Introduction
Consensus mechanism | Energy consumption | Response time | Degree of decentralization | Consistency | Fault tolerance rate (%) |
---|---|---|---|---|---|
PoW | High | Minute | Completely | Weak | 50 |
PoS | Low | Minute | Completely | Weak | 50 |
DPoS | Low | Second | Incompletely | Weak | 50 |
PBFT | Low | Second | Incompletely | Strong | 33 |
RAFT | Low | Second | Incompletely | Strong | 50 |
Preliminaries
PBFT consensus mechanism
Additive linguistic term sets
Probabilistic linguistic term set
Multiple attribute decision-making analysis
Primary node election based on PLTS-CI
The concept of the PLTS-CI
The score function of the PLTS-CI
Attribute weights calculation based on Score-ESCA
TOPSIS method based on Score-ESCA
Decision-making process for primary node election
Decision problem description
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | s2, [0.9,1] | s0, [0.7,1] | s3, [0.3,0.4] | s0, [0.6,0.9] |
N2 | s2, [0.3,0.6] | s6, [0.2,0.3] | s6, [0.6,0.7] | s6, [0.8,0.9] |
N3 | s5, [0.6,0.8] | s0, [0.5,0.6] | s2, [0.7,0.8] | s4, [0.6,0.8] |
N4 | s1, [0.6,0.8] | s3, [0.1,0.2] | s0, [0.1,0.4] | s3, [0.6,0.7] |
N5 | s0, [0.6,0.7] | s0, [0.4,0.7] | s5, [0.1,0.4] | s0, [0.3,0.6] |
N6 | s2, [0.6,0.7] | s1, [0.4,0.7] | s4, [0.1,0.3] | s6, [0.7,1] |
N7 | s5, [0.2,0.3] | s3, [0.8,1] | s5, [0.1,0.4] | s0, [0.9,1] |
N8 | s4, [0.7,0.8] | s6, [0.9,1] | s0, [0.1,0.4] | s2, [0.8,1] |
N9 | s0, [0.7,1] | s3, [0.2,0.5] | s4, [0.4,0.6] | s1, [0.6,0.7] |
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | s1, [0.6,0.8] | s4, [0.2,0.3] | s0, [0.1,0.2] | s0, [0.3,0.4] |
N2 | s4, [0.6,0.8] | s4, [0.6,0.7] | s0, [0.1,0.3] | s5, [0.2,0.3] |
N3 | s0, [0.8,1] | s3, [0.3,0.5] | s6, [0.4,0.7] | s2, [0.1,0.4] |
N4 | s4, [0.4,0.7] | s0, [0.8,1] | s1, [0.5,0.8] | s0, [0.9,1] |
N5 | s3, [0.9,1] | s3, [0.7,0.9] | s5, [0.9,1] | s0, [0.2,0.5] |
N6 | s1, [0.3,0.6] | s3, [0.9,1] | s0, [0.4,0.7] | s4, [0.6,0.7] |
N7 | s4, [0.8,0.9] | s3, [0.5,0.8] | s6, [0.9,1] | s0, [0.4,0.7] |
N8 | s6, [0.1,0.4] | s0, [0.4,0.7] | s1, [0.9,1] | s5, [0.2,0.4] |
N9 | s1, [0.8,1] | s0, [0.7,0.8] | s0, [0.4,0.5] | s4, [0.2,0.5] |
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | s4, [0.6,0.9] | s1, [0.3,0.5] | s3, [0.4,0.5] | s6, [0.8,1] |
N2 | s3, [0.1,0.4] | s0, [0.5,0.6] | s3, [0.9,1] | s3, [0.6,0.7] |
N3 | s2, [0.6,0.9] | s0, [0.9,1] | s4, [0.6,0.8] | s3, [0.7,0.8] |
N4 | s0, [0.1,0.3] | s2, [0.9,1] | s2, [0.6,0.9] | s1, [0.9,1] |
