# Agricultural Tractor Selection: A Hybrid and Multi-Attribute Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### Problem Research and Objectives

## 2. Materials and Methods

#### 2.1. Tractor Characterization

#### 2.2. Questionnaire Application and Validation

^{®}(IBM, New York, NY, USA)and MS Office Excel

^{®}(Washington, DC, USA) for a descriptive analysis. In addition, tests were performed to detect missing values, and since the data contained in the surveys was on an ordinal scale (Likert scale), missing values were replaced by the median [34]. In addition, tests were performed to identify extreme values or “outliers” by standardizing the data and only considering a value extreme if the standardized absolute value was greater than four [34,35].

#### 2.3. Descriptive Analysis

#### 2.4. The Proposed Model

#### 2.4.1. Analytic Hierarchy Process

_{ij}in matrix

**A**of paired comparisons, as shown in (1). The reciprocal values of these comparisons are placed in the position a

_{ji}in

**A**, in order to preserve the consistency of the judgment.

Value | Definition |
---|---|

1 | Equal importance |

2 | Weak |

3 | Moderate importance |

4 | Moderate plus |

5 | Strong importance |

6 | Strong plus |

7 | Very strong |

8 | Very strong plus |

9 | Extreme importance |

Reciprocals of above | If attribute i has one of the above non-zero numbers assigned to it when compared to attribute j, then j has the reciprocal value when compared to i |

**A**= reciprocal pairwise comparisons matrix;- $w$ = eigenvector for the maximum eigenvalue in
**A**; - ${\lambda}_{\mathrm{max}}$ = maximum eigenvalue in
**A**.

_{max}is the maximum eigenvalue for the pairwise comparison matrix and n is the number of attributes evaluated.

Matrix Size | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|

AI | 0.58 | 0.9 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |

#### 2.4.2. Matrix Approach in Multi-Attribute Assessment

**A**,

^{1}**A**, …,

^{2}**A**. However, in multi-attribute assessment, two different kinds of attribute are integrated: qualitative (subjective) and quantitative (objective), which are defined as follows:

^{k}#### Objective and Subjective Attribute Determination

**X**,

_{1}**X**, ...,

_{2}**X**and the L subjective attributes by

_{J}**X**,

_{J+1}**X**, ...,

_{J+2}**X**[14]. The method to determine these attributes is explained in the following paragraphs.

_{J+L}#### Objective Attribute Values Matrix

**OV**). Equation (6) displays that matrix.

#### Subjective Attribute Values Matrix

**SV**) as indicated in Equation (7), and finally, there must be P matrixes, one for each farmer.

**SV**P matrices provided by farmers were added term by term to generate a total subjective values matrix, in which each one of its elements is divided by the value of P (number of farmers), to obtain an arithmetic mean value that represents the groups’ judgment; however, we assume that the P experts are rational in their judgment. Thus, the total subjective values matrix, which we will call

^{p}**TSV**, is determined by Equation (8).

**k**= 1,...K,

**l**= 1,...L is the mean score of P experts for the A

^{k}alternative with respect to the X

_{j+i}attribute.

#### Final Decision Matrix

**FDM**) is constructed by combining matrices

**OV**and

**TSV**, as shown in Equation (9). Every line or row in

**FDM**represents a tractor, and every column represents an attribute to be evaluated.

#### 2.4.3. TOPSIS Technique and Its Methodology

**A**is considered a vector in a Euclidian space, as shown in Equation (10).

^{k}- (1)
- As some attributes are usually expressed in different scales or measurement units ($, dollars for cost; m/s, meter by seconds for speed; kg, for load capacity; etc.), the first task in TOPSIS is to normalize each attribute
**X**vector and convert them to_{n}**TX**following Equation (14). Thus, the values will be dimensionless._{n}$$T{X}_{n}=\frac{{X}_{n}}{\Vert {X}_{n}\Vert}=\left(\frac{{x}_{n}^{1}}{\Vert {X}_{n}\Vert},\mathrm{......}\frac{{x}_{n}^{k}}{\Vert {X}_{n}\Vert}\right)$$

- (2)
- According to Equations (19) and (20), calculate the existing weighted Euclidian distances between the points represented by each alternative and those represented by the ideal and anti-ideal alternatives.$$\rho ({A}^{k},{A}^{+})=\Vert w\times (T{A}^{k}-T{A}^{+})\Vert $$$$\rho ({A}^{k},{A}^{-})=\Vert w\times (T{A}^{k}-T{A}^{-})\Vert $$Here,
**w**represents the attributes’ weight obtained using AHP by the geometric mean method. - (3)
- Sort the alternatives according to their distance from the ideal and anti-ideal solutions, as given by Equation (21).$$RC({A}^{+},{A}^{i})=\frac{\rho ({A}^{k},{A}^{+})}{\rho ({A}^{k},{A}^{+})+\rho ({A}^{k},{A}^{-})}$$

^{k}, A

^{+}).

