z","timestamp":1760146878000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1825"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,14]]},"references-count":34,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["e24121825"],"URL":"https:\/\/doi.org\/10.3390\/e24121825","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,14]]}}}