Picture Fuzzy ARAS Method for Freight Distribution Concept Selection
Abstract
:1. Introduction
2. Literature Review
2.1. Research Methods for Analyzing the Freight Distribution Concept
2.2. Applications of the ARAS Method
- Uncertainty is the key factor influencing the selection of a freight distribution concept. However, uncertainty analysis is mainly ignored in the available studies.
- The available MCDM methods for outsourcing logistics do not take into account the neutral/refusal information.
- The available system analysis methods for selection of FDC are inadequate in situations when decision-makers’ opinions involve more answers, such as yes, abstain, no, and refusal.
- Advanced methodological approaches for solving outsourcing logistics problems, which can capture a higher degree of uncertainty and take into account numerous conflicting criteria, are missing.
- No previous work has elucidated the criteria for the selection of a freight distribution concept.
- Deterministic numbers or type-1 fuzzy sets have been used in the majority of the previous studies for solving outsourcing logistics problems.
- A picture fuzzy set based MCDM approach for solving transportation problems has not been applied in previous research.
- The ARAS method has not been extended before using picture fuzzy sets.
3. Methodology
3.1. Picture Fuzzy Sets
3.2. Picture Fuzzy ARAS Method
4. Case Study
- Vehicle procurement cost (C11). This emerges when the company procures its transport fleet. The cost can be considered as a relatively high burden, especially for start-ups.
- Vehicle maintenance cost (C12). This cost is expressed in terms of parts consumption and maintenance. It is the amount spent for servicing during transport fleets’ life cycle.
- Time to achieve the equilibrium point of investment (C13). The period after which the invested funds start to bring benefits to the company.
- Financial performance (C14). Indication of the company’s endurance. Sound financial performance ensures the stability of services.
- Human capital cost (C15). This cost is related to employees, such as costs for drivers, dispatchers, training, etc. The core aim of outsourcing logistics is to decrease this cost.
- Workspace cost (C16). This includes the costs of garages, parking places, warehouses, and other auxiliary facilities.
- Number of kilometers driven (C17). If the company expects that its distribution system would require a relatively high number of kilometers to cover, then it should invest in its own fleet of vehicles.
- Air pollution (C21). This represents the percentage of air pollution by a certain transport fleet. Emissions could vary in proportion to the alternative that is selected.
- Noise pollution (C22). This has a negative impact on both natural ecosystems and urban populations. It causes discomfort, complaints, sleep disorders, etc.
- Effect on public health (C23). This represents the occurrence of injuries, threats to health and life, fires, explosions, and other hazards. It is important to apply technical/technological and organizational solutions that minimize the effect on public health.
- Energy consumption (C24). The pollution from energy consumption is not only restricted to carbon emissions; other types of air pollution, from smog to acid rain, have harmful effects.
- Vehicle utilization (C25). This is determined mainly by delivery requirements and exploitation of the backhauling and transport fleet management. If each company were to have its own transport fleet, it could result in poor vehicle utilization.
- Social reputation (C31). This is based on the social appraisal in terms of prestige in society. Adhering to ethical business practices such as supplying quality products on time and acting according to what is agreed secures a high social reputation.
- Brand building (C32). Successful brand building is essential to introduce new products and services. It can be considered as a catalyst for the development of a modern company.
- Enterprise culture construction (C33). This improves competitiveness by providing a guarantee, feedback, and long-term effect mechanisms.
- Job opportunities (C34). This is the number and quality of jobs created.
- Local community influence (C35). This encompasses service infrastructure, public services, community projects, etc.
- Quality of service (C41). This is the most important factor in obtaining customer loyalty. It is measured by the standard of customer service satisfaction.
- Flexibility (C42). This is the ability to react faster to turbulences in the market.
- Workforce availability (C43). The total number of workers can also influence a decision about purchasing a fleet of vehicles.
- Land availability (C44). The availability of enough land is a vital infrastructure prerequisite.
- Vehicle reliability index (C45). This is the number of reliable vehicles in relation to the total fleet of vehicles.