## 3. Results

#### 3.1. Sample Description

Crops | Land Availability for Main Crop | |||||
---|---|---|---|---|---|---|

<1 Ha | 1 to 5 Ha | 5 to 20 Ha | 20 to 50 Ha | >50 Ha | Total | |

Corn | 0 | 10 | 65 | 28 | 5 | 108 (25.96%) |

Banana | 0 | 19 | 39 | 29 | 5 | 92 (22.12%) |

Lemon | 1 | 21 | 43 | 11 | 2 | 78 (18.75%) |

Alfalfa | 8 | 12 | 19 | 11 | 0 | 50 (12.02%) |

Flowers | 12 | 15 | 1 | 0 | 0 | 28 (6.73%) |

Coconut | 0 | 2 | 5 | 9 | 1 | 17 (4.09%) |

Sugarcane | 2 | 4 | 8 | 1 | 0 | 15 (3.61%) |

Sorghum | 0 | 2 | 3 | 4 | 2 | 11 (2.64%) |

Wheat | 0 | 3 | 5 | 0 | 2 | 10 (2.40%) |

Oat | 2 | 1 | 2 | 1 | 1 | 7 (1.68%) |

Total | 25 (6.1%) | 89 (21.39%) | 190 (45.67%) | 94 (22.59%) | 18 (4.33%) | 416 (100%) |

#### 3.2. Descriptive Analysis of Attributes

Attribute Description | Median | 25th Percentile | 75th Percentile | IR |
---|---|---|---|---|

Initial cost | 8.47 | 8.40 | 8.70 | 0.30 |

Cost of energy consumption | 8.41 | 8.15 | 8.88 | 0.73 |

Annual maintenance cost | 8.35 | 7.90 | 8.55 | 0.65 |

Number of tools to adapt (adapted) | 8.25 | 7.78 | 8.37 | 0.59 |

Availability of spare parts | 8.23 | 5.89 | 6.35 | 0.46 |

Availability of customer service | 8.22 | 8.00 | 8.71 | 0.71 |

Flexibility of attachments | 8.21 | 8.03 | 8.53 | 0.50 |

Engine power | 8.16 | 7.69 | 8.47 | 0.78 ^{‡} |

Maintainability | 8.12 | 7.67 | 8.42 | 0.75 |

Quality customer service | 8.03 | 7.83 | 8.08 | 0.26 ^{*} |

Variety of attachments available | 7.96 | 7.91 | 8.02 | 0.10 ^{*} |

Expandability | 7.95 | 7.88 | 8.40 | 0.52 |

Cost of parts | 7.84 | 7.45 | 8.02 | 0.57 |

Safety maneuver | 7.16 | 6.85 | 7.63 | 0.77 ^{‡} |

Brand name | 7.09 | 6.81 | 7.42 | 0.61 |

Comfort to maneuver | 7.06 | 6.63 | 7.28 | 0.65 |

Safety when performing maintenance | 6.33 | 5.89 | 6.81 | 0.91 ^{‡} |

Tractor model | 6.17 | 6.05 | 6.25 | 0.21 ^{*} |

^{‡}high values in IR.

#### 3.3. A Numerical Example

- Initial cost of the tractor (IC, $), representing the amount of money, expressed in Mexican pesos, that the rural cooperative must pay if they get the tractor in a single instalment. The minimum value of this attribute is desirable.
- Rated power (RP, HP), representing engine power. This attribute is expressed in horsepower (HP), and the maximum value is desirable.
- Number of cylinders (NC), representing the number of cylinders in the engine. This value is expressed with a crisp value, and minimum values are desirables, because they are associated with diesel consumption.
- Displacement (DI, cm
^{3}) is the volume swept by all of the pistons inside the cylinders of an internal combustion engine in a single movement from top dead center (TDC) to bottom dead center (BDC). This value is expressed in cubic centimeters, and minimum values are desirable. - Safety of the operator when maneuvering the tractor (SO), representing a subjective value that indicates the decision maker’s assessment regarding the operator’s safety. Maximum values are desirable.
- After-sale customer service from suppliers (CS), representing a subjective value that indicates the decision maker’s assessment regarding services they feel they will obtain from suppliers following the purchase of the tractor. In this attribute, maximum values are desirable.

