A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions
Abstract
:1. Introduction
2. Literature Review
2.1. Competence Sets
2.2. Technology Roadmaps
2.3. MOP and FMOP
2.4. Research Gaps
3. Research Methods
3.1. Modified Delphi Method
3.2. Competence Set Expansion
3.3. Fuzzy Parametric Programming
3.4. Competence Set Expansion Based on FMOP
4. Empirical Study
4.1. Selection of the Technology by the Modified Delphi Method
4.2. Expanding Technology Competence Sets
4.3. Defining the Roadmap for SIPs Required for Future Application Specific Integrated Circuits of Unmanned Vehicles
4.4. Sensitivity Analysis
5. Discussion
5.1. Advances in Roadmapping Techniques
5.2. Discussion of the Results of Sensitivity Analysis
5.3. Strengths and Weaknesses of the Work
5.4. Future Research Possibilities
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
x0 | N.A. | [65,80], | [52,63], | [41,76], | [51,63], | [52,63], | [76,80], | [52,77], | [59,63], | [41,76], | [52,76], | [76,80], | [41,76], | [41,52], | [45,63], | [55,69] |
x1 | N.A. | N.A. | [41,63], | [52,76], | [52,76], | [52,76], | [49,63], | [48,63], | [41,78], | [52,76], | [41,100], | [52,76], | [52,63], | [41,52], | [44,54], | [44,76] |
x2 | N.A. | [41,63], | N.A. | [52,76], | [52,63], | [41,79], | [41,54], | [41,63], | [52,76], | [54,77], | [52,100], | [52,63], | [52,76], | [52,80], | [63,64], | [43,69] |
x3 | N.A. | [52,63], | [41,100], | N.A. | [43,63], | [41,76], | [52,63], | [51,76], | [52,76], | [41,76], | [80,100], | [52,76], | [52,63], | [52,80], | [54,66], | [57,63] |
x4 | N.A. | [42,63], | [52,100], | [76,80], | N.A. | [52,79], | [52,76], | [48,76], | [41,76], | [76,80], | [80,100], | [52,76], | [42,76], | [41,80], | [57,63], | [56,63] |
x5 | N.A. | [43,63], | [41,63], | [41,63], | [41,76], | N.A. | [30,54], | [41,76], | [52,77], | [52,63], | [59,100], | [58,76], | [42,76], | [41,52], | [55,63], | [59,76] |
x6 | N.A. | [52,54], | [52,63], | [52,76], | [41,76], | [52,76], | N.A. | [48,76], | [52,77], | [77,80], | [52,76], | [52,76], | [60,63], | [52,80], | [63,66], | [59,100] |
x7 | N.A. | [41,63], | [41,63], | [52,63], | [41,76], | [52,79], | [55,63], | N.A. | [77,80], | [53,76], | [41,76], | [41,76], | [41,76], | [41,52], | [37,63], | [56,63] |
x8 | N.A. | [42,63], | [45,100], | [41,63], | [44,63], | [52,76], | [52,63], | [51,63], | N.A. | [41,76], | [52,100], | [41,76], | [42,76], | [52,80], | [55,63], | [43,76] |
x9 | N.A. | [43,63], | [52,76], | [52,76], | [44,76], | [41,79], | [52,63], | [51,63], | [52,76], | N.A. | [52,76], | [52,76], | [52,76], | [52,55], | [55,63], | [58,63] |
x10 | N.A. | [41,54], | [41,76], | [41,63], | [44,76], | [52,79], | [52,100], | [52,76], | [41,76], | [52,63], | N.A. | [41,76], | [41,76], | [52,80], | [57,63], | [43,63] |
x11 | N.A. | [52,63], | [41,100], | [41,76], | [41,63], | [52,79], | [52,63], | [48,100], | [59,78], | [52,76], | [52,100], | N.A. | [41,63], | [52,55], | [54,55], | [56,63] |