- Parking space utilization index (C46). This is the ratio of the required number of vehicles to the number of available parking spaces.
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Authors (Publication Year) | Research Focus | Methods |
---|---|---|
Bajec and Jakomin [21] | Make-or-buy decision process for outsourcing | Theoretical study—technological consideration |
Pirannejad et al. [22] | Defining outsourcing priorities of public organizations | ANP method |
Liou and Chuang [23] | Outsourcing provider selection problem | DEMATEL, ANP, VIKOR |
Cheng and Lee [24] | Outsourcing reverse logistics of high-technology manufacturers | ANP method |
Aktas et al. [25] | Motives for outsourcing logistics activities | Statistical analysis |
Solakivi et al. [26] | Motives for outsourcing logistics activities | Statistical analysis |
Hsu et al. [27] | Outsourcing provider selection problem | DEMATEL, ANP, and GRT |
Rezaeisaray et al. [28] | Outsourcing provider selection problem | DEMATEL, FANP, and DEA |
Chen et al. [29] | Evaluation and selection of the best outsourcing service country in East and Southeast Asia | AHP |
Kahraman et al. [30] | Evaluation of outsource manufacturers | Fuzzy-AHP and TOPSIS |
Arif and Jawab [31] | The impact of the outsourcing strategy on logistics performance | Theoretical study—technological consideration |
Pedregosa et al. [32] | Determinants of success in transport services outsourcing | Partial least squares simultaneous equation models (PLS-SEM) |
Hwang and Kim [33] | Effects of in-house and outsourced logistics services | Statistical analysis |
Wan et al. [34] | Drivers of outsourcing decisions | Fuzzy-set qualitative comparative analysis (fsQCA) |
Bucovetchi et al. [35] | Key performance indicators—in-house or outsourcing | Statistical analysis |
Zarbakhshnia et al. [36] | Outsourcing sustainable reverse logistics providers | Fuzzy-AHP and MOORA-G |
Kiani et al. [37] | Prioritizing outsourceable activities in universities | Fuzzy MCDM (Fuzzy-AHP, Fuzzy-SAW, Fuzzy-TOPSIS, Fuzzy-VIKOR) |
Vazifehdan & Darestani [38] | Evaluation of the drivers of outsourcing for green logistics | Fuzzy-ANP, QFD, and SIR |
Sayed et al. [39] | Comparing in-house and outsourcing implementation | Statistical analysis |
Mokrini and Aouam [40] | Risk evaluation in healthcare logistics outsourcing | Fuzzy-AHP, Fuzzy-TOPSIS, Fuzzy-PROMETHEE |
Tavana et al. [41] | Outsourcing reverse logistics activities | Fuzzy-AHP and SWOT |
Wu et al. [42] | Supplier selection in nuclear power industry | Extended VIKOR method |
Our study | Freight distribution concept selection—in-house or outsourcing | Picture fuzzy ARAS method |
