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
Fuzzy soft topology considers only membership value.It has nothing to do with the non-membership value.So an extension was needed in this direction.Vague soft topology addresses bothmembership and non-membership value...Fuzzy soft topology considers only membership value.It has nothing to do with the non-membership value.So an extension was needed in this direction.Vague soft topology addresses bothmembership and non-membership values simultaneously.Sometimes vague soft topology(single structure)is unable to address some complex structures.So an extension to vague soft bi-topology(double structure)was needed in this direction.To make this situation more meaningful,a new concept of vague soft bi-topological space is introduced and its structural characteristics are attempted with a new definition.In this article,new concept of vague soft bi-topological space(VSBTS)is initiated and its structural behaviors are attempted.This approach is based on generalized vague soft open sets,known as vague softβopen sets.An ample of examples are given to understand the structures.For the non-validity of some results,counter examples are provided to pay the price.Pair-wise vague softβopen and pair-wise vague softβclose sets are alsoaddressedwith examples in(VSBTS).Vague soft separation axioms are initiatedin(VSBTS)concerning soft points of the space.Other separation axioms are also addressed relative to soft points of the space.Vague soft bi-topological properties are studied with the application of vague softβopen sets with respect to soft points of the spaces.The characterization of vague softβclose as well as vague softβopen sets,characteristics of Bolzano Weirstrass property,vague soft compactness and its marriage with sequences,interconnection between sequential compactness and countable compactness in(VSBTS)with respect to softβopen sets are addressed.展开更多
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.
文摘Fuzzy soft topology considers only membership value.It has nothing to do with the non-membership value.So an extension was needed in this direction.Vague soft topology addresses bothmembership and non-membership values simultaneously.Sometimes vague soft topology(single structure)is unable to address some complex structures.So an extension to vague soft bi-topology(double structure)was needed in this direction.To make this situation more meaningful,a new concept of vague soft bi-topological space is introduced and its structural characteristics are attempted with a new definition.In this article,new concept of vague soft bi-topological space(VSBTS)is initiated and its structural behaviors are attempted.This approach is based on generalized vague soft open sets,known as vague softβopen sets.An ample of examples are given to understand the structures.For the non-validity of some results,counter examples are provided to pay the price.Pair-wise vague softβopen and pair-wise vague softβclose sets are alsoaddressedwith examples in(VSBTS).Vague soft separation axioms are initiatedin(VSBTS)concerning soft points of the space.Other separation axioms are also addressed relative to soft points of the space.Vague soft bi-topological properties are studied with the application of vague softβopen sets with respect to soft points of the spaces.The characterization of vague softβclose as well as vague softβopen sets,characteristics of Bolzano Weirstrass property,vague soft compactness and its marriage with sequences,interconnection between sequential compactness and countable compactness in(VSBTS)with respect to softβopen sets are addressed.