x12 | N.A. | [32,63], | [52,100], | [63,80], | [41,63], | [52,79], | [63,80], | [51,63], | [60,76], | [54,76], | [59,63], | [52,63], | N.A. | [41,52], | [55,63], | [44,63] |
x13 | N.A. | [41,65], | [52,76], | [52,76], | [51,76], | [79,80], | [55,63], | [52,77], | [41,78], | [52,76], | [58,100], | [52,76], | [52,76], | N.A. | [54,55], | [55,100] |
x14 | N.A. | [32,54], | [41,63], | [39,76], | [44,63], | [52,76], | [55,63], | [52,63], | [41,76], | [54,76], | [30,100], | [52,63], | [61,76], | [41,52], | N.A. | [56,63] |
x15 | N.A. | [32,54], | [52,76], | [52,76], | [52,63], | [52,79], | [49,100], | [51,63], | [59,78], | [52,76], | [52,76], | [41,63], | [61,76], | [41,50], | [44,54], | N.A. |
x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
x0 | N.A. | [41,63], | [52,76], | [52,63], | [43,63], | [41,79], | [41,63], | [41,76], | [52,76], | [53,63], | [58,76], | [41,76], | [52,100], | [41,52], | [54,55], | [56,100] |
x1 | N.A. | N.A. | [52,100], | [63,80], | [43,76], | [41,79], | [52,63], | [51,77], | [41,78], | [53,77], | [52,100], | [52,76], | [52,63], | [52,55], | [54,57], | [55,69] |
x2 | N.A. | [52,63], | N.A. | [52,76], | [52,63], | [52,76], | [55,76], | [52,77], | [78,80], | [52,77], | [30,100], | [41,76], | [52,76], | [41,52], | [63,64], | [50,63] |
x3 | N.A. | [54,80], | [45,100], | N.A. | [41,63], | [79,80], | [63,80], | [52,63], | [52,76], | [54,77], | [52,100], | [41,76], | [42,76], | [64,80], | [54,66], | [63,68] |
x4 | N.A. | [41,63], | [45,76], | [76,80], | N.A. | [41,79], | [41,63], | [52,76], | [52,78], | [76,80], | [52,100], | [41,76], | [52,76], | [52,62], | [50,63], | [43,69] |
x5 | N.A. | [43,65], | [42,100], | [52,63], | [63,80], | N.A. | [52,63], | [52,76], | [76,80], | [41,63], | [52,100], | [41,76], | [52,76], | [52,60], | [57,63], | [43,76] |
x6 | N.A. | [41,63], | [41,100], | [52,76], | [52,63], | [41,79], | N.A. | [52,76], | [52,78], | [77,80], | [41,76], | [52,63], | [52,76], | [64,80], | [63,66], | [44,63] |
x7 | N.A. | [52,54], | [41,100], | [39,76], | [44,76], | [52,79], | [49,63], | N.A. | [77,80], | [52,76], | [52,100], | [41,76], | [52,76], | [52,64], | [37,54], | [43,63] |
x8 | N.A. | [30,54], | [41,100], | [76,80], | [52,63], | [52,79], | [52,63], | [51,76], | N.A. | [52,76], | [80,100], | [41,76], | [52,63], | [52,80], | [57,63], | [66,100] |
x9 | N.A. | [43,63], | [42,63], | [52,76], | [51,76], | [41,100], | [63,80], | [52,76], | [52,78], | N.A. | [52,76], | [52,76], | [52,76], | [41,52], | [45,63], | [66,76] |
x10 | N.A. | [42,63], | [41,100], | [52,76], | [41,63], | [41,79], | [63,80], | [51,76], | [41,76], | [53,77], | N.A. | [76,80], | [52,63], | [41,52], | [63,65], | [66,100] |
x11 | N.A. | [41,63], | [42,63], | [52,63], | [41,63], | [41,79], | [52,54], | [52,76], | [52,78], | [52,77], | [59,100], | N.A. | [52,63], | [52,80], | [54,55], | [57,76] |
x12 | N.A. | [41,63], | [42,100], | [63,80], | [41,63], | [52,76], | [63,80], | [51,76], | [59,78], | [54,63], | [52,100], | [41,63], | N.A. | [52,80], | [58,63], | [58,63] |
