Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy se...Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approxima- tion operators of vague sets based on vague relations, and investigate the basic properties of approximation opera- tors on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transi- tive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.展开更多
To remedy the defects of the existing research achievements,the dynamic vague region relations without kernel and the non-same-plane vague region relations without kernel based on the conception of the vague sets were...To remedy the defects of the existing research achievements,the dynamic vague region relations without kernel and the non-same-plane vague region relations without kernel based on the conception of the vague sets were studied systematically.The formalized definitions of the vague intersection set,the vague cut sets and vague region partition etc were given.Based on the vague sets,the eight vague region relations in the same plane and the ten vague region relations in the different plane were given.Furthermore,the coessential intersection and the heterogeneous intersection were proposed to simplify the representation for the dynamic vague region relations without kernel and the rotation-corresponding relations between the two kinds of the relations were also studied.The production in this paper laid the foundation for the applications and research of the vague region relations without kernel in the spatial database.展开更多
The problem of decision making in an imprecise environment has found paramount importance in recent years. In this paper, we define vague soft relation and similarity measure of vague soft sets. Using these definition...The problem of decision making in an imprecise environment has found paramount importance in recent years. In this paper, we define vague soft relation and similarity measure of vague soft sets. Using these definitions, some novel methods of object recognition from an imprecise multiobserver data has been presented. Moreover, we introduce the notion of generalized vague soft sets and study some of its properties. The similarity measure of generalized vague soft sets is also presented and an application of this measure in decision making problems has been shown.展开更多
文摘Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approxima- tion operators of vague sets based on vague relations, and investigate the basic properties of approximation opera- tors on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transi- tive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.
基金Sponsored by the Science and Tecnology Research Project of Education Department Heilongjiang Province(Grant No.11551084)
文摘To remedy the defects of the existing research achievements,the dynamic vague region relations without kernel and the non-same-plane vague region relations without kernel based on the conception of the vague sets were studied systematically.The formalized definitions of the vague intersection set,the vague cut sets and vague region partition etc were given.Based on the vague sets,the eight vague region relations in the same plane and the ten vague region relations in the different plane were given.Furthermore,the coessential intersection and the heterogeneous intersection were proposed to simplify the representation for the dynamic vague region relations without kernel and the rotation-corresponding relations between the two kinds of the relations were also studied.The production in this paper laid the foundation for the applications and research of the vague region relations without kernel in the spatial database.
基金supported by the National Natural Science Foundation of China under Grant Nos.11571276,11501444the Postdoctoral Science Foundation of China under Grant Nos.2013M532079,2014T70932+1 种基金the Science Research Foundation of Education Department of Shanxi Provincial Government under Grant No.15JK1735the Science Research Foundation of Northwest University under Grant No.12NW04
文摘The problem of decision making in an imprecise environment has found paramount importance in recent years. In this paper, we define vague soft relation and similarity measure of vague soft sets. Using these definitions, some novel methods of object recognition from an imprecise multiobserver data has been presented. Moreover, we introduce the notion of generalized vague soft sets and study some of its properties. The similarity measure of generalized vague soft sets is also presented and an application of this measure in decision making problems has been shown.
