基于犹豫模糊集的不等长序列识别方法及应用

doi:10.11959/j.issn.1000-436x.2021118

摘要/Abstract

摘要：

针对不等长序列难以识别的问题，提出了一种基于犹豫模糊距离测度的识别方法。首先，从模糊数的角度对问题加以描述，用格贴近度建立了不等长序列的犹豫模糊信息识别模型。其次，定义了犹豫模糊数的均值、方差、相对范围、犹豫度4个特征，结合较短部分的隶属度差值，定义了犹豫模糊广义集成特征距离测度和广义加权集成特征距离测度，其满足度量空间的相关性质，并给出了严格的数学证明过程。最后，提出了用于确定权重信息的熵测度法和支撑度法，给出了基于犹豫距离测度的 VIKOR 识别方法。从数值算例、能源策略选择和目标识别3个方面进行了仿真验证，结果验证了所提方法的有效性和可行性。

关键词: 犹豫模糊集, 距离测度, 不等长序列识别

Abstract:

Aiming at the problem that unequal length sequences were difficult to recognize, a recognition method based on hesitant fuzzy distance measure was proposed.Firstly, the problem was described from the perspective of fuzzy value, and the hesitant fuzzy information recognition model of unequal length sequence was established by lattice closeness degree.Secondly, the mean value, variance, relative range and hesitancy degree of hesitant fuzzy values were defined.Combined with membership difference of the shorter part, the generalized integrated feature distance measure and the generalized weighted integrated feature distance measure were defined to meet relevant properties of metric space, and the strict mathematical proof process was given.Finally, entropy measure and support measure were proposed to determine the weight, and the VIKOR recognition method based on hesitant distance measure was given.The simulation results verify the effectiveness and feasibility of proposed method from numerical examples, energy strategy selection and target recognition respectively.

Key words: hesitant fuzzy set, distance measure, recognition for unequal length sequences

中图分类号:

TP391

李双明, 关欣, 孙贵东. 基于犹豫模糊集的不等长序列识别方法及应用[J]. 通信学报, 2021, 42(7): 41-51.

Shuangming LI, Xin GUAN, Guidong SUN. Recognition method based on hesitant fuzzy set for unequal length sequences and its application[J]. Journal on Communications, 2021, 42(7): 41-51.

图/表 12

表1

犹豫模糊数表示的决策信息"

类别	工作模式	特征1	特征2	…	特征p
	$m_{1, 1}$	$s_{11}^{m_{1, 1}}$	$s_{12}^{m_{1, 1}}$	…	$s_{1 p}^{m_{1, 1}}$
1	?	?	?	$⋱$	?
	$m_{1, n_{1}}$	$s_{11}^{m_{1, n_{1}}}$	$s_{12}^{m_{1, n_{1}}}$	…	$s_{1 p}^{m_{1, n_{1}}}$
	$m_{2, 1}$	$s_{21}^{m_{2, 1}}$	$s_{22}^{m_{2, 1}}$	…	$s_{2 p}^{m_{2, 1}}$
2	?	?	?	$⋱$	?
	$m_{2, n_{2}}$	$s_{21}^{m_{2, n_{2}}}$	$s_{22}^{m_{2, n_{2}}}$	…	$s_{2 p}^{m_{2, n_{2}}}$
?	?	?	?	?	?
	$m_{n, 1}$	$s_{n 1}^{m_{n, 1}}$	$s_{n 2}^{m_{n, 1}}$	…	$s_{n p}^{m_{n, 1}}$
n	?	?	?	$⋱$	?
	$m_{n, n_{n}}$	$s_{n 1}^{m_{n, n_{n}}}$	$s_{n 2}^{m_{n, n_{n}}}$	…	$s_{n p}^{m_{n, n_{n}}}$

表1

表2

表3

表4

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表6

表7

图1

图2

图3

图4

图5

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方法	距离	d(h₀,h₁)	d(h₀,h₂)	d(h₀,h₁)<d(h₀,h₂)
	λ= 1	0.233 3	0.23 3	FALSE
	λ= 2	0.234 5	0.234 5	FALSE
文献[7]方法	λ= 3	0.235 6	0.235 6	FALSE
	λ= 6	0.238 5	0.238 5	FALSE
	λ=10	0.241 5	0.241 5	FALSE
	λ=1	0.200 0	0.116 7	FALSE
	λ= 2	0.203 4	0.165 8	FALSE
文献[9-10]方法	λ= 3	0.206 9	0.187 0	FALSE
	λ= 6	0.216 4	0.212 5	FALSE
	λ=10	0.225 7	0.225 2	FALSE
	λ= 1	0.216 7	0.175 0	FALSE
	λ= 2	0.219 5	0.203 1	FALSE
文献[11]方法	λ= 3	0.222 2	0.214 1	FALSE
	λ= 6	0.228 8	0.223 7	FALSE
	λ=10	0.234 7	0.234 5	FALSE
	λ= 1	0.129 5	0.180 0	TRUE
	λ= 2	0.155 1	0.213 2	TRUE
本文方法	λ= 3	0.168 9	0.230 3	TRUE
	λ= 6	0.187 2	0.255 4	TRUE
	λ=10	0.197 5	0.271 1	TRUE