N5 | s6, [0.9,1] | s2, [0.8,1] | s3, [0.5,0.7] | s3, [0.2,0.5] |
N6 | s1, [0.9,1] | s2, [0.3,0.4] | s0, [0.3,0.5] | s5, [0.5,0.7] |
N7 | s3, [0.2,0.5] | s3, [0.7,0.8] | s0, [0.4,0.7] | s0, [0.6,0.8] |
N8 | s3, [0.2,0.3] | s0, [0.1,0.2] | s0, [0.9,1] | s4, [0.4,0.5] |
N9 | s0, [0.4,0.6] | s4, [0.1,0.4] | s0, [0.6,0.7] | s5, [0.6,0.7] |
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | s3, [0.4,0.7] | s2, [0.2,0.5] | s6, [0.3,0.5] | s1, [0.2,0.5] |
N2 | s3, [0.8,0.9] | s4, [0.2,0.5] | s4, [0.3,0.4] | s2, [0.1,0.3] |
N3 | s2, [0.9,1] | s5, [0.4,0.6] | s4, [0.5,0.8] | s3, [0.8,0.9] |
N4 | s4, [0.7,0.9] | s0, [0.7,0.8] | s5, [0.3,0.5] | s0, [0.6,0.8] |
N5 | s6, [0.5,0.8] | s4, [0.9,1] | s0, [0.4,0.6] | s0, [0.3,0.4] |
N6 | s4, [0.4,0.6] | s0, [0.2,0.4] | s4, [0.8,1] | s1, [0.4,0.5] |
N7 | s3, [0.7,1] | s6, [0.2,0.5] | s3, [0.2,0.5] | s4, [0.7,0.9] |
N8 | s6, [0.5,0.6] | s1, [0.2,0.3] | s0, [0.8,1] | s3, [0.8,0.9] |
N9 | s0, [0.5,0.8] | s5, [0.9,1] | s3, [0.4,0.7] | s5, [0.8,0.9] |
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | s0, [0.3,0.4] | s4, [0.3,0.6] | s3, [0.7,1] | s2, [0.4,0.7] |
N2 | s0, [0.7,0.9] | s2, [0.9,1] | s4, [0.6,0.7] | s4, [0.6,0.9] |
N3 | s2, [0.9,1] | s4, [0.4,0.5] | s6, [0.8,1] | s0, [0.7,0.8] |
N4 | s0, [0.2,0.3] | s4, [0.1,0.4] | s6, [0.8,1] | s1, [0.4,0.5] |
N5 | s4, [0.6,0.8] | s3, [0.3,0.6] | s6, [0.9,1] | s3, [0.1,0.3] |
N6 | s4, [0.4,0.5] | s3, [0.9,1] | s0, [0.2,0.5] | s6, [0.1,0.3] |
N7 | s1, [0.2,0.5] | s2, [0.5,0.7] | s2, [0.4,0.7] | s6, [0.3,0.4] |
N8 | s1, [0.1,0.3] | s5, [0.2,0.5] | s4, [0.9,1] | s2, [0.6,0.8] |
N9 | s2, [0.1,0.2] | s6, [0.3,0.5] | s3, [0.3,0.5] | s5, [0.2,0.3] |
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | s0, [0.3,0.4] | s4, [0.3,0.6] | s3, [0.7,1] | s2, [0.4,0.7] |
N2 | s0, [0.7,0.9] | s2, [0.9,1] | s4, [0.6,0.7] | s2, [0.6,0.9] |
N3 | s2, [0.9,1] | s4, [0.4,0.5] | s6, [0.8,1] | s0, [0.7,0.8] |
N4 | s0, [0.2,0.3] | s4, [0.1,0.4] | s6, [0.8,1] | s1, [0.4,0.5] |
N5 | s4, [0.6,0.8] | s3, [0.3,0.6] | s6, [0.9,1] | s3, [0.1,0.3] |
N6 | s4, [0.4,0.5] | s3, [0.9,1] | s0, [0.2,0.5] | s6, [0.1,0.3] |
N7 | s1, [0.2,0.5] | s2, [0.5,0.7] | s2, [0.4,0.7] | s6, [0.3,0.4] |
N8 | s1, [0.1,0.3] | s5, [0.2,0.5] | s4, [0.9,1] | s2, [0.6,0.8] |
N9 | s2, [0.1,0.2] | s6, [0.3,0.5] | s3, [0.3,0.5] | s5, [0.2,0.3] |
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | s4, [0.8,0.9] | s3, [0.7,0.9] | s0, [0.6,0.8] | s4, [0.4,0.6] |
