1. Introduction

The problem of optimizing the layout of facilities has been subject of many researches in the last sixty years. Several recent publications, conferences and researches confirmed the importance of the layout of facilities to meet the requirements set by the market and to achieve the goals of the company [1, 2, 3, 4]. The layout of facilities is an important issue not only for production but also for organizations providing services. Since the 1990s, an additional emphasis on this issue came from the strong requirement of the market for mass satisfying of customers in terms of the required product, quantity, variety, place and time of delivery, and this problem is further complicated because of an increase in the degree of uncertainty and ambiguity. Satisfying these demands requires quick reaction and rearrangement of facilities in the shortest possible time and best possible way, in order to reduce costs. The importance of the problem of layout is also reflected by the fact that the costs of material handling, and other costs which depend on the layout, constitute 2050% of total operating costs [5]. Requirement to have an efficient process of supply for point of receipt from the point of supply implies the establishment of a logistics system that will allow supply of the right product, in the right condition, at the right time, right place, and at minimum cost.

Complexity of the logistics system imposes the need for multicriteria optimization and decision-making in order to achieve the basic logistical goal: a smooth flow of goods and information through the system. In order to achieve this goal, it is necessary for the facilities layout to be optimal. The facilities include physical entities such as machines, work centers, production cells, workshops, sections, warehouses and everything else that facilitates achievement of set or expected performances of work. optimum design of a facility minimizes the costs of handling of the material, the production cycle duration, capital investment, inventories, increases efficiency of work and use of space, safety and comfort of employees, eliminates bottlenecks, enables visual control and maintains flexibility in changing conditions. "Multicriteria optimization can significantly facilitate and accelerate the decision making process" [6].

The facilities layout problem is a point of interest for employees at all levels in the organizational hierarchy. Top management is interested in this problem in terms of the size and efficiency of capital investment. Managers at lower levels are interested in this problem in terms of costs and efficiency of operations, and the workers have interest in terms of safety, comfort, their productivity and earnings.

There are many objectives to be achieved in the making of the facilities layout. They can be shown in the form of functions or in the form of evaluation criteria. According to Langevin and Riopel [7], the objectives of the facilities layout are divided into the following three groups:

* strategic objectives,

* tactical objectives,

* operational objectives.

Due to the complexity of the facilities layout problem, different models used just a few of a large number of layout objectives, and the most commonly used objectives are optimization of the flow (materials, information and personnel), minimization of material handling costs, optimization of equipment use and optimization of capital investment.

The development of fuzzy logic and its application in these models enabled better use of quality objectives (or criteria for the evaluation of the layout alternatives) that are difficult to measure or are difficult to quantify and measure without the use of fuzzy logic (classic).

The facilities layout problem solved in this paper is formulated as a problem of fuzzy multiple criteria (multiple attribute) decision making.

The main objective of this paper is to develop a model for the evaluation and selection of solutions from the Pareto set of solutions (alternatives for layout facilities) using the theory of fuzzy sets and fuzzy logic in multicriteria logistics decision making. The model should also include the criteria (quantitative and qualitative) for strategic, tactical and operational level, which are immanent to the real problems of logistics decision making on the facilities layout, when a decision maker is unable to accurately determine the value of individual criteria or when they are hardly measurable.

2. Fuzzy logistics multicriteria decision making model forfacilities layout

The development of the model is implemented through a series of steps:

1. Selection of the decision making criteria

2. Selection of methods for multicriteria decision aid

3. Structuring of the decision making hierarchy

4. Application of the Fuzzy Analytic Hierarchy Process method with checking the consistency of matrices

5. Testing of the model.

2.1 Decision criteria

The criteria are selected in accordance with the logistics objectives and they are immanent to real problems of logistics decision making on the facilities layout. It is possible to evaluate the extent to which a certain alternative contributes to achieving the objective referred to each other and to compare alternatives on the basis of criteria (attributes of alternatives). Analogous to division of logistical objectives, the criteria are also divided into 3 groups of criteria:

* Strategic level criteria (12 criteria given in Table 1)

* Tactical level criteria (9 criteria given in Table 2)

* Operational level criteria (9 criteria given in Table 3).