方法	距离	d(h₁,h₂)	d(h₁,h₃)	d(h₂,h₃)	d(h₁,h₂)<d(h₁,h₃)+d(h₂,h₃)
	λ= 1	0.4221	0.3817	0.0332	FALSE
	λ= 2	0.4665	0.4067	0.0335	FALSE
文献[7]方法	λ= 3	0.4888	0.4334	0.0338	FALSE
	λ= 6	0.5555	0.4989	0.0348	FALSE
	λ=10	0.5985	0.5440	0.0359	FALSE
	λ= 1	0.3055	0.2857	0.0531	TRUE
	λ= 2	0.3398	0.3168	0.0556	TRUE
本文方法	λ= 3	0.3755	0.3497	0.0582	TRUE
	λ= 6	0.4632	0.4334	0.0652	TRUE
	λ=10	0.5292	0.4969	0.0711	TRUE

方法	距离	d(h₁,h₂)	d(h₁,h₃)	d(h₂,h₃)	d(h₁,h₂)<d(h₁,h₃)+d(h₂,h₃)
	λ= 1	0.5167	0.1833	0.2500	FALSE
	λ= 2	0.5172	0.2901	0.3536	TRUE
文献[11]方法	λ= 3	0.5178	0.3468	0.3969	TRUE
	λ= 6	0.5194	0.4163	0.4454	TRUE
	λ=10	0.5218	0.4480	0.4665	TRUE
	λ= 1	0.4000	0.1500	0.1667	FALSE
	λ= 2	0.4486	0.2525	0.2887	TRUE
文献[17]方法	λ= 3	0.4705	0.3152	0.3467	TRUE
	λ= 6	0.4951	0.3969	0.4163	TRUE
	λ=10	0.5070	0.4353	0.4480	TRUE
	λ= 1	0.3275	0.1275	0.2000	TRUE
	λ= 2	0.4075	0.2259	0.3162	TRUE
本文方法	λ= 3	0.4435	0.2926	0.3684	TRUE
	λ= 6	0.4840	0.3824	0.4292	TRUE
	λ=10	0.5022	0.4257	0.4562	TRUE

方案/准则	C₁	C₂	C₃	C₄
P₁	{0.5,0.4,0.3}	{0.9,0.8,0.7,0.1}	{0.5,0.4,0.2}	{0.9,0.6,0.5,0.3}
P₂	{0.5,0.3}	{0.9,0.7,0.6,0.5,0.2}	{0.8,0.6,0.5,0.1}	{0.7,0.3,0.4}
P₃	{0.7,0.6}	{0.9,0.6}	{0.7,0.5,0.3}	{0.6,0.4}
P₄	{0.8,0.7,0.4,0.3}	{0.7,0.4,0.2}	{0.8,0.1}	{0.9,0.8,0.6}
P₅	{0.9,0.7,0.6,0.3,0.1}	{0.8,0.7,0.6,0.4}	{0.9,0.8,0.7}	{0.9,0.7,0.6,0.3}

方法	距离	P₁	P₂	P₃	P₄	P₅	排序结果
	λ= 1	0.479 9	0.502 7	0.402 5	0.429 2	0.355 8	P ₅>P₃>P₄>P_2.>P₁
文献[7]方法	λ=2	0.537 8	0.545 1	0.436 6	0.505 2	0.412 9	P ₅>P₃>P₄>P_2.>P₁
	λ=6	0.659 9	0.647 6	0.515 6	0.670 4	0.569 9	P ₃>P₅>P₂>P₁>P₄
	λ=10	0.721 3	0.704 6	0.560 7	0.737 3	0.653 7	P ₃>P₅>P₂>P₁>P₄
	λ=1	0.477 9	0.502 7	0.402 5	0.429 2	0.355 8	P ₅>P₃>P₄>P₁>P₂
文献[13]方法	λ=2	0.537 8	0.545 1	0.436 6	0.505 2	0.412 9	P ₅>P₃>P₄>P₁>P₂
	λ= 6	0.659 9	0.647 6	0.515 6	0.670 4	0.569 9	P ₃>P₅>P₂>P₁>P₄
	λ=10	0.721 3	0.704 7	0.560 3	0.737 4	0.653 7	P ₃>P₅>P₂>P₁>P₄
	Φ₁w(with r=1)	0.240 0	0.250 0	0.275 0	0.195 0	0.130 0	P ₅>P₄>P₁>P₂>P₃
文献[16]方法	Φ₂w(with r=2)	0.780 0	0.735 0	0.530 0	0.665 0	0.620 0	P ₃>P₅>P₄>P₂>P₁
	Φ₃w(with r=3)	0.359 0	0.350 5	0.436 3	0.312 1	0.239 1	P ₅>P₄>P₂>P₁>P₃
	Φ₄w(with r=4)	0.400 2	0.480 0	0.363 3	0.320 4	0.288 5	P ₅>P₄>P₃>P₁>P₂
	λ=1	0.141 8	0.147 6	0.121 9	0.094 7	0.138 2	P ₃>P₅>P₄>P₂>P₁
本文方法	λ=2	0.237 1	0.267 5	0.224 5	0.200 1	0.267 9	P ₃>P₅>P₄>P₂>P₁
	λ=6	0.490 8	0.448 1	0.367 9	0.428 2	0.489 5	P ₃>P₄>P₅>P₂>P₁
	λ=10	0.576 1	0.516 5	0.412 9	0.511 0	0.575 9	P ₃>P₄>P₂>P₅>P₁