Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators
Abstract
:1. Introduction
2. Preliminaries
2.1. 2TLTs
- (1)
- The set is ordered:, if;
- (2)
- Max operator:, if;
- (3)
- Min operator:, if. For example, S can be defined as
2.2. PFSs
2.3. 2TLPFSs
- (1)
- ,
- (2)
- ,
- (3)
- ,
- (4)
- ,
- (5)
- ,
- (1)
- (2)
- (3)
- (4)
2.4. HM Operator
3. Some 2TLPFHM Operators
3.1. 2TLPFHM Operator
3.2. The 2TLPFWHM Operator
3.3. The 2TLPFDHM Operator
3.4. The 2TLPFDWHM Operator
4. Numerical Example and Comparative Analysis
4.1. Numerical Example
- Step 1. According to 2TLPFNs , we fuse all 2TLPFNs by 2-tuple linguistic Pythagorean fuzzy weighted average (2TLPFWA) operator or 2-tuple linguistic Pythagorean fuzzy weighted geometric (2TLPFWG) operator to get the overall 2TLPFNs of the green suppliers . Then the fused results are listed in Table 4.
4.2. Influence of the Parameter on the Final Result
4.3. Comparative Analysis
- (1)
- The methods developed by Garg [74] aggregate the linguistic Pythagorean fuzzy information easily. The drawbacks of Garg’s methods [74] are they assume that the input arguments are not correlated, that is, they fail to consider the relationships between the input arguments. Nevertheless, our developed operators can capture the correlations among all the input arguments, and fuse the 2TLPFNs more flexibly by the parameter vector. Therefore, our developed approaches are more general and flexible comparing with that proposed by Garg’s methods [74].
- (2)
- Moreover, the methods developed by Garg [74] don’t have the ability that dynamic adjust to the parameter according to the decision maker’s risk attitude, so it is difficult to solve the risk multiple attribute decision making in real practice. Nevertheless, our developed operators have the ability that dynamic adjust to the parameter according to the decision maker’s risk attitude. Thus, our method can overcome the drawbacks of the methods developed by Garg [74], because the 2TLPFWHM and 2TLPFDWHM operators operator can provides more flexible and robust in information fusion and make it more adequate to solve risk multiple attribute decision making in which the attributes are independent.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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G1 | G2 | G3 | G4 | |
---|---|---|---|---|
A1 | <(s4,0), (s2,0)> | <(s3,0), (s2,0)> | <(s2,0), (s1,0)> | <(s1,0), (s4,0)> |
A2 | <(s5,0), (s1,0)> | <(s5,0), (s3,0)> | <(s4,0), (s2,0)> | <(s5,0), (s2,0)> |
A3 | <(s2,0), (s3,0)> | <(s1,0), (s2,0)> | <(s3,0), (s4,0)> | <(s3,0), (s2,0)> |
A4 | <(s5,0), (s3,0)> | <(s3,0), (s5,0)> | <(s2,0), (s3,0)> | <(s3,0), (s1,0)> |
A5 | <(s4,0), (s3,0)> | <(s2,0), (s1,0)> | <(s2,0), (s4,0)> | <(s3,0), (s3,0)> |
G1 | G2 | G3 | G4 | |
---|---|---|---|---|
A1 | <(s3,0), (s3,0)> | <(s2,0), (s3,0)> | <(s3,0), (s3,0)> | <(s2,0), (s3,0)> |
A2 | <(s4,0), (s2,0)> | <(s4,0), (s1,0)> | <(s5,0), (s2,0)> | <(s4,0), (s2,0)> |
A3 | <(s1,0), (s4,0)> | <(s2,0), (s3,0)> | <(s4,0), (s3,0)> | <(s4,0), (s3,0)> |
A4 | <(s4,0), (s4,0)> | <(s2,0), (s4,0)> | <(s1,0), (s2,0)> | <(s2,0), (s2,0)> |
A5 | <(s3,0), (s4,0)> | <(s1,0), (s2,0)> | <(s3,0), (s5,0)> | <(s3,0), (s3,0)> |
G1 | G2 | G3 | G4 | |
---|---|---|---|---|
A1 | <(s3,0), (s4,0)> | <(s4,0), (s2,0)> | <(s2,0), (s4,0)> | <(s3,0), (s4,0)> |