#### 3.3.1. Weighting the Attributes: AHP Stage

A^{k} | Attributes | |||||
---|---|---|---|---|---|---|

IC | RP | NC | DI | SO | CS | |

A^{1} | ^{*} 748,223 | 80 | ^{‡} 4 | 4530 | ^{‡} 8.8 | ^{‡} 8.6 |

A^{2} | 520,730 | ^{*} 75 | ^{‡} 4 | 4500 | 7.3 | 7.3 |

A^{3} | ^{‡} 425,232.50 | 80 | ^{‡} 4 | 4070 | ^{*} 6.2 | ^{*} 5.3 |

A^{4} | 649,477.50 | 100 | ^{*} 6 | ^{*} 6000 | 7.3 | 6.2 |

A^{5} | 585,305 | 95 | ^{‡} 4 | ^{‡} 4000 | 8.2 | 8.3 |

A^{6} | 702,590 | ^{‡} 110 | ^{*} 6 | ^{*} 6000 | 8.6 | 8.5 |

A+ | 425,232.50 | 110 | 4 | 4000 | 8.8 | 8.6 |

A- | 748,223 | 75 | 6 | 6000 | 6.2 | 5.3 |

Optimization | Min | Max | Min | Min | Max | Max |

W_{i} | 0.23857 | 0.08151 | 0.10869 | 0.11593 | 0.07696 | 0.37834 |

^{‡}Best values according to the optimization criteria for an attribute. * Worst value according to the optimization criteria for an attribute.

#### 3.3.2. Alternatives‘ Evaluation: TOPSIS stage

**A+**and

**A-**and the optimization criteria for every attribute. Thus, the ideal tractor for a decision group of five farmers must have an initial cost (IC) of $425,232.50 from

**A**, a rated power (RP) of 110 H.P from

^{3}**A**, with four cylinders (NC) from

^{6}**A**,

^{1}**A**,

^{2}**A**and

^{3}**A**, a displacement of 4000 cm

^{5}^{3}from

**A**, operator’s safety of 8.8 from

^{5}**A**and, finally, an after-sale customer service of 8.6 from

^{1}**A**; note that the best values are indicated with the

^{1}^{‡}symbol. The worst tractor for farmers is that which has an IC of $748,223 from