Author(s) | Research Focus | Application Type | Multi-Criteria Group Decision-Making | Parameter Type | |
---|---|---|---|---|---|
Criterion | Alternative | ||||
Tupenaite et al. [43] | Human environment renovation | Real-life | No | Deterministic | |
Turskis and Zavadskas [44] | Logistics center location | Illustrative example | Yes | Deterministic | Fuzzy |
Turskis and Zavadskas [45] | Supplier selection | Illustrative example | No | Interval | |
Zavadskas and Turskis [10] | Microclimate in offices | Illustrative example | Yes | Deterministic | |
Zavadskas et al. [11] | Foundation installment | Illustrative example | No | Deterministic | |
Keršulienė and Turskis [46] | Personnel selection | Illustrative example | Yes | Deterministic | Fuzzy |
Baležentis et al. [47] | Economic sector comparison | Real-life | No | Fuzzy | |
Dadelo et al. [48] | Personnel selection | Illustrative example | Yes | Deterministic | |
Zavadskas et al. [49] | Construction technology | Real-life | Yes | Deterministic | |
Zavadskas et al. [50] | Personnel selection | Illustrative example | Yes | Deterministic | |
Turskis et al. [51] | Built heritage | Real-life | Yes | Deterministic | Interval |
Keršulienė and Turskis [52] | Personnel selection | Illustrative example | Yes | Deterministic | Fuzzy |
Kutut et al. [53] | Historic building preservation | Real-life | Yes | Deterministic | |
Zamani et al. [54] | Brand extension strategy selection | Real-life | Yes | Deterministic | Fuzzy |
Medineckiene et al. [55] | Sustainable building certification | Illustrative example | No | Deterministic | |
Stanujkic [56] | Website evaluation | Illustrative example | Yes | Fuzzy | Interval fuzzy |
Zavadskas et al. [57] | Seaport location | Real-life | Yes | Deterministic | Fuzzy |
Liao et al. [58] | Green supplier selection | Illustrative example | Yes | Deterministic | Fuzzy |
Nguyen et al. [59] | Conveyor selection | Illustrative example | Yes | Fuzzy | |
Štreimikienė et al. [60] | Electricity generation technology | Real-life | Yes | Deterministic | |
Rostamzadeh et al. [12] | Supply chain performance measurement | Illustrative example | Yes | Fuzzy | |
Büyüközkan and Göçer [61] | Digital supply chain supplier selection | Real-life | Yes | Interval intuitionistic fuzzy | |
Dahooie et al. [62] | Personnel selection | Illustrative example | Yes | Deterministic | Interval |
Dahooie et al. [63] | Oil and gas well drilling | Real-life | Yes | Deterministic | Interval fuzzy |
Radović et al. [64] | Transportation company | Real-life | Yes | Deterministic | Rough interval |
Bahrami et al. [65] | Mineral potential mapping | Real-life | Yes | Deterministic | |
Dahooie et al. [66] | Financial performances | Real-life | No | Deterministic | Fuzzy |