2.2 Selection of multicriteria decision making method

Due to the complexity of the logistics system and large interdependence of decisions on strategic, tactical and operational level as well as due to number and nature of the criteria imposed by the need to rely on the assessment, Fuzzy Analytic Hierarchy Process is selected and applied as a multicriteria decision making method, which, in its essence is the most appropriate for the problem and the context of decision making. The applied Fuzzy Analytic Hierarchy Process method is based on Chang's fuzzy extent analysis [8]. The basic concept, i.e. hierarchical structure of decision making, pairwise comparison and the bottom up synthesis of priorities through the hierarchy is the same as in classical Analytic Hierarchy Process. The key difference compared to the classical Analytic Hierarchy Process is that with the Fuzzy Analytic Hierarchy Process, decision makers are not required to give strict assessment, but instead, imprecision in the evaluation is allowed.

2.3 Hierarchy of decision making and model parameters

The problem of decision making is structured in a hierarchy that has 4 hierarchical levels:

1. Objective: selection of the best alternative from the Pareto set of alternatives for facilities layout

2. criteria groups

3. Criteria (listed in the criteria groups)

4. Alternatives (Pareto set of alternatives).

The number of alternatives is a variable in the model and the specific parameters of the model are:

1. Number of levels in a hierarchical structure (4),

2. Number of criteria groups (3),

3. Total number of criteria (30),

4. Number of strategic level criteria (12),

5. Number of tactical level criteria (9),

6. Number of operational level criteria (9).

2.4 Input/output

Inputs for the model are expert assessments of criteria importance and priorities of alternatives that are entered into pairwise comparison matrices:

1. Pairwise comparison matrix of criteria groups with respect to the objective

2. Pairwise comparison matrix of strategic level criteria with respect to the corresponding group

3. Pairwise comparison matrix of tactical level criteria with respect to the corresponding group

4. Pairwise comparison matrix of operational level criteria with respect to the corresponding group

5. Pairwise comparison matrices of alternatives with respect to each of the criterion.

The outputs of the model are priority values for alternatives sorted from largest to smallest. The best alternative has the highest value of priority.

2.5 Consistency check

Pairwise comparison matrices are positive, squared and reciprocal. Elements of matrices are triangular fuzzy numbers from a fuzzy scale obtained through appropriate fuzzification of Saaty's scale [9] in order to derive corresponding classical matrices from the fuzzy matrices and to check the consistency. Consistency of a classical matrix implies consistency of the correspondent fuzzy matrix. Fuzzy scale is shown in Table 4.

2.6 Algorithm model

The model can be realized through the algorithm whose flowchart is presented in Figure 1.

3. Testing model on a concrete example

The developed model is tested on a concrete example of the selection problem for the best layout alternatives of 3 "workplaces" in a design office, using a Java application made on the basis of the algorithm of the developed model. The facilities here are "workplaces" (desk and chair on an area envisaged to accommodate the movement of the chair when sitting/getting up and working. Layouts of the "workplaces", work desk and floor space envisaged to accommodate furniture and movement of the chair have a form of a rectangle. Layout options (alternatives) from the pareto set are presented in Figure 2 a-c.

The decision maker is a sector manager (tactical level) and directly manages the work of employees who will be assigned to "workplaces". Along with the previous explanations of the hierarchical structure of decision making and the use of the Java application, the decision maker made the pairwise comparisons to give assessment of importance of criteria groups with respect to the objective (matrix 1 in Table 1), assessment of criteria importance with respect to the corresponding criteria group (matrices 2-4 in Table 1) and the assessment of the priorities of alternatives with respect to each of the criteria (matrices 5-34 in Table 2). The results are given in Table 7.

According to Fuzzy Analytic Hierarchy Process the best alternative is A1, while according to classical Analytic Hierarchy Process the best alternative is A2. Result (A1) is the expected.

4. Conclusion

In this paper facilities layout problem formulated as a problem of fuzzy multicriteria (multi attributive) decision making is solved and a model for evaluation and selection of solution from Pareto set of solutions (facilities layout alternatives) applying theory for fuzzy sets and fuzzy logic in multicriteria logistics decision is developed. The proposed fuzzy model for logistics multicriteria decision making on the facilities layout, developed on the basis of systemic thinking and a holistic approach to solving logistics problems, includes a relatively large number of criteria (quantitative and qualitative) is applicable in situations where it is difficult to measure criteria or it is difficult to quantify and measure them without the application of fuzzy logic.