**A**, a rated power (RP) of 75 HP from

^{1}**A**, with six cylinders (NC) from

^{2}**A**and

^{4}**A**, a displacement of 6000 cm

^{6}^{3}from

**A**and

^{4}**A**, operator’s safety of 6.2 from

^{6}**A**and, finally, an after-sale customer service of 5.3 from

^{3}**A**; note that the best values are indicated with the

^{3}^{*}symbol. Observe that in an alternative represented by

**A**, there are three attributes that belong to the ideal alternative.

^{1}A^{k} | Attributes | |||||
---|---|---|---|---|---|---|

IC | RP | NC | DI | SO | CS | |

A^{1} | 0.4966 | 0.3594 | 0.3430 | 0.3758 | 0.4615 | 0.4699 |

A^{2} | 0.3456 | 0.3369 | 0.3430 | 0.3733 | 0.3828 | 0.3989 |

A^{3} | 0.2822 | 0.3594 | 0.3430 | 0.3376 | 0.3251 | 0.2896 |

A^{4} | 0.4311 | 0.4492 | 0.5145 | 0.4977 | 0.3828 | 0.3388 |

A^{5} | 0.3885 | 0.4268 | 0.3430 | 0.3318 | 0.4300 | 0.4535 |

A^{6} | 0.4663 | 0.4942 | 0.5145 | 0.4977 | 0.4510 | 0.4645 |

A+ | 0.2822 | 0.4942 | 0.3430 | 0.3318 | 0.4615 | 0.4699 |

A- | 0.4966 | 0.3369 | 0.5145 | 0.4977 | 0.3251 | 0.2896 |

Norm | 1,506,604.043 | 222.598 | 11.662 | 12,055.530 | 19.070 | 18.301 |

A^{k} | Attributes | |||||
---|---|---|---|---|---|---|

IC | RP | NC | DI | SO | CS | |

A^{1} | 0.1185 | 0.0293 | 0.0373 | 0.0436 | 0.0355 | 0.1778 |

A^{2} | 0.0825 | 0.0275 | 0.0373 | 0.0433 | 0.0295 | 0.1509 |

A^{3} | 0.0673 | 0.0293 | 0.0373 | 0.0391 | 0.0250 | 0.1096 |

A^{4} | 0.1028 | 0.0366 | 0.0559 | 0.0577 | 0.0295 | 0.1282 |

A^{5} | 0.0927 | 0.0348 | 0.0373 | 0.0385 | 0.0331 | 0.1716 |

A^{6} | 0.1113 | 0.0403 | 0.0559 | 0.0577 | 0.0347 | 0.1757 |

A+ | 0.0673 | 0.0403 | 0.0373 | 0.0385 | 0.0355 | 0.1778 |

A- | 0.1185 | 0.0275 | 0.0559 | 0.0577 | 0.0250 | 0.1096 |

Alternative | Distance to Ideal Alternative | ||||||

CI | MC | LDH | SO | MA | CS | $\rho ({A}^{k},{A}^{+})$ | |

A^{1} | 0.00262 | 0.00012 | 0.00000 | 0.00003 | 0.00000 | 0.00000 | 0.05256 |

A^{2} | 0.00023 | 0.00016 | 0.00000 | 0.00002 | 0.00004 | 0.00072 | 0.03428 |

A^{3} | 0.00000 | 0.00012 | 0.00000 | 0.00000 | 0.00011 | 0.00465 | 0.06990 |

A^{4} | 0.00126 | 0.00001 | 0.00035 | 0.00037 | 0.00004 | 0.00246 | 0.06701 |

A^{5} | 0.00064 | 0.00003 | 0.00000 | 0.00000 | 0.00001 | 0.00004 | 0.02678 |

A^{6} | 0.00193 | 0.00000 | 0.00035 | 0.00037 | 0.00000 | 0.00000 | 0.05149 |

Alternative | Distance to Anti-Ideal Solution | ||||||

CI | MC | LDH | SO | MA | CS | $\rho ({A}^{k},{A}^{-})$ | |

A^{1} | 0.00000 | 0.00000 | 0.00035 | 0.00020 | 0.00011 | 0.00465 | 0.07290 |

A^{2} | 0.00680 | 0.00075 | 0.00139 | 0.00187 | 0.00087 | 0.02278 | 0.18563 |

A^{3} | 0.00453 | 0.00086 | 0.00139 | 0.00153 | 0.00063 | 0.01201 | 0.14472 |

A^{4} | 0.01058 | 0.00134 | 0.00313 | 0.00333 | 0.00087 | 0.01643 | 0.18887 |

A^{5} | 0.00859 | 0.00121 | 0.00139 | 0.00148 | 0.00110 | 0.02944 | 0.20786 |

A^{6} | 0.01238 | 0.00162 | 0.00313 | 0.00333 | 0.00120 | 0.03088 | 0.22922 |

A^{k} | $\rho ({A}^{k},{A}^{+})$ | $\rho ({A}^{k},{A}^{-})$ | RC Index | Order |
---|---|---|---|---|

A^{1} | 0.05256 | 0.07290 | 0.41892251 | 6 |

A^{2} | 0.03428 | 0.18563 | 0.15587252 | 2 |

A^{3} | 0.06990 | 0.14472 | 0.32567311 | 5 |

A^{4} | 0.06701 | 0.18887 | 0.26187764 | 4 |

A^{5} | 0.02678 | 0.20786 | 0.11411747 | 1 |

A^{6} | 0.05149 | 0.22922 | 0.18343005 | 3 |

**A**, and that alternative must be selected; however, attending to distance from the anti-ideal solution, the biggest distance is represented by

^{5}**A**; however, due to the weights in attributes, the best RC index is for

^{6}**A**, and this alternative must be the one selected.