Iordache et al. [67] | Hydrogen storage site selection | Real-life | Yes | Interval type-2 hesitant fuzzy | |
Fu [68] | Catering supplier selection | Real-life | Yes | Deterministic | |
Naicker and Thopil [69] | Renewable energy systems | Real-life | Yes | Deterministic | |
Pehlivan and Gürsoy [70] | Life satisfaction | Real-life | Yes | Fuzzy | |
Turskis et al. [71] | Structural solutions for buildings | Real-life | Yes | Deterministic | Fuzzy |
Ghenai et al. [14] | Renewable energy systems | Illustrative example | Yes | Deterministic | |
Our study | Freight distribution concept selection | Real-life | Yes | Picture fuzzy |
Criterion | Expert | ||||
---|---|---|---|---|---|
D1 | D2 | D3 | D4 | D5 | |
C1 | Yes | Abstain | Yes | Yes | Yes |
C2 | Yes | Yes | Abstain | No | Abstain |
C3 | No | No | No | Abstain | Abstain |
C4 | Abstain | Abstain | Abstain | Abstain | No |
Criterion | Degree of Positive Membership | Degree Of Neutral Membership | Degree of Negative Membership | Weight |
---|---|---|---|---|
C1 | 0.8 | 0.2 | 0 | 0.4286 |
C2 | 0.4 | 0.4 | 0.2 | 0.2857 |
C3 | 0 | 0.4 | 0.6 | 0.0952 |
C4 | 0 | 0.8 | 0.2 | 0.1905 |
Criterion | Sub-Criterion | Expert | ||||
---|---|---|---|---|---|---|
D1 | D2 | D3 | D4 | D5 | ||
C1 | C11 | Yes | Yes | Yes | Abstain | Yes |
C12 | Abstain | Abstain | No | Refusal | Yes | |
C13 | Abstain | Refusal | Abstain | Yes | Refusal | |
C14 | Yes | Yes | Yes | Yes | Abstain | |
C15 | Abstain | No | Abstain | Refusal | No | |
C16 | Abstain | Abstain | Refusal | Abstain | No | |
C17 | Yes | Yes | Abstain | Abstain | Refusal | |
C2 | C21 | Yes | Abstain | No | Yes | Yes |
C22 | No | Refusal | Abstain | Abstain | No | |
C23 | Abstain | No | Refusal | Abstain | Refusal | |
C24 | Abstain | Abstain | Abstain | Refusal | No | |
C25 | Yes | Yes | Yes | Yes | Yes | |
C3 | C31 | Refusal | Abstain | Yes | Abstain | Yes |
C32 | Abstain | Yes | Abstain | Abstain | Refusal | |
C33 | Abstain | Abstain | Abstain | Refusal | No | |
C34 | Yes | Abstain | No | Yes | Yes | |
C35 | Refusal | No | Refusal | Abstain | Yes | |
C4 | C41 | Yes | Yes | Yes | Yes | Yes |
C42 | Yes | Yes | Yes | Abstain | Yes | |
C43 | Abstain | Abstain | Refusal | No | Yes | |
C44 | Refusal | No | Refusal | No | Abstain | |
C45 | Abstain | Yes | No | Abstain | No | |
C46 | Abstain | Refusal | No | Refusal | No |
Criterion | Sub-Criterion | Degree of Positive Membership | Degree of Neutral Membership | Degree of Negative Membership | Weight |
---|---|---|---|---|---|
C1 | C11 | 0.8 | 0.2 | 0 | 0.2083 |
C12 | 0.2 | 0.4 | 0.2 | 0.1157 | |
C13 | 0.2 | 0.4 | 0 | 0.1481 | |
C14 | 0.8 | 0.2 | 0 | 0.2083 | |
C15 | 0 | 0.4 | 0.4 | 0.0602 | |
C16 | 0 | 0.6 | 0.2 | 0.0880 | |
