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Current Situation and Optimization Strategy of Family Service Industry in Hebei Province Based on Fuzzy Mathematical Model Processing

Youzi Liang

Youzi Liang

College of Business Administration, Hebei Vocational University of Industry and TechnologyShijiazhuang, China
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Liang, Youzi
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Huan Zhao

Huan Zhao

College of Business Administration, Hebei Vocational University of Industry and TechnologyShijiazhuang, China
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Zhao, Huan
  
Mar 24, 2025
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Published Online: Mar 24, 2025
Received: Nov 10, 2024
Accepted: Feb 18, 2025
DOI: https://doi.org/10.2478/amns-2025-0704
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© 2025 Youzi Liang et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Integrated level of development of family service industry
Integrated level of development of family service industry

Figure 2.

Kernel density estimation of the development level of family service industry
Kernel density estimation of the development level of family service industry

Main influencing factors of optimization scheme and its evaluation indexes

Comparison project Solution 1 Solution 2 Solution 3 Solution 4 Solution 5
Index Sort Index Sort Index Sort Index Sort Index Sort
F1 300 5 600 2 500 3 1000 1 400 4
F2 4573 4 5624 1 4482 5 5036 2 4975 3
F3 26.79 4 32.83 2 34.96 1 23.54 5 28.97 3
F4 72.38 4 72.46 3 72.38 4 75.49 2 77.67 1
F5 34.78 4 35.94 3 33.26 5 41.05 1 37.86 2
F6 538 2 694 1 372 5 409 4 533 3
F7 Bad 3 Good 2 Bad 3 Good 2 Better 1
F8 Better 1 Bad 3 Good 2 Better 1 Good 2
F9 Good 2 Good 2 Better 1 Better 1 Bad 3

Family service indicator system

Primary indicator Secondary indicator
Policy level(A) Policy perfection(A1)
Industry standard formulation(A2)
Social security policy(A3)
Construction level(B) Relevant enterprise size(B1)
Brand construction(B2)
Talent level(C) Training mechanism(C1)
Personnel structure(C2)
Service identity(C3)
Mechanism level(D) Specialized agency(D1)
Platform construction(D2)
Innovation level(E) Internet application(E1)
Work on innovation(E2)
Technical innovation(E3)
Innovation of ideas(E4)

Space Markov probability transfer matrix

Interval Type I II III IV
I I 0.1047 0.2219 0.3748 0.2785
II 0.0003 0.2493 0.1257 0.6194
III 0.0001 0.6638 0.3319 0.0003
IV 0.0000 0.0001 0.0005 0.0000
II I 0.6638 0.1089 0.1094 0.1109
II 0.3976 0.4976 0.1403 0.0001
III 0.0005 0.5538 0.4175 0.0000
IV 0.0003 0.0000 0.0002 0.0001
III I 0.0003 0.0003 0.0001 0.0000
II 0.3976 0.3976 0.1986 0.0005
III 0.3764 0.2107 0.3766 0.0002
IV 0.1386 0.0698 0.3581 0.4173
IV I 0.0005 0.0001 0.0005 0.0000
II 0.0001 0.0003 0.3368 0.0001
III 0.0000 1.0000 0.0003 0.0004
IV 0.4278 0.2486 0.1864 0.1189

The relation between the tone operator and the quantitative sort

Tone operator Quantification Scale Relative Membership
T1 0.000 0.500 0.986 0.901
T2 0.100 0.550 0.803 0.732
T3 0.200 0.600 0.679 0.604
T4 0.300 0.650 0.541 0.473
T5 0.400 0.700 0.426 0.372
T6 0.500 0.750 0.317 0.286
T7 0.600 0.800 0.254 0.205
T8 0.700 0.850 0.183 0.147
T9 0.800 0.900 0.109 0.083
T10 0.900 0.950 0.057 0.029
T11 1.000 ─ 0.000 ─
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Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other
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