N2 | s4, [0.7,0.8] | s3, [0.2,0.3] | s1, [0.1,0.4] | s2, [0.4,0.6] |
N3 | s6, [0.6,0.9] | s2, [0.1,0.3] | s0, [0.8,1] | s6, [0.5,0.8] |
N4 | s0, [0.2,0.4] | s0, [0.7,0.9] | s3, [0.5,0.6] | s5, [0.3,0.4] |
N5 | s0, [0.7,0.8] | s4, [0.6,0.8] | s2, [0.2,0.4] | s3, [0.8,1] |
N6 | s4, [0.4,0.5] | s2, [0.8,1] | s3, [0.4,0.5] | s6, [0.4,0.5] |
N7 | s2, [0.7,1] | s2, [0.9,1] | s3, [0.9,1] | s3, [0.6,0.7] |
N8 | s4, [0.6,0.7] | s1, [0.3,0.4] | s5, [0.8,1] | s0, [0.4,0.6] |
N9 | s5, [0.4,0.6] | s0, [0.2,0.3] | s0, [0.4,0.7] | s3, [0.3,0.5] |
Decision-making process
A1 | A2 | A3 | A4 | |
---|---|---|---|---|
N1 | {s4(2/7,[0.7,0.9]), s5(1/7,[0.3,0.4]), s2(1/7,[0.9,1]), s3(1/7,[0.4,0.7]), s1(1/7,[0.6,0.8]), s0(1/7,[0.3,0.4])} | {s4(2/7,[0.25,0.45]), s3(1/7,[0.7,0.9]), s2(1/7,[0.2,0.5]), s1(1/7,[0.3,0.5]), s0(2/7,[0.4,0.7]), s0(0,[1,1])} | {s3(3/7,[0.47,0.63]), s6(1/7,[0.3,0.5]), s0(3/7,[0.33,0.5])s0(0,[1,1]), s0(0,[1,1]), s0(0,[1,1])} | {s6(1/7,[0.8,1]), s2(2/7,[0.65,0.85]), s4(1/7,[0.4,0.6]), s1(1/7,[0.2,0.5]), s0(2/7,[0.45,0.65]), s0(0,[1,1])} |
N2 | {s4(2/7,[0.65,0.8]), s3(2/7,[0.5,0.73]), s2(1/7,[0.3,0.6]), s0(1/7,[0.7,0.9]), s0(0,[1,1]), s0(0,[1,1])} | {s4(2/7,[0.4,0.6]), s6(1/7,[0.2,0.3]), s2(1/7,[0.9,1]), s1(1/7,[0.8,0.9]), s3(1/7,[0.2,0.3]), s0(1/7,[0.5,0.6])} | {s4(3/7,[0.37,0.57]), s6(1/7,[0.6,0.7]), s3(1/7,[0.9,1]), s1(1/7,[0.1,0.4]), s0(1/7,[0.1,0.3]), s0(0,[1,1])} | {s6(1/7,[0.8,0.9]), s3(1/7,[0.6,0.7]), s5(1/7,[0.2,0.3]), s2(3/7,[0.37,0.6]), s0(1/7,[0.9,1]), s0(0,[1,1])} |
N3 | {s6(2/7,[0.45,0.7]), s5(1/7,[0.6,0.8]), s0(1/7,[0.8,1]), s2(3/7,[0.8,0.97]), s0(0,[1,1]), s0(0,[1,1])} | {s3(1/7,[0.3,0.5]), s5(1/7,[0.4,0.6]), s4(1/7,[0.4,0.5]), s2(1/7,[0.1,0.3]), s0(3/7,[0.77,0.87]), s0(0,[1,1])} | {s6(2/7,[0.6,0.85]), s4(2/7,[0.55,0.8]), s5(1/7,[0.2,0.4]), s2(1/7,[0.7,0.8]), s0(1/7,[0.8,1]), s0(0,[1,1])} | {s6(1/7,[0.5,0.8]), s4(1/7,[0.6,0.8]), s2(1/7,[0.1,0.4]), s3(3/7,[0.63,0.73]), s0(1/7,[0.7,0.8]), s0(0,[1,1])} |
N4 | {s4(2/7,[0.55,0.8]), s5(1/7,[0.5,0.6]), s1(1/7,[0.6,0.8]), s0(3/7,[0.17,0.33]), s0(0,[1,1]), s0(0,[1,1])} | {s2(1/7,[0.9,1]), s4(1/7,[0.1,0.4]), s1(1/7,[0.8,1]), s3(1/7,[0.1,0.2]), s0(3/7,[0.73,0.9]), s0(0,[1,1])} | {s6(1/7,[0.8,1]), s5(2/7,[0.35,0.5]), s3(1/7,[0.5,0.6]), s2(1/7,[0.6,0.9]), s1(1/7,[0.5,0.8]), s0(1/7,[0.1,0.4]),} | {s5(1/7,[0.3,0.4]), s3(1/7,[0.6,0.7]), s6(1/7,[0.1,0.2]), s1(2/7,[0.65,0.75]), s0(2/7,[0.75,0.9]), s0(0,[1,1])} |