C17 | 0.4 | 0.4 | 0 | 0.1713 | |
C2 | C21 | 0.6 | 0.2 | 0.2 | 0.2593 |
C22 | 0 | 0.4 | 0.4 | 0.0963 | |
C23 | 0 | 0.4 | 0.2 | 0.1333 | |
C24 | 0 | 0.6 | 0.2 | 0.1407 | |
C25 | 1 | 0 | 0 | 0.3704 | |
C3 | C31 | 0.4 | 0.4 | 0 | 0.2517 |
C32 | 0.2 | 0.6 | 0 | 0.2109 | |
C33 | 0 | 0.6 | 0.2 | 0.1293 | |
C34 | 0.6 | 0.2 | 0.2 | 0.2381 | |
C35 | 0.2 | 0.2 | 0.2 | 0.1701 | |
C4 | C41 | 1 | 0 | 0 | 0.3086 |
C42 | 0.8 | 0.2 | 0 | 0.2778 | |
C43 | 0.2 | 0.4 | 0.2 | 0.1543 | |
C44 | 0 | 0.2 | 0.4 | 0.0679 | |
C45 | 0.2 | 0.4 | 0.4 | 0.1235 | |
C46 | 0 | 0.2 | 0.4 | 0.0679 |
Alternative | Expert | Sub-Criterion | ||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C11 | C12 | C13 | C14 | C15 | C16 | C17 | C21 | C22 | C23 | C24 | C25 | C31 | C32 | C33 | C34 | C35 | C41 | C42 | C43 | C44 | C45 | C46 | ||
A1 | D1 | Y | Y | A | Y | A | N | Y | N | N | A | N | N | A | Y | A | Y | Y | Y | A | Y | N | A | A |
D2 | Y | A | Y | R | Y | A | A | R | N | A | N | N | Y | Y | A | A | N | A | Y | Y | N | Y | A | |
D3 | A | Y | Y | N | A | N | A | A | Y | Y | A | A | A | R | N | Y | A | Y | Y | A | N | N | Y | |
D4 | Y | Y | Y | A | A | N | R | Y | A | R | N | N | Y | A | Y | Y | Y | Y | A | R | A | A | N | |
D5 | Y | Y | Y | A | Y | A | Y | A | R | A | N | N | A | A | Y | Y | A | Y | Y | Y | N | A | A | |
A2 | D1 | N | N | A | A | N | N | R | A | N | A | Y | Y | A | Y | Y | A | A | A | A | A | A | N | A |
D2 | A | N | A | A | N | A | N | R | Y | N | A | A | Y | N | Y | A | N | A | Y | A | Y | A | R | |
D3 | N | A | N | A | N | N | A | N | R | A | Y | Y | A | N | A | N | R | Y | Y | N | A | Y | A | |
D4 | N | N | N | A | A | A | N | A | A | R | Y | Y | R | A | Y | Y | A | Y | N | A | N | A | A | |
D5 | N | N | N | Y | A | A | N | N | A | R | Y | Y | A | Y | N | Y | Y | N | Y | R | A | A | A | |
A3 | D1 | Y | A | Y | Y | Y | A | A | N | N | N | Y | A | N | N | A | N | N | Y | A | A | A | Y | A |
D2 | A | R | N | N | A | R | Y | A | Y | A | Y | Y | A | N | A | R | N | A | Y | A | Y | A | N | |
D3 | A | A | A | N | N | A | A | N | A | R | Y | Y | N | N | N | A | R | Y | Y | N | N | A | A | |
D4 | N | A | Y | Y | A | N | Y | R | A | A | A | N | N | R | Y | N | A | Y | A | A | A | Y | A | |
D5 | A | Y | Y | A | Y | Y | Y | A | A | Y | A | A | N | A | R | N | N | A | Y | N | A | A | A |
Criterion | Sub-Criterion | Alternative | ||
---|---|---|---|---|
A1 | A2 | A3 | ||
C1 | C11 | <0.8, 0.2, 0> | <0, 0.2, 0.8> | <0.2, 0.6, 0.2> |
C12 | <0.8, 0.2, 0> | <0, 0.2, 0.8> | <0.2, 0.6, 0> | |
C13 | <0.8, 0.2, 0> | <0, 0.4, 0.6> | <0.6, 0.2, 0.2> | |
C14 | <0.2, 0.4, 0.2> | <0.2, 0.8, 0> | <0.4, 0.2, 0.4> | |
C15 | <0.4, 0.6, 0> | <0, 0.4, 0.6> | <0.4, 0.4, 0.2> | |
C16 | <0, 0.4, 0.6> | <0, 0.6, 0.4> | <0.2, 0.4, 0.2> | |