^{5}## 4. Conclusions

- This hybrid technique does not require the use of specialized and expensive software for the evaluation of alternatives, as occurs with other techniques that, given their complexity, need to be integrated into specific computer applications.
- This hybrid technique can be applied using any spreadsheet, such as Excel, which is a component of Microsoft Office© and is present in most company computer equipment, therefore widely available to users. With the spreadsheet, the application is made just integrating the attributes weighting process with AHP, as well as the alternatives’ comparison with TOPSIS.
- Given that the analysis can be performed with software widely integrated into desktops and laptops, most farmers or decision makers, people who know the selection problem, are able to evaluate tractors alternatives by themselves; this includes small, medium and large agribusinesses worldwide, since Microsoft Office is widely-used commercial software present in almost all systems.
- Therefore, as the selection and decision process is carried out by the company’s staff, farmers avoid outsourcing this task and decision to experts in multicriteria techniques, who are usually unaware of the investment problem and farmers’ needs.
- Furthermore, consequential costs incurred due to outsourcing external staff to perform the selection process are avoided.
- The AHP and TOPSIS techniques are very simple to understand and implement, so the time spent performing the evaluation is minimal, allowing managers and farmers to carry out other activities.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

AHP: Analytic hierarchy process |

TOPSIS: Technique for order of preference by similarity to the ideal solution |

AT: Advanced technology |

ET: Economic techniques |

NPV: Net present value |

IRR: Internal rate of return |

PB: Pay back |

ST: Strategic techniques |

CEO: Chief Executive Officer |

LAM: Linear additive model |

ATA: Advanced technology in agriculture |

AMT: Advanced manufacturing technology |

SAGARPA: Ministry of Agriculture, Livestock, Rural Development, Fisheries and Food (in Mexico). |

