This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -l...This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.展开更多
An option prioritization technique is developed to efficiently elicit the preferences, both unknown and crisp, of decision makers （DMs） in strategic conflicts. In the Graph Model for Conflict Resolution, each DM has...An option prioritization technique is developed to efficiently elicit the preferences, both unknown and crisp, of decision makers （DMs） in strategic conflicts. In the Graph Model for Conflict Resolution, each DM has one or more options, each of which may be selected or not. A state, or possible scenario, is formed when all DMs make an option selection. The software GMCR II contains an option prioritization procedure that makes it easy for a modeUer to enter a DM＇s crisp preference ordering over the states using prioritized statements describing the DM＇s preferred option combinations. This procedure is extended by adding two new logical connectives that describe uncertainty of preference. For each DM, a range of possible scores for each feasible state can then be calculated, facilitating the determination of a preference ordering containing uncertainty by comparing and ranking scores. To demonstrate how this new methodology can be used to represent tmknown preferences in a real-world decision problem, it is applied to a Canadian dispute over proposed water exports.展开更多
基金supported by grants from the National Natural Science Foundation of China(Nos.61075120, 60673096 and 60773174)the Natural Science Foundation of Zhejiang Province in China(No.Y107262).
文摘This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.
基金Acknowledgments This work was supported by the Scientific Innovation Project of Graduate Students in Jiangsu Province in China （Grant No. CXZZ12-0263）, the National Natural Science Foundation of China （Grant No. 71471087）, as well as by the Natural Sciences and Engineering Research Council of Canada. The authors wish to express their sincere appreciation to the anonymous referees, the Associate Editor, and the editor-in-chief for furnishing comments and constructive suggestions that significantly improved the quality of their article. The authors would also like to thank Mr. Conrad Hipel for editing the paper.
文摘An option prioritization technique is developed to efficiently elicit the preferences, both unknown and crisp, of decision makers （DMs） in strategic conflicts. In the Graph Model for Conflict Resolution, each DM has one or more options, each of which may be selected or not. A state, or possible scenario, is formed when all DMs make an option selection. The software GMCR II contains an option prioritization procedure that makes it easy for a modeUer to enter a DM＇s crisp preference ordering over the states using prioritized statements describing the DM＇s preferred option combinations. This procedure is extended by adding two new logical connectives that describe uncertainty of preference. For each DM, a range of possible scores for each feasible state can then be calculated, facilitating the determination of a preference ordering containing uncertainty by comparing and ranking scores. To demonstrate how this new methodology can be used to represent tmknown preferences in a real-world decision problem, it is applied to a Canadian dispute over proposed water exports.