N5 | {s6(2/7,[0.7,0.9]), s4(1/7,[0.6,0.8]), s3(1/7,[0.9,1]), s0(3/7,[0.5,0.6]), s0(0,[1,1]), s0(0,[1,1])} | {s4(3/7,[0.57,0.7]), s3(2/7,[0.5,0.75]), s2(1/7,[0.8,1]), s0(1/7,[0.4,0.7]), s0(0,[1,1]), s0(0,[1,1])} | {s6(1/7,[0.9,1]), s5(2/7,[0.5,0.7]), s3(1/7,[0.5,0.7]), s1(1/7,[0.7,0.9]), s2(1/7,[0.2,0.4]), s0(1/7,[0.4,0.6])} | {s3(4/7,[0.325,0.525]), s0(3/7,[0.27,0.5]), s0(0,[1,1]), s0(0,[1,1]), s0(0,[1,1]), s0(0,[1,1])} |
N6 | {s4(3/7,[0.4,0.53]), s2(1/7,[0.6,0.7]), s1(2/7,[0.6,0.8]), s0(1/7,[0.8,1]), s0(0,[1,1]), s0(0,[1,1])} | {s3(2/7,[0.9,1]), s2(3/7,[0.47,0.63]), s1(1/7,[0.4,0.7]), s0(1/7,[0.2,0.4]), s0(0,[1,1]), s0(0,[1,1])} | {s4(3/7,[0.57,0.73]), s3(1/7,[0.4,0.5]), s0(3/7,[0.3,0.57]), s0(0,[1,1]), s0(0,[1,1]), s0(0,[1,1])} | {s6(3/7,[0.4,0.6]), s5(1/7,[0.5,0.7]), s4(1/7,[0.6,0.7]), s1(1/7,[0.4,0.5]), s0(1/7,[0.9,1]), s0(0,[1,1])} |
N7 | {s3(3/7,[0.53,0.83]), s4(1/7,[0.8,0.9]), s2(1/7,[0.7,1]), s5(1/7,[0.2,0.3]), s1(1/7,[0.2,0.5]), s1(0,[1,1])} | {s3(3/7,[0.67,0.87]), s6(1/7,[0.2,0.5]), s5(1/7,[0.2,0.5]), s2(2/7,[0.7,0.85]), s2(0,[1,1]), s2(0,[1,1])} | {s6(1/7,[0.9,1]), s5(2/7,[0.1,0.4]), s4(1/7,[0.4,0.7]), s3(1/7,[0.55,0.75]), s2(1/7,[0.4,0.7]), s0(1/7,[0.4,0.7])} | {s3(2/7,[0.55,0.75]), s4(1/7,[0.7,0.9]), s6(1/7,[0.3,0.4]), s0(3/7,[0.63,0.83]), s0(0,[1,1]), s0(0,[1,1])} |
N8 | {s4(2/7,[0.65,0.75), s6(2/7,[0.3,0.45]), s3(1/7,[0.2,0.3]), s1(1/7,[0.1,0.3]), s0(1/7,[0.6,0.7]), s0(0,[1,1])} | {s6(1/7,[0.9,1]), s5(1/7,[0.2,0.5]), s1(2/7,[0.25,0.35]), s0(3/7,[0.43,0.6]), s0(0,[1,1]), s0(0,[1,1])} | {s4(2/7,[0.6,0.8]), s5(1/7,[0.8,1]), s1(1/7,[0.9,1]), s0(3/7,[0.6,0.8]), s0(0,[1,1]), s0(0,[1,1])} | {s2(3/7,[0.6,0.83]), s3(1/7,[0.8,0.9]), s4(1/7,[0.4,0.5]), s5(1/7,[0.2,0.4]), s0(1/7,[0.4,0.6]), s0(0,[1,1])} |
N9 | {s6(1/7,[0.9,1]), s5(1/7,[0.4,0.6), s1(1/7,[0.8,1]), s2(1/7,[0.1,0.2]), s0(3/7,[0.53,0.8]), s0(0,[1,1])} | {s5(1/7,[0.9,1), s6(1/7,[0.3,0.5]), s4(1/7,[0.1,0.4]), s3(1/7,[0.2,0.5]), s0(3/7,[0.43,0.57]), s0(0,[1,1])} | {s3(2/7,[0.35,0.6]), s4(1/7,[0.4,0.6]), s2(1/7,[0.7,1]), s0(3/7,[0.47,0.63]), s0(0,[1,1]), s0(0,[1,1])} | {s4(1/7,[0.2,0.5]), s3(1/7,[0.3,0.5]), s1(1/7,[0.6,0.7]), s2(1/7,[0.1,0.2]), s5(3/7,[0.53,0.63]), s1(0,[1,1])} |
Comparative analysis
Comparison with the classical decision method
Total votes | For | Abstention | Against | |
---|---|---|---|---|
N1 | 28 | 9 | 5 | 14 |
N2 | 28 | 11 | 6 | 11 |
N3 | 28 | 12 | 4 | 12 |
N4 | 28 | 9 | 3 | 16 |
N5 | 28 | 9 | 8 | 11 |
N6 | 28 | 11 | 3 | 14 |
N7 | 28 | 10 | 9 | 9 |
N8 | 28 | 11 | 2 | 15 |