Compared to models based on the classic Analytic Hierarchy Process method, the advantage of the proposed model based on the Fuzzy Analytic Hierarchy Process method is reflected in the fact that the expert assessments expressed verbally do not appear as strict assessments, but as to some extent overlapping normal, convex fuzzy sets (triangular fuzzy numbers) that are a more realistic presentation of expert assessments of the relative importance of the criteria and the relative priority of alternatives.

Future research can be carried out to the direction of integration of the proposed model for multicriteria decision making with models for the generation of facilities layout alternatives and to the direction of the modification of the model for team decision-making.

DOI: 10.2507/27th.daaam.proceedings.094

5. References

[1] Yang L., Deuse J. (2012): Multiple-attribute Decision Making for an Energy Efficient Facility Layout Design, Procedia CIRP, Vol 3, Pages 149-154, 45th CIRP Conference on Manufacturing Systems 2012

[2] Karande P., Chakraborty S.: A Facility Layout Selection Model using MACBETH Method, Proceedings of the 2014 International Conference on Industrial Engineering and Operations Management Bali, Indonesia, January 7-9, 2014.

[3] Bacudio L, Esmeria G. J., Promentilla M. A.: A Fuzzy Analytic Hierarchy Process Approach for Optimal Selection of Manufacturing Layout, Presented at the DLSU Research Congress 2016, De La Salle University, Manila, Philippines, March 7-9, 2016.

[4] Shokri H., Ashjari B., Saberi M., Yoon J. H (2013): An Integrated AHP-VIKOR Methodology for Facility Layout Design, Industrial Engineering & Management Systems, Vol 12, No 4, December 2013

[5] Tompkins J A., White J. A., Bozer Y. A. & Tanchoco, J. M. A.: Facilities Planning, 4th Edition, John Wiley & Sons, Inc, USA, 2010.,

[6] Vucijak, B., Pasic, M. & Zorlak, AJ. (2015). Use of Multi-criteria Decision Aid Methods for Selection of the Best Alternative for the Highway Tunnel Doors, 25th DAAAM International Symposium on Intelligent Manufacturing and Automation, DAAAM 2014, Procedia Engineering, Vol. 100, (2015), pp. 656-665

[7] Langevin A., Riopel D. (2005): Logistics Systems: Design and Optimization, Springer Science + Business Media, New York

[8] Kahraman, C. (2008) Fuzzy Multi-Criteria Decision Making, Theory and Applications with Recent Developments, New Jork, Springer Science+Business Media, LLC.

[9] Saaty, T. L. (1980), Analytic hierarchy process, New York, McGraw-Hill

This Publication has to be referred as: Lavic, Z[edina]; Pasic, M[ugdim]; Vucijak, B [ranko] & Dukic, N[edzad] (2016). Fuzzy Logistics Multicriteria Decision Making Model for Facilities Layout, Proceedings of the 27th DAAAM International Symposium, pp.0650-0657, B. Katalinic (Ed.), Published by DAAAM International, ISBN 978-3-902734-08-2, ISSN 1726-9679, Vienna, Austria

Caption: Fig. 1. Flowchart of algorithm model

Caption: Fig. 2 a) A1, b) A2, c) A3

Table 1. Strategic level criteria

             Criteria                 Designation      Unit of
                                                       Measure

Share of unrealized                       SC1             %
(unfulfilled) purchase orders
(ordered quantity), caused by
lack of capacity, in total
ordered quantities per year

Modularity (plan for future               SC2        Linguistic
expansion)                                              value

Consistency with company                  SC3        Linguistic
image, promotional value,                               value
public or community relations

Net present value                         SC4            BAM

Internal rate of return                   SC5             %

                                          SC6         Number of
                                                        years

Installation period                       SC7             h

Noise emission level                      SC8            dB

Quantity of pollutants'                   SC9          t/year
emission to the air

Quantity of energy used for               SC10         J/year
conditioning, heating and
cooling

