{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T22:09:56Z","timestamp":1767910196119,"version":"3.49.0"},"reference-count":42,"publisher":"Institution of Engineering and Technology (IET)","issue":"1","license":[{"start":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T00:00:00Z","timestamp":1616716800000},"content-version":"vor","delay-in-days":25,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["ietresearch.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["CAAI Trans on Intel Tech"],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The objective of the authors is to establish an innovative concept of the complex hesitant fuzzy set (CHFS), which is the combination of the hesitant fuzzy set and the complex fuzzy set to manage complex and awkward information in the real\u2010decision theory. The structure and the basic properties of the proposed set are studied in detail. Based on the internal structure of the set and to find the degree of the discrimination between the pairs of the CHFSs, the generalized distance measures and modified generalized distance measures are defined. Several properties and their relationship between them are derived in detail. Also, several cases of the proposed measures are exposed which reduce them to the existing studies. Furthermore, based on these proposed measures, a decision\u2010making approach is established under the uncertain environment and several numerical examples are given to examine the feasibility and validity of the explored measures. Finally, the credibility of the modified and parameterized distance measures based on CHFSs is verified by comparing them with some existing measures.<\/jats:p>","DOI":"10.1049\/cit2.12016","type":"journal-article","created":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T09:19:54Z","timestamp":1616750394000},"page":"93-122","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["CHFS: Complex hesitant fuzzy sets\u2010their applications to decision making with different and innovative distance measures"],"prefix":"10.1049","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9099-8422","authenticated-orcid":false,"given":"Harish","family":"Garg","sequence":"first","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering and Technology Deemed University  Patiala Punjab India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3871-3845","authenticated-orcid":false,"given":"Tahir","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics International Islamic University  Islamabad Pakistan"}]},{"given":"Ubaid ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics International Islamic University  Islamabad Pakistan"}]},{"given":"Zeeshan","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics International Islamic University  Islamabad Pakistan"}]}],"member":"265","published-online":{"date-parts":[[2021,3,26]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2014.12.012"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2016.11.001"},{"key":"e_1_2_7_5_1","first-page":"388","article-title":"A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning.","author":"Szmidt E.","year":"2004","journal-title":"In: International conference on artificial intelligence and soft computing"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00365-7"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/padm.12007"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.01.016"},{"key":"e_1_2_7_9_1","doi-asserted-by":"crossref","unstructured":"Lemmi A.A. Betti G.(eds.).:Fuzzy Set Approach to Multidimensional Poverty Measurement.Springer Science & Business Media US(2006)","DOI":"10.1007\/978-0-387-34251-1"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.3390\/math7121180"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.3390\/math7080685"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.3390\/math7111091"},{"issue":"1","key":"e_1_2_7_13_1","article-title":"Measuring the solar cell parameters using fuzzy set technique","volume":"1","author":"Rasheed M.S.","year":"2019","journal-title":"Insight\u2010Electronic"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-017-3325-9"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/91.995119"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00354-011-0302-1"},{"key":"e_1_2_7_17_1","doi-asserted-by":"crossref","unstructured":"Li C. Chiang T.W.:Complex neuro\u2010fuzzy self\u2010learning approach to function approximation. In:Asian conference on intelligent information and database systems. pp.289\u2013299.Springer Berlin Heidelberg(2010)","DOI":"10.1007\/978-3-642-12101-2_30"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.01.010"},{"key":"e_1_2_7_19_1","first-page":"1045","article-title":"Ninth IEEE international conference on fuzzy systems","volume":"2","author":"Nguyen H.T.","year":"2000","journal-title":"Complex fuzzy sets: towards new foundations FUZZ\u2010IEEE 2000 (Cat. No. 00CH37063)"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2004.839669"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12559-019-09678-4"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-019-09772-x"},{"key":"e_1_2_7_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/int.20418"},{"key":"e_1_2_7_24_1","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2180"},{"key":"e_1_2_7_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2015.12.005"},{"key":"e_1_2_7_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.12.017"},{"key":"e_1_2_7_27_1","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161430"},{"key":"e_1_2_7_28_1","doi-asserted-by":"publisher","DOI":"10.3390\/sym12020191"},{"key":"e_1_2_7_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-018-0103-8"},{"key":"e_1_2_7_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-019-0765-0"},{"issue":"2","key":"e_1_2_7_31_1","first-page":"192","article-title":"Similarity measures for fuzzy sets","volume":"8","author":"Beg I.","year":"2009","journal-title":"Appl. Comput. Math"},{"key":"e_1_2_7_32_1","doi-asserted-by":"publisher","DOI":"10.3390\/math7010096"},{"key":"e_1_2_7_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.01.028"},{"key":"e_1_2_7_34_1","first-page":"584","volume-title":"Modified Distance Measure on Hesitant Fuzzy Sets and its Application in Multi\u2010Criteria Decision Making Problem","author":"Singha B.","year":"2020"},{"key":"e_1_2_7_35_1","doi-asserted-by":"publisher","DOI":"10.3390\/sym10110557"},{"key":"e_1_2_7_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2014.12.012"},{"key":"e_1_2_7_37_1","doi-asserted-by":"publisher","DOI":"10.3390\/info11010005"},{"key":"e_1_2_7_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12559\u2010020\u201009750\u20104"},{"key":"e_1_2_7_39_1","doi-asserted-by":"publisher","DOI":"10.1002\/int.22308"},{"key":"e_1_2_7_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-03993-6"},{"key":"e_1_2_7_41_1","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-181253"},{"key":"e_1_2_7_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40747\u2010020\u201000150\u20107"},{"key":"e_1_2_7_43_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00521\u2010020\u201004859\u2010x"}],"container-title":["CAAI Transactions on Intelligence Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1049\/cit2.12016","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1049\/cit2.12016","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/pdf\/10.1049\/cit2.12016","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T12:46:57Z","timestamp":1761655617000},"score":1,"resource":{"primary":{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/10.1049\/cit2.12016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1049\/cit2.12016"],"URL":"https:\/\/doi.org\/10.1049\/cit2.12016","archive":["Portico"],"relation":{},"ISSN":["2468-6557","2468-2322"],"issn-type":[{"value":"2468-6557","type":"print"},{"value":"2468-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3]]},"assertion":[{"value":"2020-06-17","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-09-30","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-26","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}