{"id":"https://openalex.org/W7118398481","doi":"https://doi.org/10.1109/tsmc.2025.3647125","title":"Backpropagation-Based Counterfactual Explanations for Quasi-Nonlinear Fuzzy Cognitive Maps","display_name":"Backpropagation-Based Counterfactual Explanations for Quasi-Nonlinear Fuzzy Cognitive Maps","publication_year":2026,"publication_date":"2026-01-06","ids":{"openalex":"https://openalex.org/W7118398481","doi":"https://doi.org/10.1109/tsmc.2025.3647125"},"language":null,"primary_location":{"id":"doi:10.1109/tsmc.2025.3647125","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2025.3647125","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054823527","display_name":"Marios Tyrovolas","orcid":"https://orcid.org/0000-0002-4903-3204"},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Marios Tyrovolas","raw_affiliation_strings":["Department of Informatics and Telecommunications, University of Ioannina, Arta, Greece"],"raw_orcid":"https://orcid.org/0000-0002-4903-3204","affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications, University of Ioannina, Arta, Greece","institution_ids":["https://openalex.org/I194019607"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120618810","display_name":"Gonzalo N\u00e1poles","orcid":null},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Gonzalo N\u00e1poles","raw_affiliation_strings":["Department of Intelligent Systems, Tilburg University, Tilburg, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-1936-3701","affiliations":[{"raw_affiliation_string":"Department of Intelligent Systems, Tilburg University, Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009967164","display_name":"Chrysostomos Stylios","orcid":"https://orcid.org/0000-0002-2888-6515"},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Chrysostomos Stylios","raw_affiliation_strings":["Department of Informatics and Telecommunications, University of Ioannina, Arta, Greece"],"raw_orcid":"https://orcid.org/0000-0002-2888-6515","affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications, University of Ioannina, Arta, Greece","institution_ids":["https://openalex.org/I194019607"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054823527"],"corresponding_institution_ids":["https://openalex.org/I194019607"],"apc_list":null,"apc_paid":null,"fwci":35.3865,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.983582,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"56","issue":"3","first_page":"1706","last_page":"1720"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12805","display_name":"Cognitive Science and Mapping","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12805","display_name":"Cognitive Science and Mapping","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10241","display_name":"Functional Brain Connectivity Studies","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13062","display_name":"Cognitive Computing and Networks","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/counterfactual-thinking","display_name":"Counterfactual thinking","score":0.8848999738693237},{"id":"https://openalex.org/keywords/counterfactual-conditional","display_name":"Counterfactual conditional","score":0.7336999773979187},{"id":"https://openalex.org/keywords/fuzzy-cognitive-map","display_name":"Fuzzy cognitive map","score":0.5026999711990356},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4810999929904938},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4458000063896179},{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.39169999957084656},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3828999996185303},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.34299999475479126},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3422999978065491}],"concepts":[{"id":"https://openalex.org/C108650721","wikidata":"https://www.wikidata.org/wiki/Q1783253","display_name":"Counterfactual thinking","level":2,"score":0.8848999738693237},{"id":"https://openalex.org/C71889745","wikidata":"https://www.wikidata.org/wiki/Q1783264","display_name":"Counterfactual conditional","level":3,"score":0.7336999773979187},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5888000130653381},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.552299976348877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5152000188827515},{"id":"https://openalex.org/C5041914","wikidata":"https://www.wikidata.org/wiki/Q5511107","display_name":"Fuzzy cognitive map","level":5,"score":0.5026999711990356},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4810999929904938},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.39169999957084656},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35910001397132874},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.3393999934196472},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.33009999990463257},{"id":"https://openalex.org/C169900460","wikidata":"https://www.wikidata.org/wiki/Q2200417","display_name":"Cognition","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C115086926","wikidata":"https://www.wikidata.org/wiki/Q17004651","display_name":"Causal reasoning","level":3,"score":0.29109999537467957},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C8521452","wikidata":"https://www.wikidata.org/wiki/Q203790","display_name":"Connectionism","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.27300000190734863},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C2780695315","wikidata":"https://www.wikidata.org/wiki/Q3799040","display_name":"Unobservable","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.2547999918460846},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2025.3647125","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2025.3647125","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4996814429759979}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,63],"growing":[1],"demand":[2],"for":[3,122],"eXplainable":[4],"AI":[5],"(XAI)":[6],"has":[7],"renewed":[8],"interest":[9],"in":[10,60],"fuzzy":[11,70],"cognitive":[12],"maps":[13],"(FCMs)":[14],"due":[15],"to":[16,38,50,154],"their":[17,32],"interpretability,":[18],"causal":[19],"transparency,":[20],"and":[21,72,78,92,98,145,159,177],"hybrid":[22],"intelligence":[23],"capabilities.":[24],"However,":[25],"current":[26],"FCM":[27],"explanation":[28,120],"methods":[29,88],"either":[30],"overlook":[31],"dynamic":[33],"behavior":[34],"or":[35],"limit":[36],"themselves":[37],"feature":[39,90],"attribution.":[40],"Counterfactual":[41],"explanations,":[42],"which":[43,126],"describe":[44],"the":[45,83,109,112,139,164,169,186,190],"minimal":[46],"input":[47],"changes":[48],"required":[49],"alter":[51],"outcomes,":[52],"address":[53],"this":[54,106],"gap":[55],"but":[56],"remain":[57],"largely":[58],"unexplored":[59],"these":[61,104],"models.":[62],"only":[64],"existing":[65],"FCM-specific":[66],"approach":[67],"relies":[68],"on":[69],"discretization":[71],"predefined":[73],"rules,":[74],"producing":[75],"causally":[76,157],"invalid":[77],"overly":[79],"conservative":[80],"explanations.":[81],"On":[82],"other":[84],"hand,":[85],"generic":[86],"model-agnostic":[87,183],"assume":[89],"independence":[91],"suffer":[93],"from":[94],"instability,":[95],"restrictive":[96],"assumptions,":[97],"high":[99],"computational":[100],"costs.":[101],"To":[102],"overcome":[103],"limitations,":[105],"article":[107],"presents":[108],"counterfactuals":[110],"via":[111],"backpropagation":[113],"(CF-BP)":[114],"algorithm,":[115],"a":[116,128],"first":[117],"backpropagation-based":[118],"counterfactual":[119,161,195],"method":[121,192],"quasi-nonlinear":[123],"FCMs":[124,132],"(q-FCMs),":[125],"is":[127],"generalization":[129],"of":[130,168,189],"traditional":[131],"that":[133],"resolves":[134],"convergence":[135],"issues.":[136],"CF-BP":[137],"exploits":[138],"similarity":[140],"between":[141],"q-FCMs\u2019":[142],"recurrent":[143],"reasoning":[144],"neural":[146],"network":[147],"forward":[148],"propagation,":[149],"using":[150],"exact":[151],"analytical":[152],"gradients":[153],"generate":[155],"precise,":[156],"consistent,":[158],"robust":[160],"explanations":[162],"within":[163],"continuous":[165],"state":[166],"space":[167],"model.":[170],"Extensive":[171],"evaluations,":[172],"including":[173],"hyperparameter":[174],"sensitivity":[175],"analysis":[176],"benchmarking":[178],"against":[179],"eight":[180],"state-of-the-art":[181],"(SOTA)":[182],"methods,":[184],"confirm":[185],"superior":[187],"performance":[188],"proposed":[191],"across":[193],"key":[194],"quality":[196],"metrics.":[197]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-02-24T06:16:03.338239","created_date":"2026-01-08T00:00:00"}