SEDER: Ministry of Rural Development (in Mexico) |

CI: Consistency Index |

CR: Consistency ratio |

AI: Random Index |

OV: Objective values |

SV: Subjective values |

TSV: Total subjective values |

FDM: Final decision matrix |

IC: Initial cost of the tractor |

RP: Rated power |

NC: Number of cylinders |

DI: Displacement |

SO: Safety for operator |

CS: Customer service |

## References

- Kimoto, R.; Ronquillo, D.; Caamaño, M.C.; Martinez, G.; Schubert, L.; Rosado, J.L.; Garcia, O.; Long, K.Z. Food, eating and body image in the lives of low socioeconomic status rural Mexican women living in Queretaro State, Mexico. Health Place
**2014**, 25, 34–42. [Google Scholar] [CrossRef] [PubMed] - Zeng, D.-Z.; Zhao, L. Globalization, interregional and international inequalities. J. Urban Econ.
**2010**, 67, 352–361. [Google Scholar] [CrossRef] - Tudisca, S.; Di Trapani, A.M.; Donia, E.; Sgroi, F.; Testa, R. Entrepreneurial strategies of Etna wine farms. Int. J. Entrep. Small Bus.
**2014**, 21, 155–164. [Google Scholar] [CrossRef] - Tudisca, S.; Di Trapani, A.M.; Donia, E.; Sgroi, F.; Testa, R. The Market Reorientation of Farms: The Case of Olive Growing in the Nebrodi Area. J. Food Prod. Mark.
**2015**, 21, 179–192. [Google Scholar] [CrossRef] - Bandini, M.; Guerrieri, G.; Sediari, T. Istituzioni di Economia e Politica Agraria; Edagricole: Bologna, Italy, 1989. (In Italian) [Google Scholar]
- Hua, Y. Influential factors of farmers’ demands for agricultural science and technology in China. Technol. Forecast. Social Chang.
**2015**, 100, 249–254. [Google Scholar] [CrossRef] - Carter, M.R.; Cheng, L.; Sarris, A. Where and how index insurance can boost the adoption of improved agricultural technologies. J. Dev. Econ.
**2016**, 118, 59–71. [Google Scholar] [CrossRef] - Sun, B.; Ma, W. An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application. Omega
**2015**, 51, 83–92. [Google Scholar] [CrossRef] - Chuu, S.-J. Selecting the advanced manufacturing technology using fuzzy multiple attributes group decision making with multiple fuzzy information. Comput. Ind. Eng.
**2009**, 57, 1033–1042. [Google Scholar] [CrossRef] - Evans, L.; Lohse, N.; Summers, M. A fuzzy-decision-tree approach for manufacturing technology selection exploiting experience-based information. Expert Syst. Appl.
**2013**, 40, 6412–6426. [Google Scholar] [CrossRef] - Ilgin, M.A.; Gupta, S.M.; Battaïa, O. Use of MCDM techniques in environmentally conscious manufacturing and product recovery: State of the art. J. Manuf. Syst.
**2015**, 37, 746–758. [Google Scholar] [CrossRef] - Veisi, H.; Liaghati, H.; Alipour, A. Developing an ethics-based approach to indicators of sustainable agriculture using analytic hierarchy process (AHP). Ecol. Indic.
**2016**, 60, 644–654. [Google Scholar] [CrossRef] - Braglia, M.; Gabbrielli, R. Dimensional analysis for investment selection in industrial robots. Int. J. Prod. Res.
**2000**, 38, 4843–4848. [Google Scholar] [CrossRef] - Yue, Z. Extension of TOPSIS to determine weight of decision maker for group decision making problems with uncertain information. Expert Syst. Appl.
**2012**, 39, 6343–6350. [Google Scholar] [CrossRef] - Goh, C.-H.; Tung, Y.-C.A.; Cheng, C.-H. A revised weighted sum decision model for robot selection. Comp. Ind. Eng.
**1996**, 30, 193–199. [Google Scholar] [CrossRef] - Knott, K.; Getto, R.D. A model for evaluating alternative robot systems under uncertainty. Int. J. Prod. Res.
**1982**, 20, 155–165. [Google Scholar] [CrossRef] - Wei, C.-C.; Kamrani, A.K.; Wiebe, H. Animated simulation of the robot process capability. Comput. Ind. Eng.
**1992**, 23, 237–240. [Google Scholar] [CrossRef] - Offodile, O.; Lambert, B.; Dudek, R. Development of a computer aided robot selection procedure (CARSF). Int. J. Prod. Res.
**1987**, 25, 1109–1121. [Google Scholar] - Imany, M.M.; Schlesinger, R.J. Decision Models for Robot Selection: A Comparison of Ordinary Least Squares and Linear Goal Programming Methods. Decis. Sci.
**1989**, 20, 40–53. [Google Scholar] [CrossRef] - Boubekri, N.; Sahoui, M.; Lakrib, C. Development of an expert system for industrial robot selection. Comput. Ind. Eng.
**1991**, 20, 119–127. [Google Scholar] [CrossRef] - Sabaghi, M.; Mascle, C. Application of DOE-TOPSIS Technique in Decision-Making Problems. IFAC
**2015**, 48, 773–777. [Google Scholar] [CrossRef] - Russell, N.P.; Milligan, R.A.; LaDue, E.L. A stochastic simulation model for evaluating forage machinery performance. Agric. Syst.
**1983**, 10, 39–63. [Google Scholar] [CrossRef] - Elhorst, J.P. The estimation of investment equations at the farm level. Eur. Rev. Agric. Econ.
