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Research on uncertainty of interval-valued intuitionistic fuzzy rough sets
LIU Hongwei, WANG Yanping
School of Science, Liaoning University of Technology, Jinzhou 121001, China
Abstract: The uncertainty of an approximate set in interval-value intuitionistic fuzzy information system is researched in this paper and the uncertainty measurement formula of interval-value intuitionistic fuzzy rough sets are given. Firstly,a pair of new interval-value intuitionistic fuzzy upper and lower approximation operators with symmetry is defined in the interval-value intuitionistic fuzzy approximation space. Secondly,the corresponding definition of rough membership functions on interval-value intuitionistic fuzzy is given and properties are discussed. Finally,the fuzzy entropy of interval-value intuitionistic fuzzy rough set is defined by interval-value intuitionistic fuzzy entropy of the interval-value intuitionistic fuzzy rough membership functions. The necessary and sufficient conditions when the fuzzy entropy on interval intuitice fuzzy rough set is zero are discussed. In addition,the rough measurement values of classic set and residual set are equal in the interval-value intuitionistic fuzzy approximate space,thereby proving the rationality of the definition.
Key words: rough sets     fuzzy sets     interval-valued intuitionistic fuzzy sets     interval-value intuitionistic fuzzy information system     interval-valued intuitionistic fuzzy relations     approximation operators     interval-valued intuitionistic fuzzy entropy     rough membership function

1 区间直觉模糊粗糙集的基本理论

U上所有IVIF集构成的集合为IVIF(U).

[a1,b1]=[a2,b2] iff a1=a2,b1=b2

[a1,b1]≤[a2,b2] iff a1a2,b1b2

[a1,b1]〈[a2,b2] iff [a1,b1]≤[a2,b2]且[a1,b1]≠[a2,b2].

1)

2)

3)

 (1)

1)

2)

3)

4)

5)

6)

7)

2 区间直觉模糊集的粗糙隶属函数

 (2)

1)∀A,B∈IVIF(U)，若AB,则

R(A)⊆R(B)

2)若AP(U)，则R(~A)=~R(A)。

2)若AP(U)，则，当∀xA时，μA(x)=[1,1],υA(x)=[0,0]。由式(2)可得

3 区间直觉模糊熵

 (3)

E(A)为A的区间直觉模糊熵。

4 区间直觉模糊粗糙集不确定性度量

 (4)

1)对∀xA，有

,即对，应有，则μR(x,y)=[0,0]，所以由式(2)得

2)对，有

(⇒)设IVIFR(A)=0，由定义8可知，对∀xU，应有

3)若xA，即μA(x)=[1,1],υA(x)=[0,0]，由式(2)可知：

4)若，即,

，则yA，有μR(x,y)=[0,0],υR(x,y)=[1,1]，所以

5 结束语

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DOI: 10.3969/j.issn.1673-4785.201307007

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#### 文章信息

LIU Hongwei, WANG Yanping

Research on uncertainty of interval-valued intuitionistic fuzzy rough sets

CAAI Transactions on Intelligent Systems, 2014, 9(5): 613-617
http://dx.doi.org/10.3969/j.issn.1673-4785.201307007