N9 | 28 | 10 | 4 | 14 |
Comparison with the election strategy
Total votes | For | Abstention | Against | Vote result | |
---|---|---|---|---|---|
N1 | 28 | 9 | 5 | 14 | − 5 |
N2 | 28 | 11 | 6 | 11 | 0 |
N3 | 28 | 12 | 4 | 12 | 0 |
N4 | 28 | 9 | 3 | 16 | − 7 |
N5 | 28 | 9 | 8 | 11 | − 2 |
N6 | 28 | 11 | 3 | 14 | − 3 |
N7 | 28 | 10 | 9 | 9 | 1 |
N8 | 28 | 11 | 2 | 15 | − 4 |
N9 | 28 | 10 | 4 | 14 | − 4 |
Comparison with the voting method based on vague set
Total | For | Abstention | Against | Vague value | Fuzzy value | |
---|---|---|---|---|---|---|
N1 | 28 | 9 | 5 | 14 | [0.32,0.5] | 0.4051 |
N2 | 28 | 11 | 6 | 11 | [0.39,0.61] | 0.4971 |
N3 | 28 | 12 | 4 | 12 | [0.43,0.57] | 0.5007 |
N4 | 28 | 9 | 3 | 16 | [0.32,0.43] | 0.3696 |
N5 | 28 | 9 | 8 | 11 | [0.32,0.61] | 0.4597 |
N6 | 28 | 11 | 3 | 14 | [0.39,0.5] | 0.4984 |
N7 | 28 | 10 | 9 | 9 | [0.36,0.68] | 0.5216 |
N8 | 28 | 11 | 2 | 15 | [0.39,0.47] | 0.4253 |
N9 | 28 | 10 | 4 | 14 | [0.36,0.5] | 0.4266 |
Comparison with the extended TOPSIS method
Analysis and experimental discussion
Methods | Rankings of the methods |
---|---|
Classical method [30] | \(N_{3} \succ N_{2} = N_{6} = N_{8} \succ N_{7} = N_{9} \succ N_{1} = N_{4} = N_{5} .\) |
Li et al.’s method [47] | \(N_{7} \succ N_{3} = N_{2} \succ N_{5} \succ N_{6} \succ N_{8} = N_{9} \succ N_{1} \succ N_{4} .\) |
Xu et al.’s method [49] | \(N_{7} \succ N_{3} \succ N_{6} \succ N_{2} \succ N_{5} \succ N_{9} \succ N_{8} \succ N_{1} \succ N_{4} .\) |
Pang et al.’s method [53] | \(N_{6} \succ N_{5} \succ N_{3} \succ N_{7} \succ N_{9} \succ N_{2} \succ N_{8} \succ N_{1} \succ N_{4} .\) |
Our proposed method | \(N_{3} \succ N_{5} \succ N_{6} \succ N_{7} \succ N_{2} \succ N_{8} \succ N_{9} \succ N_{1} \succ N_{4}\) |
Method | Numbers of linguistic terms | Multi attribute | Features of linguistic terms | The behavior of decision-maker |
---|---|---|---|---|
Classical method [30] | Single | No | – | No |
Li et al.’s method [47] | Three | No | Balanced | No |
Xu et al.’s method [49] | Three | No | Balanced | No |
Liu et al.’s method [50] | Four | No | Balanced | Weight setting |
Pang et al.’s method [53] | Seven | Yes | Balanced | No |
Our proposed method | Seven | Yes | Unbalanced | Bounded confidence |
Metrics | Parameter configuration |
---|---|
CPU | Intel(R) Core (TM) i5-1135G7 |
Operating system | Ubuntu 16.04 LTS |
Memory | 8 G |
The Fabric version | v 1.2 |
The Caliper version | v 0.3.0 |