Distance of output / input from           SC11            m
the place of loading /
unloading

Total distance of exit from               SC12            m
the entrance to other
facilities

             Criteria                 Max/Min

Share of unrealized                     Min
(unfulfilled) purchase orders
(ordered quantity), caused by
lack of capacity, in total
ordered quantities per year

Modularity (plan for future             Max
expansion)

Consistency with company                Max
image, promotional value,
public or community relations

Net present value                       Max

Internal rate of return                 Max

                                        Min

Installation period                     Min

Noise emission level                    Min

Quantity of pollutants'                 Min
emission to the air

Quantity of energy used for             Min
conditioning, heating and
cooling

Distance of output / input from         Min
the place of loading /
unloading

Total distance of exit from             Min
the entrance to other
facilities

Table 2. Tactical level criteria

             Criteria                Designation      Unit of
                                                      Measure

Fits into the organizational             TC1        Linguistic
structure                                              value

Facilitating the monitoring,             TC2        Linguistic
control and communications                             value

Optimizing the use of space              TC3        Linguistic
                                                       value

Number of requests for non-              TC4             #
standard elements (equipment,
tools, work surfaces, ...)

Maintain flexibility in                  TC5        Linguistic
scheduling and operations                              value

Average time from service                TC6             h
request to service
implementation

Number of departments in which           TC7             #
the intensity of daylight is
not sufficient

Facilitating the maintenance             TC8        Linguistic
and household                                          value

Distance of departments                  TC9             m
staffed by employees with
disabilities to the
departments with which they
are in close cooperation, or
restaurant, toilets

             Criteria                Max/Min

Fits into the organizational           Max
structure

Facilitating the monitoring,           Max
control and communications

Optimizing the use of space            Max

Number of requests for non-            Min
standard elements (equipment,
tools, work surfaces, ...)

Maintain flexibility in                Max
scheduling and operations

Average time from service              Min
request to service
implementation

Number of departments in which         Min
the intensity of daylight is
not sufficient

Facilitating the maintenance           Max
and household

Distance of departments                Min
staffed by employees with
disabilities to the
departments with which they
are in close cooperation, or
restaurant, toilets

Table 3. Operational level criteria

                                                       Unit of
            Criteria                Designation        Measure

"Work in progress" turnover             OC1                #

Cost of material flow                   OC2               BAM

Cost of the flow of                     OC3               BAM
information and personnel

Handling optimization                   OC4         Linguistic value

Number of injuries of                   OC5                #
employees per year

Number of thefts of materials           OC6                #
and equipment per year

To provide convenience for              OC7         Linguistic value
workers and improve job
satisfaction

Percentage of equipment that            OC8                %
performs the function in the
observed period

Daily effective engagement of           OC9              h/day
employees

                                    Max/
            Criteria                Min

"Work in progress" turnover         Max

Cost of material flow               Min

Cost of the flow of                 Min
information and personnel

Handling optimization               Max

Number of injuries of               Min
employees per year

Number of thefts of materials       Min
and equipment per year

To provide convenience for          Max
workers and improve job
satisfaction

Percentage of equipment that        Max
performs the function in the
observed period

Daily effective engagement of       Max
employees

Table 4. Fuzzified Saaty's scale

       Definition             Importance intensity

Equal importance                   (1, 1, 1)
Moderate importance                (2, 3, 4)
Strong importance                  (4, 5, 6)
Very strong importance             (6, 7, 8)
Extreme importance                 (9, 9, 9)
Intermediate values          (1, 2, 3), (3, 4, 5),
                            (5, 6, 7) and (7, 8, 9)

       Definition                         Reciprocals

Equal importance                           (1, 1, 1)
Moderate importance                     (1/4, 1/3, 1/2)
Strong importance                       (1/6, 1/5, 1/4)
Very strong importance                  (1/8, 1/7, 1/6)
Extreme importance                      (1/9, 1/9, 1/9)
Intermediate values          (1/3, 1/2, 1), (1/5, 1/4, 1/3), (1/7,
                                 1/6, 1/5) and (1/9, 1/8, 1/7)

Table 5. Pairwise comparison matrices 1-4

Matrix No                       Matrix                       CR (%)

