Game Theoretic Approaches to Three-Way Decisions

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Doctoral -- first

Discipline thesis:degree_discipline

Computer Science

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2018

Author dc:creator

• Zhang, Yan

Advisor dc:contributor.advisor

• Yao, JingTao

Committee members dc:contributor.committeemember

• Yao, Yiyu
• Zilles, Sandra
• Paranjape, Raman

Language dc:language.iso

en

DOI

https://doi.org/10.82465/4189

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/8509