C17 | <0.4, 0.4, 0> | <0, 0.2, 0.6> | <0.6, 0.4, 0> | |
C2 | C21 | <0.2, 0.4, 0.2> | <0, 0.4, 0.4> | <0, 0.4, 0.4> |
C22 | <0.2, 0.2, 0.4> | <0.2, 0.4, 0.2> | <0.2, 0.6, 0.2> | |
C23 | <0.2, 0.6, 0> | <0, 0.4, 0.2> | <0.2, 0.4, 0.2> | |
C24 | <0, 0.2, 0.8> | <0.8, 0.2, 0> | <0.6, 0.4, 0> | |
C25 | <0, 0.2, 0.8> | <0.8, 0.2, 0> | <0.4, 0.4, 0.2> | |
C3 | C31 | <0.4, 0.6, 0> | <0.2, 0.6, 0> | <0, 0.2, 0.8> |
C32 | <0.4, 0.4, 0> | <0.4, 0.2, 0.4> | <0, 0.2, 0.6> | |
C33 | <0.4, 0.4, 0.2> | <0.6, 0.2, 0.2> | <0.2, 0.4, 0.2> | |
C34 | <0.8, 0.2, 0> | <0.4, 0.4, 0.2> | <0, 0.2, 0.6> | |
C35 | <0.4, 0.4, 0.2> | <0.2, 0.4, 0.2> | <0, 0.2, 0.6> | |
C4 | C41 | <0.8, 0.2, 0> | <0.4, 0.4, 0.2> | <0.6, 0.4, 0> |
C42 | <0.6, 0.4, 0> | <0.6, 0.2, 0.2> | <0.6, 0.4, 0> | |
C43 | <0.6, 0.2, 0> | <0, 0.6, 0.2> | <0, 0.6, 0.4> | |
C44 | <0, 0.2, 0.8> | <0.2, 0.6, 0.2> | <0.2, 0.6, 0.2> | |
C45 | <0.2, 0.6, 0.2> | <0.2, 0.6, 0.2> | <0.4, 0.6, 0> | |
C46 | <0.2, 0.6, 0.2> | <0, 0.8, 0> | <0, 0.8, 0.2> |
Criterion | Sub-Criterion | Alternative | ||
---|---|---|---|---|
A1 | A2 | A3 | ||
C1 | C11 | <0, 0.2, 0.8> | <0.8, 0.2, 0> | <0.2, 0.6, 0.2> |
C12 | <0, 0.2, 0.8> | <0.8, 0.2, 0> | <0, 0.6, 0.2> | |
C13 | <0, 0.2, 0.8> | <0.6, 0.4, 0> | <0.2, 0.2, 0.6> | |
C14 | <0.2, 0.4, 0.2> | <0.2, 0.8, 0> | <0.4, 0.2, 0.4> | |
C15 | <0, 0.6, 0.4> | <0.6, 0.4, 0> | <0.2, 0.4, 0.4> | |
C16 | <0.6, 0.4, 0> | <0.4, 0.6, 0> | <0.2, 0.4, 0.2> | |
C17 | <0.4, 0.4, 0> | <0, 0.2, 0.6> | <0.6, 0.4, 0> | |
C2 | C21 | <0.2, 0.4, 0.2> | <0.4, 0.4, 0> | <0.4, 0.4, 0> |
C22 | <0.4, 0.2, 0.2> | <0.2, 0.4, 0.2> | <0.2, 0.6, 0.2> | |
C23 | <0, 0.6, 0.2> | <0.2, 0.4, 0> | <0.2, 0.4, 0.2> | |
C24 | <0.8, 0.2, 0> | <0, 0.2, 0.8> | <0, 0.4, 0.6> | |
C25 | <0, 0.2, 0.8> | <0.8, 0.2, 0> | <0.4, 0.4, 0.2> | |
C3 | C31 | <0.4, 0.6, 0> | <0.2, 0.6, 0> | <0, 0.2, 0.8> |
C32 | <0.4, 0.4, 0> | <0.4, 0.2, 0.4> | <0, 0.2, 0.6> | |
C33 | <0.4, 0.4, 0.2> | <0.6, 0.2, 0.2> | <0.2, 0.4, 0.2> | |
C34 | <0.8, 0.2, 0> | <0.4, 0.4, 0.2> | <0, 0.2, 0.6> | |
C35 | <0.4, 0.4, 0.2> | <0.2, 0.4, 0.2> | <0, 0.2, 0.6> | |
C4 | C41 | <0.8, 0.2, 0> | <0.4, 0.4, 0.2> | <0.6, 0.4, 0> |
C42 | <0.6, 0.4, 0> | <0.6, 0.2, 0.2> | <0.6, 0.4, 0> | |
C43 | <0.6, 0.2, 0> | <0, 0.6, 0.2> | <0, 0.6, 0.4> | |
C44 | <0, 0.2, 0.8> | <0.2, 0.6, 0.2> | <0.2, 0.6, 0.2> | |
C45 | <0.2, 0.6, 0.2> | <0.2, 0.6, 0.2> | <0.4, 0.6, 0> | |
C46 | <0.2, 0.6, 0.2> | <0, 0.8, 0> | <0, 0.8, 0.2> |
Alternative | Criterion | |||
---|---|---|---|---|
C1 | C2 | C3 | C4 | |
A1 | <0.097, 0.296, 0.567> | <0.152, 0.277, 0.506> | <0.517, 0.376, 0.065> | <0.531, 0.299, 0.14> |
A2 | <0.419, 0.340, 0.145> | <0.389, 0.281, 0.220> | <0.367, 0.350, 0.204> | <0.367, 0.398, 0.188> |