    1        [(1, 1, 1) (1/3, 1/2, 1) (1/3, 1/2, 1)          5,23
             | (1, 2, 3) (1, 1, 1) (1, 2, 3) | (1, 2,
             3) (1/3, 1/2, 1) (1, 1, 1) |]

    2        [(1, 1, 1) (1, 2, 3) (1, 2, 3) (1/4, 1/         7,96
             3, 1/2) (1/3, 1/2, 1) (1/3, 1/2, 1) (1/
             5, 1/4, 1/3) (1, 1, 1) (1, 1, 1)  (1/5,
             1/4, 1/3) (1/3, 1/2, 1) (1/3, 1/2, 1) |
             (1/3, 1/2, 1) (1, 1, 1) (1/3, 1/2, 1)
             (2, 3, 4) (1, 1, 1) (1, 1, 1)  (1, 2, 3)
             (2, 3, 4) (1, 1, 1) (1, 1, 1) (1, 2, 3)
             (3, 4, 5) | (1/3, 1/2, 1) (1, 2, 3) (1,
             1, 1) (1/3, 1/2, 1) (1/3,  1/2, 1) (1/
             3, 1/2, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1)
             (1, 2, 3) (1, 2, 3) (1, 2, 3) | (2, 3,
             4) (1/4, 1/3, 1/2) (1,  2, 3) (1, 1, 1)
             (1/4, 1/3, 1/2) (1/4, 1/3, 1/2) (1, 1,
             1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1,
             1) (1, 2, 3) | (1,  2, 3) (1, 1, 1) (1,
             2, 3) (2, 3, 4) (1, 1, 1) (1, 1, 1) (1,
             2, 3) (2, 3, 4) (1, 1, 1) (1, 1, 1) (1,
             2, 3) (2, 3, 4)  | (1, 2, 3) (1, 1, 1)
             (1, 2, 3) (2, 3, 4) (1, 1, 1) (1, 1, 1)
             (1, 2, 3) (2, 3, 4) (1, 1, 1) (1, 1, 1)
             (1, 2, 3) (2,  3, 4) | (3, 4, 5) (1/3,
             1/2, 1) (1, 1, 1) (1, 1, 1) (1/3, 1/2,
             1) (1/3, 1/2, 1) (1, 1, 1) (1, 2, 3) (1,
             1, 1) (1,  1, 1) (1, 2, 3) (2, 3, 4) |
             (1, 1, 1) (1/4, 1/3, 1/2) (1, 1, 1) (1,
             1, 1) (1/4, 1/3, 1/2) (1/4, 1/3, 1/2)
             (1/3,  1/2, 1) (1, 1, 1) (1/4, 1/3, 1/
             2) (1, 1, 1) (1, 1, 1) (2, 3, 4) | (1,
             1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1,
             1, 1)  (1, 1, 1) (1, 1, 1) (2, 3, 4) (1,
             1, 1) (1, 1, 1) (1, 2, 3) (2, 3, 4) |
             (3, 4, 5) (1, 1, 1) (1/3, 1/2, 1) (1, 1,
             1)  (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1,
             1) (1, 1, 1) (1, 1, 1) (1, 2, 3) (2, 3,
             4) | (1, 2, 3) (1/3, 1/2, 1) (1/3, 1/2,
             1) (1, 1, 1) (1/3, 1/2, 1) (1/3, 1/2, 1)
             (1/3, 1/2, 1) (1, 1, 1) (1/3, 1/2, 1)
             (1/3, 1/2, 1) (1, 1, 1) (1, 1, 1) |  (1,
             2, 3) (1/5, 1/4, 1/3) (1/3, 1/2, 1) (1/
             3, 1/2, 1) (1/4, 1/3, 1/2) (1/4, 1/3, 1/
             2) (1/4, 1/3, 1/2) (1/4, 1/3,  1/2) (1/
             4, 1/3, 1/2) (1/4, 1/3, 1/2) (1, 1, 1)
             (1, 1, 1) |]

