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
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.
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.
