{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/8509"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/8509","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Game Theoretic Approaches to Three-Way Decisions","abstract":"Uncertainty and imprecision are intrinsic features of available data about the real world. An object is uncertain if we cannot make sure decisions about if the object belongs to a target concept. Three-way decisions provide three options, i.e., accept, reject, and non-commitment, in the face of uncertainty. All objects are divided into three regions according to which option is selected for each object. The determination of three-way decisions is a key issue of analyzing uncertain data. When multiple evaluation measures are involved, determining three-way decisions from a tradeoff perspective is a challenging process. The thesis focuses on determining three-way decisions from a tradeoff perspective by combining game theory with uncertain data analysis approaches, i.e., rough sets and shadowed sets. We use game theoretic approaches to find tradeoff solutions under competitive situations. This thesis uses the Gini coefficient to evaluate the impurities of regions in prob- abilistic rough sets. Three Gini objective functions are formulated in order to derive the optimal probabilistic thresholds. Then game theoretical approaches are applied in probabilistic rough sets to determine a pair of thresholds by finding a tradeoff between the region impurities. i The quantitative measures are used to evaluate the inclusion degree of an equiva- lence class in a concept when constructing three-way decisions with quantitative rough sets. The thesis applies game theoretic approaches in quantitative rough sets to for- mulate a game for each equivalence class. The game result representing a tradeo between measures determines a region that each equivalence class belongs to. Three-way approximations of shadowed sets map the membership grades of ob- jects into a three-value set. The errors are produced during the mapping. This thesis proposes the game-theoretic shadowed sets which utilize game theoretic approaches in shadowed sets to obtain the thresholds of three-way approximations. GTSS formu- lates the games between the elevation and reduction errors. The resulting thresholds induced from the game equilibria represent a tradeoff between these errors. The game theoretic approaches presented provide a semantically meaningful way to determine three-way decisions from a tradeoff perspective. The illustrative exam- ples are used to show the feasibility of the proposed approaches.","abstract_html":"Uncertainty and imprecision are intrinsic features of available data about the real world. An object is uncertain if we cannot make sure decisions about if the object belongs to a target concept. Three-way decisions provide three options, i.e., accept, reject, and non-commitment, in the face of uncertainty. All objects are divided into three regions according to which option is selected for each object. The determination of three-way decisions is a key issue of analyzing uncertain data. When multiple evaluation measures are involved, determining three-way decisions from a tradeoff perspective is a challenging process. The thesis focuses on determining three-way decisions from a tradeoff perspective by combining game theory with uncertain data analysis approaches, i.e., rough sets and shadowed sets. We use game theoretic approaches to find tradeoff solutions under competitive situations. This thesis uses the Gini coefficient to evaluate the impurities of regions in prob- abilistic rough sets. Three Gini objective functions are formulated in order to derive the optimal probabilistic thresholds. Then game theoretical approaches are applied in probabilistic rough sets to determine a pair of thresholds by finding a tradeoff between the region impurities. i The quantitative measures are used to evaluate the inclusion degree of an equiva- lence class in a concept when constructing three-way decisions with quantitative rough sets. The thesis applies game theoretic approaches in quantitative rough sets to for- mulate a game for each equivalence class. The game result representing a tradeo between measures determines a region that each equivalence class belongs to. Three-way approximations of shadowed sets map the membership grades of ob- jects into a three-value set. The errors are produced during the mapping. This thesis proposes the game-theoretic shadowed sets which utilize game theoretic approaches in shadowed sets to obtain the thresholds of three-way approximations. GTSS formu- lates the games between the elevation and reduction errors. The resulting thresholds induced from the game equilibria represent a tradeoff between these errors. The game theoretic approaches presented provide a semantically meaningful way to determine three-way decisions from a tradeoff perspective. The illustrative exam- ples are used to show the feasibility of the proposed approaches.","abstract_has_math":false,"creators":["Zhang, Yan"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral -- first","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":["Yao, JingTao"],"committee_chairs":[],"committee_members":["Yao, Yiyu","Zilles, Sandra","Paranjape, Raman"],"year":2018,"date_issued":"2018-07","date_published":"2018-07","updated_at":"2026-07-24T04:03:34Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4189"],"render_values":[{"text":"https://doi.org/10.82465/4189","href":"https://doi.org/10.82465/4189","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/8509","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Yao, JingTao"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Yao, Yiyu","Zilles, Sandra","Paranjape, Raman"]},{"key":"dc:creator","label":"Author","values":["Zhang, Yan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-12-05T17:48:53Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-12-05T17:48:53Z"]},{"key":"dc:date.issued","label":"Date","values":["2018-07"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral -- first"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4189"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/8509"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Computer Science, University of Regina. xi, 158 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["Uncertainty and imprecision are intrinsic features of available data about the real world. An object is uncertain if we cannot make sure decisions about if the object belongs to a target concept. Three-way decisions provide three options, i.e., accept, reject, and non-commitment, in the face of uncertainty. All objects are divided into three regions according to which option is selected for each object. The determination of three-way decisions is a key issue of analyzing uncertain data. When multiple evaluation measures are involved, determining three-way decisions from a tradeoff perspective is a challenging process. The thesis focuses on determining three-way decisions from a tradeoff perspective by combining game theory with uncertain data analysis approaches, i.e., rough sets and shadowed sets. We use game theoretic approaches to find tradeoff solutions under competitive situations. This thesis uses the Gini coefficient to evaluate the impurities of regions in prob- abilistic rough sets. Three Gini objective functions are formulated in order to derive the optimal probabilistic thresholds. Then game theoretical approaches are applied in probabilistic rough sets to determine a pair of thresholds by finding a tradeoff between the region impurities. i The quantitative measures are used to evaluate the inclusion degree of an equiva- lence class in a concept when constructing three-way decisions with quantitative rough sets. The thesis applies game theoretic approaches in quantitative rough sets to for- mulate a game for each equivalence class. The game result representing a tradeo between measures determines a region that each equivalence class belongs to. Three-way approximations of shadowed sets map the membership grades of ob- jects into a three-value set. The errors are produced during the mapping. This thesis proposes the game-theoretic shadowed sets which utilize game theoretic approaches in shadowed sets to obtain the thresholds of three-way approximations. GTSS formu- lates the games between the elevation and reduction errors. The resulting thresholds induced from the game equilibria represent a tradeoff between these errors. The game theoretic approaches presented provide a semantically meaningful way to determine three-way decisions from a tradeoff perspective. The illustrative exam- ples are used to show the feasibility of the proposed approaches."]},{"key":"dc:title","label":"Title","values":["Game Theoretic Approaches to Three-Way Decisions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Yao, JingTao"],"dc:contributor.committeemember":["Yao, Yiyu","Zilles, Sandra","Paranjape, Raman"],"dc:creator":["Zhang, Yan"],"dc:date.accessioned":["2018-12-05T17:48:53Z"],"dc:date.available":["2018-12-05T17:48:53Z"],"dc:date.issued":["2018-07"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Computer Science, University of Regina. xi, 158 p."],"dc:description.abstract":["Uncertainty and imprecision are intrinsic features of available data about the real world. An object is uncertain if we cannot make sure decisions about if the object belongs to a target concept. Three-way decisions provide three options, i.e., accept, reject, and non-commitment, in the face of uncertainty. All objects are divided into three regions according to which option is selected for each object. The determination of three-way decisions is a key issue of analyzing uncertain data. When multiple evaluation measures are involved, determining three-way decisions from a tradeoff perspective is a challenging process. The thesis focuses on determining three-way decisions from a tradeoff perspective by combining game theory with uncertain data analysis approaches, i.e., rough sets and shadowed sets. We use game theoretic approaches to find tradeoff solutions under competitive situations. This thesis uses the Gini coefficient to evaluate the impurities of regions in prob- abilistic rough sets. Three Gini objective functions are formulated in order to derive the optimal probabilistic thresholds. Then game theoretical approaches are applied in probabilistic rough sets to determine a pair of thresholds by finding a tradeoff between the region impurities. i The quantitative measures are used to evaluate the inclusion degree of an equiva- lence class in a concept when constructing three-way decisions with quantitative rough sets. The thesis applies game theoretic approaches in quantitative rough sets to for- mulate a game for each equivalence class. The game result representing a tradeo between measures determines a region that each equivalence class belongs to. Three-way approximations of shadowed sets map the membership grades of ob- jects into a three-value set. The errors are produced during the mapping. This thesis proposes the game-theoretic shadowed sets which utilize game theoretic approaches in shadowed sets to obtain the thresholds of three-way approximations. GTSS formu- lates the games between the elevation and reduction errors. The resulting thresholds induced from the game equilibria represent a tradeoff between these errors. The game theoretic approaches presented provide a semantically meaningful way to determine three-way decisions from a tradeoff perspective. The illustrative exam- ples are used to show the feasibility of the proposed approaches."],"dc:identifier.doi":["https://doi.org/10.82465/4189"],"dc:identifier.uri":["https://hdl.handle.net/10294/8509"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Game Theoretic Approaches to Three-Way Decisions"],"dc:type":["master thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Doctoral -- first"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:34Z"}