    3        [(1, 1, 1) (1, 1, 1) (1, 2, 3) (2, 3,           1,67
             4) (1, 2, 3) (1, 1, 1) (1, 1, 1) (1, 2,
             3) (1, 1, 1) | (1, 1, 1) (1, 1, 1)  (1,
             1, 1) (1, 2, 3) (1, 2, 3) (1, 1, 1) (1,
             1, 1) (1, 2, 3) (1, 1, 1) | (1/3, 1/2,
             1) (1, 1, 1) (1, 1, 1) (1, 1, 1)  (1, 1,
             1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1,
             1) | (1/4, 1/3, 1/2) (1/3, 1/2, 1) (1,
             1, 1) (1, 1, 1) (1, 1, 1) (1,  1, 1) (1,
             1, 1) (1, 1, 1) (1, 1, 1) | (1/3, 1/2,
             1) (1/3, 1/2, 1) (1, 1, 1) (1, 1, 1) (1,
             1, 1) (1, 1, 1) (1, 1, 1)  (1, 1, 1) (1,
             1, 1) | (1, 1, 1) (1, 1, 1) (1, 1, 1)
             (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1)
             (1, 1, 1) (1, 1, 1) |  (1, 1, 1) (1, 1,
             1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1,
             1) (1, 1, 1) (1, 1, 1) (1, 1, 1) | (1/
             3, 1/2, 1) (1/3, 1/2,  1) (1, 1, 1) (1,
             1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1,
             1, 1) (1, 1, 1) | (1, 1, 1) (1, 1, 1)
             (1, 1, 1) (1, 1, 1)  (1, 1, 1) (1, 1, 1)
             (1, 1, 1) (1, 1, 1) (1, 1, 1) |]

    4        [(1, 1, 1) (1/3, 1/2, 1) (1/3, 1/2, 1)          6,75
             (1/3, 1/2, 1) (1/3, 1/2, 1) (1/3, 1/2,
             1) (1/4, 1/3, 1/2) (1, 1, 1) (1, 1,  1)
             | (1, 2, 3) (1, 1, 1) (1, 1, 1) (1, 1,
             1) (1, 1, 1) (2, 3, 4) (2, 3, 4) (2, 3,
             4) (2, 3, 4) | (1, 2, 3) (1, 1,  1) (1,
             1, 1) (1, 1, 1) (1, 1, 1) (2, 3, 4) (2,
             3, 4) (2, 3, 4) (2, 3, 4) | (1, 2, 3)
             (1, 1, 1) (1, 1, 1) (1, 1, 1)  (1, 1, 1)
             (1, 2, 3) (2, 3, 4) (3, 4, 5) (1, 1, 1)
             | (1, 2, 3) (1, 1, 1) (1, 1, 1) (1, 1,
             1) (1, 1, 1) (1, 1, 1) (1,  2, 3) (2, 3,
             4) (3, 4, 5) | (1, 2, 3) (1/4, 1/3, 1/
             2) (1/4, 1/3, 1/2) (1/3, 1/2, 1) (1, 1,
             1) (1, 1, 1) (1, 1, 1)  (1, 1, 1) (2, 3,
             4) | (2, 3, 4) (1/4, 1/3, 1/2) (1/4, 1/
             3, 1/2) (1/4, 1/3, 1/2) (1/3, 1/2, 1)
             (1, 1, 1) (1, 1, 1)  (1, 1, 1) (1/4, 1/
             3, 1/2) | (1, 1, 1) (1/4, 1/3, 1/2) (1/
             4, 1/3, 1/2) (1/5, 1/4, 1/3) (1/4, 1/3,
             1/2) (1, 1, 1)  (1, 1, 1) (1, 1, 1) (1,
             2, 3) | (1, 1, 1) (1/4, 1/3, 1/2) (1/4,
             1/3, 1/2) (1, 1, 1) (1/5, 1/4, 1/3) (1/
             4, 1/3, 1/2)  (2, 3, 4) (1/3, 1/2, 1)
             (1, 1, 1) |]

Table 6. Pairwise comparison matrices 5-34

 Matrix No                       Matrix                       CR(%)

     5           [ (1, 1, 1) (1, 1, 1) (1/4, 1/3, 1/2) |      1,92
                 (1, 1, 1) (1, 1, 1) (1/3, 1/2, 1) | (2,
                     3, 4) (1, 2, 3) (1, 1, 1) | ]