x13 | N.A. | [41,63], | [41,76], | [41,63], | [41,76], | [79,80], | [54,80], | [41,63], | [41,76], | [41,76], | [52,76], | [58,76], | [41,76], | N.A. | [54,55], | [57,63] |
x14 | N.A. | [52,63], | [63,80], | [30,76], | [41,76], | [52,79], | [55,76], | [52,76], | [52,76], | [41,76], | [52,76], | [52,76], | [76,80], | [80,90], | N.A. | [59,100] |
x15 | N.A. | [42,63], | [41,76], | [53,63], | [43,76], | [52,79], | [52,63], | [76,80], | [52,76], | [41,76], | [52,100], | [59,76], | [52,63], | [40,50], | [45,54], | N.A. |
x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
x0 | N.A. | [41,63], | [41,63], | [41,63], | [52,78], | [41,76], | [52,76], | [41,76], | [52,78], | [52,76], | [52,76], | [52,63], | [52,76], | [52,55], | [43,54], | [66,76] |
x1 | N.A. | N.A. | [41,100], | [52,63], | [41,76], | [41,76], | [52,54], | [41,63], | [52,76], | [52,76], | [52,76], | [52,76], | [52,76], | [52,80], | [55,63], | [66,100] |
x2 | N.A. | [42,63], | N.A. | [41,76], | [52,63], | [52,79], | [41,63], | [52,63], | [59,78], | [41,76], | [52,100], | [41,76], | [52,76], | [52,80], | [50,63], | [44,63] |
x3 | N.A. | [41,63], | [52,63], | N.A. | [41,76], | [76,80], | [52,63], | [41,76], | [59,76], | [52,76], | [41,100], | [52,63], | [41,76], | [52,60], | [44,63], | [63,66] |
x4 | N.A. | [42,63], | [52,76], | [30,76], | N.A. | [52,100], | [55,63], | [48,76], | [41,77], | [52,76], | [52,100], | [41,76], | [61,63], | [41,80], | [55,63], | [55,63] |
x5 | N.A. | [32,54], | [52,63], | [52,63], | [52,76], | N.A. | [52,63], | [41,76], | [52,76], | [53,76], | [41,100], | [52,63], | [76,80], | [41,45], | [50,54], | [43,63] |
x6 | N.A. | [52,54], | [52,100], | [30,63], | [52,76], | [52,100], | N.A. | [48,63], | [41,76], | [53,76], | [52,100], | [52,76], | [41,76], | [41,52], | [55,63], | [59,63] |
x7 | N.A. | [52,54], | [41,76], | [52,63], | [52,76], | [41,79], | [41,76], | N.A. | [41,76], | [41,76], | [52,76], | [52,76], | [41,76], | [52,80], | [55,63], | [63,68] |
x8 | N.A. | [41,54], | [52,100], | [52,63], | [43,76], | [52,79], | [52,63], | [41,63], | N.A. | [52,76], | [41,100], | [52,76], | [76,80], | [41,52], | [55,63], | [63,66] |
x9 | N.A. | [52,63], | [52,100], | [52,76], | [41,63], | [41,79], | [52,63], | [41,63], | [52,77], | N.A. | [41,100], | [76,80], | [61,76], | [52,62], | [63,64], | [63,66] |
x10 | N.A. | [41,63], | [45,100], | [63,80], | [51,76], | [52,79], | [54,55], | [41,63], | [76,80], | [52,76], | N.A. | [41,76], | [41,76], | [41,80], | [57,63], | [56,76] |
x11 | N.A. | [41,54], | [52,100], | [41,63], | [76,80], | [41,79], | [52,63], | [48,63], | [59,77], | [41,76], | [41,100], | N.A. | [52,63], | [41,52], | [57,63], | [57,63] |
x12 | N.A. | [41,63], | [42,76], | [52,76], | [52,76], | [52,100], | [52,100], | [63,80], | [52,76], | [41,76], | [41,100], | [41,63], | N.A. | [52,55], | [57,63], | [56,63] |
x13 | N.A. | [43,54], | [45,76], | [39,76], | [41,76], | [79,80], | [55,100], | [51,63], | [60,77], | [41,76], | [52,63], | [52,76], | [41,76], | N.A. | [50,63], | [59,76] |
