Introduction
Author and references | Year | Significance influences |
---|---|---|
Li et al. [54] | 2018 | To handle supplier selection situation |
Zhou et al. [55] | 2018 | Pythagorean normal cloud model for handling the economic decisions |
Bolturk [56] | 2018 | Pythagorean fuzzy CODAS were introduced to handle supplier selection process in a manufacturing firm |
Qin [57] | 2018 | To handle multiple attribute SIR group decision model |
Wan et al. [58] | 2018 | To handle the haze management problem |
Lin et al. [59] | 2018 | To analysis of inpatient stroke rehabilitation |
Chen [60] | 2018 | To handle the financial decision |
Ilbahar et al. [61] | 2018 | To handle risk assessment for occupational health and safety |
Karasan et al. [62] | 2018 | To handle landfill site selection problem |
Zeng et al. [63] | 2018 | To evaluate classroom teaching quality |
Ejegwa [64] | 2019 | Application in medical diagnosis |
Author and references | Year | Significance influences |
---|---|---|
Korukoğlu and Ballı [65] | 2011 | Crisp environment |
Kumar [66] | 2018 | Fuzzy environment PSK method |
Chhibber et al. [67] | 2019 | Type 1 and type 2 fuzzy environment |
Celik and Akyuz [68] | 2018 | Interval type 2 fuzzy environment |
Bharati [69] | 2019 | Trapezoidal intuitionistic fuzzy environment |
Bharati and Singh [22] | 2018 | Interval-valued intuitionistic fuzzy environment |
Ahmad and Adhami [70] | 2018 | Neutrosophic fuzzy environment |
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This approach helps to resolve a new set of problem with the Pythagorean fuzzy number.
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We define the TP problem below normal Pythagorean fuzzy surroundings and recommend an efficient solution to locate the corresponding crisp valued.
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Within the literature of Pythagorean fuzzy set, we tend to introduce a scoring approach in conjunction with the proposed method.
Preliminaries
Existing model in the crisp transportation environment
Proposed algorithms for solving three different types of PyF transportation models
Illustrative example
D1 | D2 | D3 | D4 | Supply | |
---|---|---|---|---|---|
O1 | (0.4, 0.7) | (0.5, 0.4) | (0.8, 0.3) | (0.6, 0.3) | 26 |
O2 | (0.4, 0.2) | (0.7, 0.3) | (0.4, 0.8) | (0.7, 0.3) | 24 |
O3 | (0.7, 0.1) | (0.8, 0.1) | (0.6, 0.4) | (0.9, 0.1) | 30 |
Demand | 17 | 23 | 28 | 12 |
D1 | D2 | D3 | D4 | Supply | |
---|---|---|---|---|---|
O1 | 0.335 | 0.545 | 0.775 | 0.635 | 26 |
O2 | 0.56 | 0.7 | 0.26 | 0.7 | 24 |
O3 | 0.74 | 0.815 | 0.6 | 0.9 | 30 |
Demand | 17 | 23 | 28 | 12 |
D1 | D2 | D3 | D4 | Supply | Penalties | ||
---|---|---|---|---|---|---|---|
O1 | 0.335 | 0.545 | 0.775 | 0.635 | 26 | 0.21 | |
O2 | 0.56 | 0.7 | 0.26 | 24 | 0.7 | 24 | 0.3 |
O3 | 0.74 | 0.815 | 0.6 | 0.9 | 30 | 0.14 | |
Demand | 17 | 23 | 4 | 12 | |||
Penalties | 0.225 | 0.155 | 0.34 | 0.065 |
D1 | D2 | D3 | D4 | Supply | Penalties | |||
---|---|---|---|---|---|---|---|---|
O1 | 0.335 | 17 | 0.545 | 0.775 | 0.635 | 9 | 0.21 | |
O2 | 0.560 | 0.700 | 0.26 | 24 | 0.700 | – |
–
| |
O3 | 0.740 | 0.815 | 0.600 | 0.900 | 30 | 0.14 | ||
Demand | 17 | 23 | 4 | 12 | ||||
Penalties | 0.405 | 0.27 | 0.175 | 0.265 |
D1 | D2 | D3 | D4 | Supply | Penalties | ||||
---|---|---|---|---|---|---|---|---|---|
O1 | 0.335 | 17 | 0.545 | 9 | 0.775 | 0.635 | 9 | 0.09 | |
O2 | 0.560 | 0.700 | 0.26 | 24 | 0.700 | – | – | ||
O3 | 0.740 | 0.815 | 0.600 | 0.900 | 30 | 0.215 | |||
Demand | – | 14 | 4 | 12 | |||||
Penalties | – | 0.27 | 0.175 | 0.265 |
D1 | D2 | D3 | D4 | Supply | Penalties | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
O1 | 0.335 | 17 | 0.545 | 9 | 0.775 | 0.635 | – | 0.09 | |||
O2 | 0.560 | 0.700 | 0.26 | 24 | 0.700 | – | – | ||||
O3 | 0.740 | 0.815 | 14 | 0.60 | 4 | 0.900 | 12 | 30 | 0.215 | ||
Demand | – | 14 | 4 | 12 | |||||||
Penalties | – | 0.27 | 0.175 | 0.265 |
D1 | D2 | D3 | D4 | Supply | |||||
---|---|---|---|---|---|---|---|---|---|
O1 | 0.335 | 17 | 0.545 | 9 | 0.775 | 0.635 | 26 | ||
O2 | 0.560 | 0.700 | 0.260 | 24 | 0.700 | 24 | |||
O3 | 0.740 | 0.815 | 14 | 0.600 | 4 | 0.900 | 12 | 30 | |
Demand | 17 | 23 | 28 | 12 |
D1 | D2 | D3 | D4 | Supply | |
---|---|---|---|---|---|
O1 | 0.0335 | 0.0545 | 0.0775 | 0.0635 | (0.7, 0.1) |
O2 | 0.056 | 0.07 | 0.026 | 0.07 | (0.8, 0.1) |
O3 | 0.074 | 0.0815 | 0.06 | 0.09 | (0.9, 0.1) |
Demand | (0.4, 0.7) | (0.7, 0.3) | (0.8, 0.1) | (0.60832, 0.4) |
D1 | D2 | D3 | D4 | Supply | |
---|---|---|---|---|---|
O1 | (0.1, 0.9) | (0.2, 0.8) | (0.1, 0.8) | (0.1, 0.9) | (0.7, 0.1) |
O2 | (0.01, 0.99) | (0.3, 0.9) | (0.3, 0.8) | (0.1, 0.7) | (0.8, 0.1) |
O3 | (0.1, 0.8) | (0.4, 0.8) | (0.4, 0.9) | (0.2, 0.9) | (0.9, 0.1) |
Demand | (0.4, 0.7) | (0.7, 0.3) | (0.8, 0.1) | (0.60832, 0.4) |
Results and discussion
Sr. no. | Example | Logical comparison with initial basic feasible solution and optimal solution |
---|---|---|
1. | Example 5.1 |
\( {\text{Initial}}\;{\text{basic}}\;{\text{feasible}}\;{\text{solution}} \ge {\text{after}}\;{\text{optimality}}\;{\text{test}} \)
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2. | Example 5.2 |
\( {\text{Initial}}\;{\text{basic}}\;{\text{feasible}}\;{\text{solution}} \ge {\text{after}}\;{\text{optimality}}\;{\text{test}} \)
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3. | Example 5.3 |
\( {\text{Initial}}\;{\text{basic}}\;{\text{feasible}}\;{\text{solution}} > {\text{after optimality}}\;{\text{test}} \)
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