基于空间信息表征的勾股模糊集空间距离测度

doi:10.12305/j.issn.1001-506X.2023.11.19

Abstract

Abstract:

Pythagorean fuzzy set expands the information representation content of intuitionistic fuzzy sets and has the advantage of reflecting larger information space. Constructing the distance measure of Pythagorean fuzzy sets is the core link of implementing Pythagorean fuzzy decision-making. Firstly, this paper deeply analyzes the defects of the existing four distance measures of Pythagorean fuzzy sets, establishes a spatial information representation model of Pythagorean fuzzy sets integrating the membership degree and nonmembership degree, hesitation degree and strength of commitment, and then puts forward a novel distance measure based on the spatial centroid of Pythagorean fuzzy sets. Secondly, the specific properties of the proposed distance measure are extended, and the advantages of this distance measure model in reflecting hesitation and solving counterintuitive situations are proven and compared. Finally, the application research of pattern recognition and medical diagnosis verifies the accuracy and superiority of this distance measure between Pythagorean fuzzy sets.

Key words: Pythagorean fuzzy sets, distance measure, space centroid, strength of commitment

CLC Number:

C934

Jiali WANG, Wenqi JIANG, Xiwen TAO. Spatial distance measure of Pythagorean fuzzy sets based on spatial information representation[J]. Systems Engineering and Electronics, 2023, 45(11): 3524-3531.

Figures/Tables 6

Fig.1

Fig.2

Fig.3

Table 1

Comparative analysis of basic properties and extended properties"

性质	对比文献
性质	文献[30]		文献[31]		文献[32]		文献[33]
性质3	a(0.26, 0.22, )		a(0.70, 0.35)		a(0.18, 0.36)		a(0.36, 0.72)
	b(0.17, 0.22, )		b(0.50, 0.25)		b(0.28, 0.56)		b(0.06, 0.12)
	c(0.58, 0.22, )		c(0.04, 0.02)		c(0.30, 0.60)		c(0.38, 0.76)
	(0.036, 0.132, 0.167)	√	(0.099, 0.305, 0.209)	√	(0.093, 0.113, 0.019)	√	(0.280, 0.022, 0.301)	√
	(0.039, 0.269, 0.308)	×	(0.158, 0.522, 0.364)	×	(0.159, 0.184, 0.033)	√	(0.408, 0.048, 0.456)	×
性质5	a(0.60, 0.55)		a(0.93, 0.18)		a(0.91, 0.34)		a(0.69, 0.65)
	b(0.16, 0.57)		b(0.04, 0.21)		b(0.16, 0.39)		b(0.07, 0.66)
	c(0.16, 0.64)		c(0.02, 0.57)		c(0.16, 0.52)		c(0.05, 0.73)
	(0.182, 0.241, 0.154)	√	(0.380, 0.408, 0.148)	√	(0.329, 0.331, 0.054)	√	(0.262, 0.268, 0.032)	√
	(0.541, 0.498, 0.313)	×	(0.690, 0.681, 0.258)	×	(0.564, 0.559, 0.084)	×	(0.504, 0.496, 0.069)	×
拓展性质1	a(0.871, 0.259)		a(0.948, 0.092)		a(0.829, 0.405)		a(0.690, 0.340)
	b(0.295, 0.106)		b(0.417, 0.067)		b(0.144, 0.355)		b(0.686, 0.337)
	c(0.218, 0.865)		c(0.429, 0.893)		c(0.168, 0.718)		c(0.466, 0.604)
	(0.261, 0.356, 0.321)	√	(0.244, 0.383, 0.365)	√	(0.295, 0.298, 0.154)	√	(0.002, 0.139, 0.138)	√
	(0.701, 0.696, 0.718)	×	(0.376, 0.579, 0.588)	×	(0.504, 0.485, 0.565)	×	(0.005, 0.419, 0.420)	×
拓展性质2	a(0.70, 0.27)		a(0.88, 0.20)		a(0.31, 0.89)		a(0.85, 0.19)
	b(0.75, 0.40)		b(0.27, 0.37)		b(0.38, 0.78)		b(0.61, 0.30)
	c(0.24, 0.74)		c(0.39, 0.66)		c(0.54, 0.81)		c(0.66, 0.38)
	(0.062, 0.263, 0.246)	√	(0.269, 0.272, 0.135)	√	(0.061, 0.10, 0.084)	√	(0.112, 0.116, 0.041)	√
	(0.138, 0.455, 0.458)	×	(0.449, 0.429, 0.222)	×	(0.105, 0.139, 0.153)	×	(0.346, 0.095, 0.330)	×
拓展性质3	a(0.91, 0.35)		a(0.66, 0.42)		a(0.35, 0.25)		a(0.83, 0.51)
	b(0.47, 0.47)		b(0.60, 0.47)		b(0.26, 0.27)		b(0.82, 0.33)
	c(0.48, 0.41)		c(0.39, 0.14)		c(0.15, 0.05)		c(0.57, 0.47)
	(0.206, 0.210, 0.025)	√	(0.032, 0.166, 0.165)	√	(0.037, 0.114, 0.099)	√	(0.087, 0.138, 0.122)	√
	(0.576, 0.564, 0.0487)	×	(0.051, 0.277, 0.281)	×	(0.072, 0.199, 0.203)	×	(0.196, 0.298, 0.355)	×
拓展性质4	a(0.87, 0.42)		a(0.48, 0.22)		a(0.86, 0.07)		a(0.47, 0.20)
	b(0.45, 0.50)		b(0.17, 0.13)		b(0.13, 0.18)		b(0.09, 0.09)
	c(0.46, 0.69)		c(0.19, 0.59)		c(0.24, 0.69)		c(0.23, 0.27)
	(0.196, 0.205, 0.084)	√	(0.188, 0.189, 0.132)	√	(0.309, 0.353, 0.217)	√	(0.101, 0.160, 0.092)	√
	(0.522, 0.473, 0.231)	×	(0.363, 0.356, 0.236)	×	(0.544, 0.521, 0.361)	×	(0.413, 0.375, 0.090)	×