A2 | <(s2,0), (s1,0)> | <(s5,0), (s1,0)> | <(s5,0), (s1,0)> | <(s4,0), (s2,0)> |
A3 | <(s3,0), (s5,0)> | <(s3,0), (s2,0)> | <(s3,0), (s2,0)> | <(s1,0), (s2,0)> |
A4 | <(s2,0), (s3,0)> | <(s3,0), (s2,0)> | <(s4,0), (s3,0)> | <(s3,0), (s4,0)> |
A5 | <(s5,0), (s3,0)> | <(s2,0), (s4,0)> | <(s3,0), (s4,0)> | <(s3,0), (s5,0)> |
A1 | <(s3,0.3093), (s3,−0.0448)> | <(s3,0.0601), (s2,0.4003)> |
A2 | <(s4,0.0210), (s1,0.3660)> | <(s5,−0.3519), (s1,0.3161)> |
A3 | <(s2,0.0830), (s4,−0.0199)> | <(s2,0.2139), (s2,0.4003)> |
A4 | <(s4,0.0210), (s3,0.4146)> | <(s3,−0.3818), (s3,0.4354)> |
A5 | <(s4,0.1069), (s3,0.4146)> | <(s2,−0.3619), (s2,0.0705)> |
A1 | <(s3,−0.4790), (s2,0.4850)> | <(s2,0.2193), (s4,−0.4857)> |
A2 | <(s5,−0.1806), (s2,−0.3755)> | <(s4,0.3332), (s2,0.0000)> |
A3 | <(s4,−0.4771), (s3,−0.1455)> | <(s3,0.2405), (s2,0.4003)> |
A4 | <(s3,−0.3420), (s2,0.4997)> | <(s3,−0.3818), (s2,0.0705)> |
A5 | <(s3,−0.2021), (s4,0.4225)> | <(s3,0.0000), (s3,0.4968)> |
2TLPFWHM | 2TLPFDWHM | |
---|---|---|
A1 | <(s5,−0.0266), (s0,0.3603)> | <(s0,0.3817), (s5,−0.0592)> |
A2 | <(s6,−0.4283), (s0,0.1014)> | <(s1,0.1114), (s4,0.2563)> |
A3 | <(s5,−0.1274), (s0,0.4190)> | <(s0,0.3407), (s5,−0.0111)> |
A4 | <(s5,0.0279), (s0,0.4290)> | <(s0,0.4412), (s5,0.0159)> |
A5 | <(s5,−0.0943), (s1,−0.4558)> | <(s0,0.4109), (s5,0.0961)> |
2TLPFWHM | 2TLPFDWHM | |
---|---|---|
A1 | (s5,0.0504) | (s1,−0.0222) |
A2 | (s6,−0.4139) | (s2,−0.4067) |
A3 | (s5,−0.0361) | (s1,−0.0644) |
A4 | (s5,0.0913) | (s1,−0.0804) |
A5 | (s5,−0.0192) | (s1,−0.1501) |
Order | |
---|---|
2TLPFWHM | A2 > A4 > A1 > A5 > A3 |
2TLPFDWHM | A2 > A1 > A3 > A4 > A5 |
s(A1) | s(A2) | s(A3) | s(A4) | s(A5) | Order | |
---|---|---|---|---|---|---|
(s5,−0.1045) | (s6,−0.4446) | (s5,−0.0918) | (s5,−0.0146) | (s5,−0.0976) | A2 > A4 > A3 > A5 > A1 | |
(s5,−0.1154) | (s6,−0.4589) | (s5,−0.1912) | (s5,−0.0819) | (s5,−0.2093) | A2 > A4 > A1 > A3 > A5 | |
(s5,0.0504) | (s6,−0.4139) | (s5,−0.0361) | (s5,0.0913) | (s5,−0.0192) | A2 > A4 > A1 > A5 > A3 | |
(s5,−0.1208) | (s6,−0.4661) | (s5,−0.2502) | (s5,−0.1206) | (s5,−0.3024) | A2 > A4 > A1 > A3 > A5 |
s(A1) | s(A2) | s(A3) | s(A4) | s(A5) | Order | |
---|---|---|---|---|---|---|
(s1,0.0604) | (s2,−0.0648) | (s1,0.0245) | (s1,0.0913) | (s1,−0.1380) | A2 > A4 > A1 > A3 > A5 | |
(s1,0.1320) | (s2,0.0166) | (s1,0.0754) | (s1,0.1140) | (s1,−0.0187) | A2 > A1 > A4 > A3 > A5 | |
(s1,−0.0222) | (s2,−0.4067) | (s1,−0.0644) | (s1,−0.0804) | (s1,−0.1501) | A2 > A1 > A3 > A4 > A5 | |
(s1,0.1687) | (s2,0.0610) | (s1,0.1079) | (s1,0.1296) | (s1,0.0780) | A2 > A1 > A4 > A3 > A5 |
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Deng, X.; Wang, J.; Wei, G.; Lu, M. Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators. Mathematics 2018, 6, 236. https://doi.org/10.3390/math6110236
Deng X, Wang J, Wei G, Lu M. Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators. Mathematics. 2018; 6(11):236. https://doi.org/10.3390/math6110236
Chicago/Turabian StyleDeng, Xiumei, Jie Wang, Guiwu Wei, and Mao Lu. 2018. "Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators" Mathematics 6, no. 11: 236. https://doi.org/10.3390/math6110236
APA StyleDeng, X., Wang, J., Wei, G., & Lu, M. (2018). Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators. Mathematics, 6(11), 236. https://doi.org/10.3390/math6110236