A3 | <0.298, 0.356, 0.306> | <0.282, 0.416, 0.23> | <0.012, 0.219, 0.633> | <0.414, 0.482, 0.103> |
Alternative | Criterion | |||
---|---|---|---|---|
C1 | C2 | C3 | C4 | |
A1 | <0.043, 0.593, 0.345> | <0.046, 0.693, 0.240> | <0.067, 0.911, 0.014> | <0.134, 0.795, 0.06> |
A2 | <0.208, 0.630, 0.104> | <0.131, 0.696, 0.125> | <0.043, 0.905, 0.040> | <0.083, 0.839, 0.064> |
A3 | <0.141, 0.642, 0.196> | <0.090, 0.778, 0.105> | <0.001, 0.865, 0.119> | <0.097, 0.870, 0.033> |
Alternative | Optimality Function | Utility Degree | Rank | |
---|---|---|---|---|
Picture Fuzzy Value | Crisp Value | |||
A0 | <0.444, 0.283, 0.112> | 0.685 | − | − |
A1 | <0.262, 0.298, 0.395> | 0.431 | 0.629 | 3 |
A2 | <0.396, 0.333, 0.18> | 0.617 | 0.901 | 1 |
A3 | <0.295, 0.376, 0.28> | 0.507 | 0.740 | 2 |
Method | Alternative | |||
---|---|---|---|---|
A1 | A2 | A3 | ||
Picture Fuzzy ARAS (our study) | Score | 0.629 | 0.901 | 0.740 |
Rank | 3 | 1 | 2 | |
Picture fuzzy TOPSIS (Torun and Gördebil [76]) | Score | 0.296 | 0.775 | 0.548 |
Rank | 3 | 1 | 2 | |
Picture fuzzy EDAS (Liang et al. [69]; Zhang et al. [77]) | Score | 0.160 | 1.0 | 0.570 |
Rank | 3 | 1 | 2 | |
Picture fuzzy TODIM (Wei [78]; Wang et al. [79]) | Score | 0.616 | 1.0 | 0.0 |
Rank | 2 | 1 | 3 | |
Picture fuzzy VIKOR (Wang et al. [80]) | Score | 1.0 | 0.015 | 0.064 |
Rank | 3 | 1 | 2 | |
Picture fuzzy MABAC (Wang et al. [81]) | Score | -0.928 | 0.344 | 0.013 |
Rank | 3 | 1 | 2 | |
Picture fuzzy cross-entropy (Wei [82]) | Score | 0.1 | 0.009 | 0.061 |
Rank | 3 | 1 | 2 | |
Picture fuzzy projection (Wei et al. [83]) | Score | 0.250 | 0.306 | 0.287 |
Rank | 3 | 1 | 2 | |
Picture fuzzy grey relational projection (Ju et al. [84]) | Score | 0.30 | 0.660 | 0.541 |
Rank | 3 | 1 | 2 | |
Picture fuzzy grey relational analysis (Liu et al. [9]) | Score | 0.580 | 0.855 | 0.613 |
Rank | 3 | 1 | 2 |
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Jovčić, S.; Simić, V.; Průša, P.; Dobrodolac, M. Picture Fuzzy ARAS Method for Freight Distribution Concept Selection. Symmetry 2020, 12, 1062. https://doi.org/10.3390/sym12071062
Jovčić S, Simić V, Průša P, Dobrodolac M. Picture Fuzzy ARAS Method for Freight Distribution Concept Selection. Symmetry. 2020; 12(7):1062. https://doi.org/10.3390/sym12071062
Chicago/Turabian StyleJovčić, Stefan, Vladimir Simić, Petr Průša, and Momčilo Dobrodolac. 2020. "Picture Fuzzy ARAS Method for Freight Distribution Concept Selection" Symmetry 12, no. 7: 1062. https://doi.org/10.3390/sym12071062
APA StyleJovčić, S., Simić, V., Průša, P., & Dobrodolac, M. (2020). Picture Fuzzy ARAS Method for Freight Distribution Concept Selection. Symmetry, 12(7), 1062. https://doi.org/10.3390/sym12071062