     6           [ (1, 1, 1) (1, 1, 1) (1/5, 1/4, 1/3) |      0,00
                  (1, 1, 1) (1, 1, 1) (1/5, 1/4, 1/3) |
                   (3, 4, 5) (3, 4, 5) (1, 1, 1) | ]

     7          [ (1, 1, 1) (1, 1, 1) (2, 3, 4) | (1, 1,      0,00
                 1) (1, 1, 1) (2, 3, 4) | (1/4, 1/3, 1/
                    2) (1/4, 1/3, 1/2) (1, 1, 1) | ]

     8          [ (1, 1, 1) (1, 1, 1) (1, 1, 1) | (1, 1,      4,79
                 1) (1, 1, 1) (1, 2, 3) | (1, 1, 1) (1/
                        3, 1/2, 1) (1, 1, 1) | ]

     9          [ (1, 1, 1) (1, 1, 1) (1, 1, 1) | (1, 1,      4,79
                 1) (1, 1, 1) (1, 2, 3) | (1, 1, 1) (1/
                        3, 1/2, 1) (1, 1, 1) | ]

    10          [ (1, 1, 1) (1, 1, 1) (1, 1, 1) | (1, 1,      4,79
                 1) (1, 1, 1) (1, 2, 3) | (1, 1, 1) (1/
                        3, 1/2, 1) (1, 1, 1) | ]

    11          [ (1, 1, 1) (1, 1, 1) (3, 4, 5) | (1, 1,      0,00
                 1) (1, 1, 1) (3, 4, 5) | (1/5, 1/4, 1/
                    3) (1/5, 1/4, 1/3) (1, 1, 1) | ]

    12          [ (1, 1, 1) (1, 1, 1) (1, 1, 1) | (1, 1,      4,79
                 1) (1, 1, 1) (1/3, 1/2, 1) | (1, 1, 1)
                        (1, 2, 3) (1, 1, 1) | ]

    13          [ (1, 1, 1) (1, 1, 1) (1, 1, 1) | (1, 1,      4,79
                 1) (1, 1, 1) (1/3, 1/2, 1) | (1, 1, 1)
                        (1, 2, 3) (1, 1, 1) | ]

    14          [ (1, 1, 1) (1, 1, 1) (1, 1, 1) | (1, 1,      4,79
                 1) (1, 1, 1) (1, 2, 3) | (1, 1, 1) (1/
                        3, 1/2, 1) (1, 1, 1) | ]

    15           [ (1, 1, 1) (1, 2, 3) (2, 3, 4) | (1/3,      0,96
                 1/2, 1) (1, 1, 1) (1, 2, 3) | (1/4, 1/
                  3, 1/2) (1/3, 1/2, 1) (1, 1, 1) | ]

    16           [ (1, 1, 1) (1, 2, 3) (2, 3, 4) | (1/3,      0,96
                 1/2, 1) (1, 1, 1) (1, 2, 3) | (1/4, 1/
                  3, 1/2) (1/3, 1/2, 1) (1, 1, 1) | ]

    17          [ (1, 1, 1) (1, 1, 1) (1, 2, 3) | (1, 1,      0,00
                 1) (1, 1, 1) (1, 2, 3) | (1/3, 1/2, 1)
                      (1/3, 1/2, 1) (1, 1, 1) | ]

    18          [ (1, 1, 1) (1, 1, 1) (2, 3, 4) | (1, 1,      1,78
                 1) (1, 1, 1) (1, 2, 3) | (1/4, 1/3, 1/
                     2) (1/3, 1/2, 1) (1, 1, 1) | ]

    19            [ (1, 1, 1) (1/3, 1/2, 1) (1, 2, 3) |       0,96
                (1, 2, 3) (1, 1, 1) (2, 3, 4) | (1/3, 1/
                  2, 1) (1/4, 1/3, 1/2) (1, 1, 1) | ]

    20          [ (1, 1, 1) (1, 1, 1) (3, 4, 5) | (1, 1,      0,00
                 1) (1, 1, 1) (3, 4, 5) | (1/5, 1/4, 1/
                    3) (1/5, 1/4, 1/3) (1, 1, 1) | ]