Table 1

Fig.4

Table 2

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序号	识别样本	方法	d(P, P₁)	d(P, P₂)	d(P, P₃)	分类结果
1	P₁={(0.33, 0.46), (0.83, 0.51), (0.49, 0.6)} P₂={(0.55, 0.14), (0.57, 0.69), (0.49, 0.25)} P₃={(0.63, 0.17), (0.74, 0.55), (0.67, 0.53)} P={(0.28, 0.92), (0.44, 0.55), (0.22, 0.4)}	文献[30]	0.828	0.676	0.889	P₂
		文献[31]	0.475	0.546	0.625	P₁
		文献[32]	0.543	0.550	0.639	P₁
		文献[33]	0.680	0.927	0.970	P₁
		本文提出方法	0.313	0.326	0.394	P₁
2	P₁={(0.42, 0.29), (0.42, 0.52), (0.12, 0.26)} P₂={(0.14, 0.35), (0.35, 0.27), (0.14, 0.12)} P₃={(0.7, 0.32), (0.23, 0.91), (0.81, 0.5)} P={(0.43, 0.65), (0.25, 0.29), (0.61, 0.62)}	文献[30]	0.687	0.629	0.750	P₂
		文献[31]	0.516	0.502	0.499	P₃
		文献[32]	0.514	0.498	0.505	P₂
		文献[33]	0.599	0.533	0.783	P₂
		本文方法	0.307	0.294	0.315	P₂
3	P₁={(0.71, 0.05), (0.05, 0.85), (0.67, 0.15)} P₂={(0.18, 0.12), (0.49, 0.06), (0.45, 0.51)} P₃={(0.59, 0.41), (0.3, 0.48), (0.94, 0.28)} P={(0.44, 0.43), (0.74, 0.55), (0.18, 0.97)}	文献[30]	0.943	0.374	0.388	P₂
		文献[31]	0.742	0.594	0.598	P₂
		文献[32]	0.722	0.626	0.576	P₃
		文献[33]	1.097	0.810	0.929	P₂
		本文方法	0.476	0.374	0.388	P₂
4	P₁={(0.89, 0.1), (0.74, 0.35), (0.34, 0.13)} P₂={(0.49, 0.5), (0.2, 0.26), (0.56, 0.39)} P₃={(0.14, 0.32), (0.51, 0.69), (0.27, 0.61)} P={(0.72, 0.33), (0.61, 0.58), (0.06, 0.35)}	文献[30]	0.316	0.628	0.532	P₁
		文献[31]	0.418	0.549	0.443	P₁
		文献[32]	0.384	0.528	0.421	P₁
		文献[33]	0.803	0.742	0.602	P₃
		本文方法	0.212	0.314	0.254	P₁

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Spatial distance measure of Pythagorean fuzzy sets based on spatial information representation

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