**1993**, 20, 167–182. [Google Scholar] [CrossRef] - Søgaard, H.T.; Sørensen, C.G. A Model for Optimal Selection of Machinery Sizes within the Farm Machinery System. Biosyst. Eng.
**2004**, 89, 13–28. [Google Scholar] [CrossRef] - Camarena, E.A.; Gracia, C.; Cabrera Sixto, J.M. A Mixed Integer Linear Programming Machinery Selection Model for Multifarm Systems. Biosyst. Eng.
**2004**, 87, 145–154. [Google Scholar] [CrossRef] - García, J.L.; Alvarado, A.; Blanco, J.; Jiménez, E.; Maldonado, A.A.; Cortés, G. Multi-attribute evaluation and selection of sites for agricultural product warehouses based on an Analytic Hierarchy Process. Comput. Electron. Agric.
**2014**, 100, 60–69. [Google Scholar] [CrossRef] - Gómez-Limón, J.A.; Arriaza, M.; Riesgo, L. An MCDM analysis of agricultural risk aversion. Eur. J. Oper. Res.
**2003**, 151, 569–585. [Google Scholar] [CrossRef] - Bazzani, G.M. An integrated decision support system for irrigation and water policy design: DSIRR. Environ. Model. Softw.
**2005**, 20, 153–163. [Google Scholar] [CrossRef] - Bartolini, F.; Bazzani, G.M.; Gallerani, V.; Raggi, M.; Viaggi, D. The impact of water and agriculture policy scenarios on irrigated farming systems in Italy: An analysis based on farm level multi-attribute linear programming models. Agric. Syst.
**2007**, 93, 90–114. [Google Scholar] [CrossRef] - André, F.J.; Riesgo, L. A non-interactive elicitation method for non-linear multiattribute utility functions: Theory and application to agricultural economics. Eur. J. Oper. Res.
**2007**, 181, 793–807. [Google Scholar] [CrossRef] - Hayashida, T.; Nishizaki, I.; Ueda, Y. Multiattribute utility analysis for policy selection and financing for the preservation of the forest. Eur. J. Oper. Res.
**2010**, 200, 833–843. [Google Scholar] [CrossRef] - Manos, B.; Chatzinikolaou, P.; Kiomourtzi, F. Sustainable Optimization of Agricultural Production. APCBEE Procedia
**2013**, 5, 410–415. [Google Scholar] [CrossRef] - Likert, R. A Technique for the measumerement of attitudes. Arch. Psychol.
**1932**, 22, 1–55. [Google Scholar] - Hair, J.; Black, W.; Babin, B.; Anderson, R. Multivariate Data Analysis; Prentice Hall: Upper Saddle River, NJ, USA, 2009. [Google Scholar]
- Kaiser, H. Mathematical Programming for Agricultural, Environmental, and Resource Economics; Wiley: Hoboken, NJ, USA, 2010. [Google Scholar]
- Cronbach, L. Coefficient alpha and the internal structure of tests. Psychometrika
**1951**, 16, 297–334. [Google Scholar] [CrossRef] - Kock, N. Using WarpPLS in e-collaboration studies: What if I have only one group and one condition. Int. J. e-Collab.
**2013**, 9, 1–12. [Google Scholar] [CrossRef] - Saaty, T. Decision Making for Leaders, 2nd ed.; RWS Publication: Pittsburgh, PA, USA, 1992. [Google Scholar]
- Gass, S.I.; Rapcsák, T. Singular value decomposition in AHP. Eur. J. Oper. Res.
**2004**, 154, 573–584. [Google Scholar] [CrossRef] - Beynon, M. DS/AHP method: A mathematical analysis, including an understanding of uncertainty. Eur. J. Oper. Res.
**2002**, 140, 148–164. [Google Scholar] [CrossRef] - Condon, E.; Golden, B.; Lele, S.; Raghavan, S.; Wasil, E. A visualization model based on adjacency data. Decis. Support Syst.
**2002**, 33, 349–362. [Google Scholar] [CrossRef] - Mikhailov, L. Group prioritization in the AHP by fuzzy preference programming method. Comput. Oper. Res.
**2004**, 31, 293–301. [Google Scholar] [CrossRef] - Srdjevic, B.; Srdjevic, Z.; Blagojevic, B.; Suvocarev, K. A two-phase algorithm for consensus building in AHP-group decision making. Appl. Math. Model.
**2013**, 37, 6670–6682. [Google Scholar] [CrossRef]

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

García-Alcaraz, J.L.; Maldonado-Macías, A.A.; Hernández-Arellano, J.L.; Blanco-Fernández, J.; Jiménez-Macías, E.; Sáenz-Díez Muro, J.C.
Agricultural Tractor Selection: A Hybrid and Multi-Attribute Approach. *Sustainability* **2016**, *8*, 157.
https://doi.org/10.3390/su8020157

**AMA Style**

García-Alcaraz JL, Maldonado-Macías AA, Hernández-Arellano JL, Blanco-Fernández J, Jiménez-Macías E, Sáenz-Díez Muro JC.
Agricultural Tractor Selection: A Hybrid and Multi-Attribute Approach. *Sustainability*. 2016; 8(2):157.
https://doi.org/10.3390/su8020157

**Chicago/Turabian Style**

García-Alcaraz, Jorge L., Aidé A. Maldonado-Macías, Juan L. Hernández-Arellano, Julio Blanco-Fernández, Emilio Jiménez-Macías, and Juan C. Sáenz-Díez Muro.
2016. "Agricultural Tractor Selection: A Hybrid and Multi-Attribute Approach" *Sustainability* 8, no. 2: 157.
https://doi.org/10.3390/su8020157