x14 | N.A. | [41,54], | [52,76], | [41,63], | [44,76], | [52,79], | [52,63], | [52,63], | [52,77], | [54,76], | [58,100], | [52,63], | [52,63], | [41,64], | N.A. | [66,76] |
x15 | N.A. | [63,80], | [52,100], | [53,63], | [43,63], | [52,76], | [41,63], | [52,76], | [76,80], | [41,63], | [59,100], | [52,76], | [52,63], | [64,80], | [63,64], | N.A. |
Appendix B
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Notations | Descriptions | Notations | Descriptions |
---|---|---|---|
An matrix | True competence set | ||
An -vector | Perceived competence set | ||
An -vector | Competence | ||
The cost of acquiring from | Subsidiary variable | ||
Fuzzy cost from to under | The ith objective under | ||
(E,t) | Time variant competence set | Membership functions | |
A given decision problem | Inverse membership functions | ||
HD | Habitual domain | ||
The objective | |||
A parameter of the model | Abbreviations | ||
skill set | FLS | Fuzzy linear system | |
Perceived acquired skill set | FMOP | Fuzzy MOP | |
time | MOP | Multiple objective programming | |
Truly required competence set | R&D | Research and development | |
Specific SIP | SIP | Silicon intellectual properties |
Education | Industry | Position |
---|---|---|
Master | ITS | General manager |
Master | IC design service | Vice president |
Master | IC design service | Manager |
Master | IC design service | Manager |
Ph.D. | Universities or research institutes | Professor |
Master | Unmanned vehicle | Vice president |
Master | Unmanned vehicle | Director |
Optimal Expansion Path | Cost | |||||||
---|---|---|---|---|---|---|---|---|
0→2 | 2→15 | 9→7 | 7→14 | 14→3 | 3→4 | 4→8 | 8→1 | |
0→5 | 5→6 | 12→11 | ||||||
0→10 | 5→9 | 833.000 | ||||||
5→13 | ||||||||
10→12 |
u | Stage 1 | Stage 2 | Stage 3 | Stage 4 | Stage 5 | Stage 6 | Stage 7 | Stage 8 | Stage 9 | Cost | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.000 | 0 | → | 2 | 2 | → | 4 | 6 | → | 1 | 1 | → | 12 | 969.000 | |||||||||||||||
0 | → | 5 | 5 | → | 3 | |||||||||||||||||||||||
0 | → | 8 | 5 | → | 6 | |||||||||||||||||||||||
0 | → | 10 | 5 | → | 9 | |||||||||||||||||||||||
0 | → | 14 | 5 | → | 13 | |||||||||||||||||||||||
8 | → | 7 | ||||||||||||||||||||||||||
12 | → | 11 | ||||||||||||||||||||||||||
12 | → | 15 | ||||||||||||||||||||||||||
0.100 | 0 | → | 2 | 2 | → | 4 | 1 | → | 12 | 944.100 | ||||||||||||||||||
0 | → | 5 | 5 | → | 3 | |||||||||||||||||||||||
0 | → | 8 | 5 | → | 6 | |||||||||||||||||||||||
0 | → | 10 | 5 | → | 9 | |||||||||||||||||||||||
0 | → | 14 | 5 | → | 13 | |||||||||||||||||||||||
8 | → | 1 | ||||||||||||||||||||||||||
8 | → | 7 | ||||||||||||||||||||||||||
12 | → | 11 | ||||||||||||||||||||||||||
12 | → | 15 | ||||||||||||||||||||||||||
0.200 | 0 | → | 2 | 2 | → | 4 | 1 | → | 12 | 919.200 | ||||||||||||||||||
0 | → | 5 | 5 | → | 3 | |||||||||||||||||||||||
0 | → | 8 | 5 | → | 6 | |||||||||||||||||||||||
