基于犹豫模糊集统计相关系数的多源异类数据融合识别
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摘要
为解决由犹豫模糊数、直觉模糊数、区间数和实数4类基本数据组成的多源异类数据的融合识别问题,在犹豫模糊框架内,提出犹豫模糊集相关系数计算方法进行识别判定。首先,将多源异类数据用犹豫模糊数统一描述;其次,分析现有的犹豫模糊集相关系数的局限性,提出了既满足统计学直觉,又不需要各犹豫模糊数中隶属度个数相同,并具有更强数学概念的犹豫模糊集统计相关系数;最后,应用到多源异类数据的融合识别中,利用最大相关系数准则进行识别判定。仿真算例对比分析验证了犹豫模糊集统计相关系数的有效性,并具有精度高、区分度好的优点。
In order to solve the multi-source heterogeneous data fusion recognition problem in which the multi-source heterogeneous data is expressed as hesitant fuzzy element(HFE),intuitionistic fuzzy number(IFN),interval number and real number,a correlation coefficient between hesitant fuzzy sets(HFSs)is proposed to recognize these data in the HFS domain.Firstly,the multi-source heterogeneous data is transformed into the HFS domain.After towards,pointing out the weakness of the existing correlation coefficients between HFS,we propose a correlation coefficient between two HFSs which has advantages in three aspects:firstly it conforms to the statistics intuition,secondly,it is not necessary to have the same length in membership,and thirdly,it is more theoretical in mathematics.Finally,apply the proposed correlation coefficient to recognize the multi-source heterogeneous data based on the principle of the maximum correlation coefficient.The simulation examples demonstrate the vadidity of the proposed correlation coefficient with a comparision analysis,and prove its advantages in high precision and discrinination.
In order to solve the multi-source heterogeneous data fusion recognition problem in which the multi-source heterogeneous data is expressed as hesitant fuzzy element(HFE),intuitionistic fuzzy number(IFN),interval number and real number,a correlation coefficient between hesitant fuzzy sets(HFSs)is proposed to recognize these data in the HFS domain.Firstly,the multi-source heterogeneous data is transformed into the HFS domain.After towards,pointing out the weakness of the existing correlation coefficients between HFS,we propose a correlation coefficient between two HFSs which has advantages in three aspects:firstly it conforms to the statistics intuition,secondly,it is not necessary to have the same length in membership,and thirdly,it is more theoretical in mathematics.Finally,apply the proposed correlation coefficient to recognize the multi-source heterogeneous data based on the principle of the maximum correlation coefficient.The simulation examples demonstrate the vadidity of the proposed correlation coefficient with a comparision analysis,and prove its advantages in high precision and discrinination.
引文
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[20]XU Z S,XIA M M.Distance and similarity measures for hesitant fuzzy sets[J].Information Sciences,2011,181(11):2128-2138.
[21]LIAO H C,XU Z S.Hesitant fuzzy decision making methodologies and applications[M].Singapore Springer,2017:1-34.
[22]XU Z S,ZHANG X L.Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J].Knowledge-Based Systems,2013,52(6):53-64.
[23]XIA M M,XU Z S.Hesitant fuzzy information aggregation in decision making[J].International Journal of Approximate Reasoning,2011,52(3):395-407.
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[2]ZADEH L A.Fuzzy sets[J].Information&Control,1965,8(3):338-353.
[3]SUN G D,GUAN X.Research on hybrid multi-attribute decision-making[C]∥Proc.of the International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery,2016:272-277.
[4]ZHANG X,XU Z,WANG H.Heterogeneous multiple criteria group decision making with incomplete weight information:a deviation modeling approach[J].Information Fusion,2015,25:49-62.
[5]WAN S P,DONG J Y.Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees[J].Information Fusion,2015,26(C):49-65.
[6]XU J,WAN S P,DONG J Y.Aggregating decision information into Atanassov’s intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making[J].Applied Soft Computing,2016,41:331-351.
[7]WAN S P,LI D F.Atanassov’s intuitionistic fuzzy program-ming method for heterogeneous multi-attribute group decision making with Atanassov’s intuitionistic fuzzy truth degrees[J].IEEE Trans.on Fuzzy Systems,2014,22(2):300-312.
[8]TORRA V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[9]TORRA V,NARUKAWA Y.On hesitant fuzzy sets and decision[C]∥Proc.of the 18th IEEE International Conference on Fuzzy Systems,2009:1378-1382.
[10]XU Z S,XIA M M.On distance and correlation measures of hesitant fuzzy inforrnation[J].International Journal of Intelligent Systems,2011,26:410-425.
[11]CHEN N,XU Z S,XIA M M.Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis[J].Applied Mathematical Modeling,2013,37(4):2197-2211.
[12]LIAO H C,XU Z S,ZENG X J.Novel correlation coefficients between hesitant fuzzy sets and their application in decision making[J].Knowledge-Based Systems,2015,82(C):115-127.
[13]EBRAHIMPOUR M K,EFTEKHARI M.Feature subset selection using information energy and correlation coefficients of hesitant fuzzy sets[C]∥Proc.of the 7th International Conference on Information and Knowledge Technology,2015:1-6.
[14]MENG F Y,CHEN X H,ZHANG Q.Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on the Shapley function[J].International Journal of Intelligent Systems,2016,31(1):17-43.
[15]WANG L,NI M F,ZHU L.Correlation measures of dual hesitant fuzzy sets[J].Journal of Applied Mathematics,Volume2013,2013(4):1-12
[16]YE J.Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making[J].Applied Mathematical Modeling,2014,38(2):659-666.
[17]TYAGI S K.Correlation coefficient of dual hesitant fuzzy sets and its applications[J].Applied Mathematical Modeling,2015,39(22):7082-7092.
[18]FARHADINIA B.Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets[J].International Journal of Intelligent Systems,2014,29(2):184-205.
[19]LIAO H C,XU Z S,ZENG X J,et al.Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets[J].Knowledge-Based Systems,2015,76(1):127-138.
[20]XU Z S,XIA M M.Distance and similarity measures for hesitant fuzzy sets[J].Information Sciences,2011,181(11):2128-2138.
[21]LIAO H C,XU Z S.Hesitant fuzzy decision making methodologies and applications[M].Singapore Springer,2017:1-34.
[22]XU Z S,ZHANG X L.Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J].Knowledge-Based Systems,2013,52(6):53-64.
[23]XIA M M,XU Z S.Hesitant fuzzy information aggregation in decision making[J].International Journal of Approximate Reasoning,2011,52(3):395-407.
[24]LIAO H C,XU Z S,XIA M M.Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making[J].International Journal of Information Technology and Decision Making,2014,13(1):47-76.