    21            [ (1, 1, 1) (1, 1, 1) (1/3, 1/2, 1) |       0,00
                 (1, 1, 1) (1, 1, 1) (1/3, 1/2, 1) | (1,
                     2, 3) (1, 2, 3) (1, 1, 1) | ]

    22            [ (1, 1, 1) (1/3, 1/2, 1) (2, 3, 4) |       5,64
                (1, 2, 3) (1, 1, 1) (2, 3, 4) | (1/4, 1/
                 3, 1/2) (1/4, 1/3, 1/2) (1, 1, 1) | ]

    23          [ (1, 1, 1) (1, 1, 1) (3, 4, 5) | (1, 1,      0,00
                 1) (1, 1, 1) (3, 4, 5) | (1/5, 1/4, 1/
                    3) (1/5, 1/4, 1/3) (1, 1, 1) | ]

    24          [ (1, 1, 1) (1, 1, 1) (2, 3, 4) | (1, 1,      0,00
                 1) (1, 1, 1) (2, 3, 4) | (1/4, 1/3, 1/
                    2) (1/4, 1/3, 1/2) (1, 1, 1) | ]

    25          [ (1, 1, 1) (1, 1, 1) (1, 2, 3) | (1, 1,      0,00
                 1) (1, 1, 1) (1, 2, 3) | (1/3, 1/2, 1)
                      (1/3, 1/2, 1) (1, 1, 1) | ]

    26          [ (1, 1, 1) (1, 1, 1) (1, 2, 3) | (1, 1,      0,00
                 1) (1, 1, 1) (1, 2, 3) | (1/3, 1/2, 1)
                      (1/3, 1/2, 1) (1, 1, 1) | ]

    27          [ (1, 1, 1) (1, 1, 1) (1, 2, 3) | (1, 1,      0,00
                 1) (1, 1, 1) (1, 2, 3) | (1/3, 1/2, 1)
                      (1/3, 1/2, 1) (1, 1, 1) | ]

    28          [ (1, 1, 1) (1, 1, 1) (2, 3, 4) | (1, 1,      0,00
                 1) (1, 1, 1) (2, 3, 4) | (1/4, 1/3, 1/
                    2) (1/4, 1/3, 1/2) (1, 1, 1) | ]

    29          [ (1, 1, 1) (1, 1, 1) (2, 3, 4) | (1, 1,      1,78
                 1) (1, 1, 1) (1, 2, 3) | (1/4, 1/3, 1/
                     2) (1/3, 1/2, 1) (1, 1, 1) | ]

    30          [ (1, 1, 1) (1, 1, 1) (3, 4, 5) | (1, 1,      0,00
                 1) (1, 1, 1) (3, 4, 5) | (1/5, 1/4, 1/
                    3) (1/5, 1/4, 1/3) (1, 1, 1) | ]

    31           [ (1, 1, 1) (1, 2, 3) (2, 3, 4) | (1/3,      0,96
                 1/2, 1) (1, 1, 1) (1, 2, 3) | (1/4, 1/
                  3, 1/2) (1/3, 1/2, 1) (1, 1, 1) | ]

    32           [ (1, 1, 1) (1, 1, 1) (1/5, 1/4, 1/3) |      0,75
                  (1, 1, 1) (1, 1, 1) (1/6, 1/5, 1/4) |
                   (3, 4, 5) (4, 5, 6) (1, 1, 1) | ]

    33          [ (1, 1, 1) (1, 1, 1) (1, 2, 3) | (1, 1,      0,00
                 1) (1, 1, 1) (1, 2, 3) | (1/3, 1/2, 1)
                      (1/3, 1/2, 1) (1, 1, 1) | ]

    34          [ (1, 1, 1) (1, 1, 1) (4, 5, 6) | (1, 1,      0,00
                 1) (1, 1, 1) (4, 5, 6) | (1/6, 1/5, 1/
                    4) (1/6, 1/5, 1/4) (1, 1, 1) | ]

Table 7. Results

Alternative    Fuzzy AHP    Clasical AHP

    A 1          0,4262        0,3868
    A 2          0,4244        0,3962
    A 3          0,1492        0,2168