0 | → | 10 | 5 | → | 9 | |||||||||||||||||||||||
0 | → | 14 | 5 | → | 13 | |||||||||||||||||||||||
8 | → | 1 | ||||||||||||||||||||||||||
8 | → | 7 | ||||||||||||||||||||||||||
12 | → | 11 | ||||||||||||||||||||||||||
12 | → | 15 | ||||||||||||||||||||||||||
0.300 | 0 | → | 2 | 2 | → | 15 | 3 | → | 4 | 12 | → | 11 | 893.367 | |||||||||||||||
0 | → | 5 | 5 | → | 3 | 1 | → | 7 | ||||||||||||||||||||
0 | → | 8 | 5 | → | 6 | 1 | → | 12 | ||||||||||||||||||||
0 | → | 10 | 5 | → | 9 | |||||||||||||||||||||||
0 | → | 14 | 5 | → | 13 | |||||||||||||||||||||||
8 | → | 1 | ||||||||||||||||||||||||||
0.400 | 0 | → | 2 | 2 | → | 15 | 3 | → | 4 | 4 | → | 8 | 8 | → | 1 | 1 | → | 7 | 7 | → | 14 | 864.533 | ||||||
0 | → | 5 | 5 | → | 3 | 12 | → | 11 | ||||||||||||||||||||
0 | → | 10 | 5 | → | 6 | |||||||||||||||||||||||
5 | → | 9 | ||||||||||||||||||||||||||
5 | → | 13 | ||||||||||||||||||||||||||
10 | → | 12 | ||||||||||||||||||||||||||
0.600 | 0 | → | 2 | 2 | → | 15 | 12 | → | 11 | 9 | → | 7 | 7 | → | 14 | 14 | → | 3 | 3 | → | 4 | 4 | → | 8 | 8 | → | 1 | 799.800 |
0 | → | 5 | 5 | → | 6 | 15 | → | 9 | ||||||||||||||||||||
0 | → | 10 | 5 | → | 13 | |||||||||||||||||||||||
10 | → | 12 | ||||||||||||||||||||||||||
0.700 | 0 | → | 5 | 5 | → | 6 | 13 | → | 7 | 7 | → | 2 | 2 | → | 15 | 3 | → | 4 | 4 | → | 8 | 8 | → | 1 | 763.767 | |||
5 | → | 13 | 7 | → | 10 | 10 | → | 12 | 12 | → | 11 | |||||||||||||||||
7 | → | 14 | 14 | → | 3 | 15 | → | 9 | ||||||||||||||||||||
0.800 | 0 | → | 7 | 7 | → | 2 | 2 | → | 15 | 15 | → | 9 | 9 | → | 5 | 5 | → | 6 | 6 | → | 10 | 10 | → | 12 | 12 | → | 11 | 725.867 |
7 | → | 14 | 14 | → | 3 | 3 | → | 4 | 4 | → | 8 | 8 | → | 1 | ||||||||||||||
0.900 | 0 | → | 7 | 7 | → | 2 | 2 | → | 10 | 3 | → | 4 | 4 | → | 8 | 5 | → | 6 | 684.567 | |||||||||
7 | → | 14 | 2 | → | 15 | 10 | → | 12 | 9 | → | 5 | 5 | → | 13 | ||||||||||||||
14 | → | 3 | 15 | → | 9 | 12 | → | 11 | 8 | → | 1 | |||||||||||||||||
1.000 | 0 | → | 7 | 7 | → | 2 | 2 | → | 10 | 3 | → | 4 | 4 | → | 8 | 8 | → | 1 | 643.000 | |||||||||
0 | → | 13 | 7 | → | 14 | 2 | → | 15 | 10 | → | 12 | 4 | → | 11 | ||||||||||||||
14 | → | 3 | 15 | → | 9 | 5 | → | 6 | ||||||||||||||||||||
9 | → | 5 |
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Huang, C.-Y.; Huang, J.-J.; Chang, Y.-N.; Lin, Y.-C. A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions. Mathematics 2021, 9, 135. https://doi.org/10.3390/math9020135
Huang C-Y, Huang J-J, Chang Y-N, Lin Y-C. A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions. Mathematics. 2021; 9(2):135. https://doi.org/10.3390/math9020135
Chicago/Turabian StyleHuang, Chi-Yo, Jih-Jeng Huang, You-Ning Chang, and Yen-Chu Lin. 2021. "A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions" Mathematics 9, no. 2: 135. https://doi.org/10.3390/math9020135
APA StyleHuang, C.-Y., Huang, J.-J., Chang, Y.-N., & Lin, Y.-C. (2021). A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions. Mathematics, 9(2), 135. https://doi.org/10.3390/math9020135