The quick changes that occur nowadays enhance the uncertainty around business and make decision-making more difficult. Real-world issues typically have complicated structures and rely on various criteria and options. As a result, fuzzy and MCDM approaches are gaining popularity. The purpose of this research is to assist a small company in selecting the best server. The fuzzy TOPSIS approach is used to manage the linguistic factors utilized by decision-makers to address the company’s difficulty in selecting a suitable server. The criteria established by the decision-makers were considered in the study and five servers were analyzed to find the most suited one.

Аннотация статьи
fuzzy logic
fuzzy decision-making
server selection
TOPSIS
fuzzy distance
closeness
Ключевые слова

Introduction

In today’s dynamic environment, companies must make appropriate decisions to keep the organization stable, achieve and maintain any competitive advantage. Most businesses recognize the value of intercompany relationships in maintaining a competitive structure and increasing market share. As a result, companies began to re-establish their relationships with providers and consumers based on partnership and the creation of shared values. The partnership formed with suppliers provides advantages for both quality improvement and cost-saving, while also boosting production flexibility.

Choosing a server is a decision-making problem that considers many criteria to obtain a result. As the complexity of the problem increases, it is getting harder to make the correct decision. To solve this kind of problem, scientific methods have become a requirement.

The goal of this study is to help a company choose the right server considering the given criteria. For this problem, the TOPSIS problem is recommended, as this problem is one of multi-criteria decision-making methods. The Fuzzy TOPSIS helps choose the right alternative based on the linguistic variables.

Definition of a problem

The selection of a server is a complex problem because we have to make a decision based on multiple criteria. There are two types of criteria. They are objective and subjective criteria.

Objective criteria are measurable. As objective criteria following are used in the server selection problem [2]:

  • Price (AZN)
  • RAM capacity (GB)
  • Processor speed (GHz)
  • Number of cores
  • Hard disk capacity (TB)

Subjective criteria aren’t measurable like objective ones. They are defined based on expert reviews and experience. As subjective criteria following are used in the server selection problem:

  • Reliability
  • Security
  • Scalability
  • Quality of services

To solve this problem, we propose the fuzzy TOPSIS method is used. There are 7 stages of the TOPSIS method. They are:

1. Define linguistic variables for both criteria and the decision (table 1, table 2).

Table 1

Linguistic variables for criteria

Linguistic variables

Triangular fuzzy numbers

Very Low(VL)

(1,1,3)

Low(L)

(1,3,5)

Medium(M)

(3,5,7)

High(H)

(5,7,9)

Very High(VH)

(7,9,9)

Table 2

Linguistic variables for decision

Linguistic variables

Triangular fuzzy numbers

Very Low(VL)

(0.1,0.1,0.1,0.3)

Low(L)

(0.1, 0.3, 0.5)

Medium(M)

(0.3, 0.5, 0.7)

High(H)

(0.5, 0.7, 0.9)

Very High(VH)

(0.7, 0.9, 0.9)

2. The decision matrix has to be normalized using the following formula [3, 4]:

 =  

3. This step is called a “normalized matrix”. The weight is defined as wj=(w1, w2, …, wn). wj  is the criteria for all j from 1 to n. The normalization of the matrix is denoted with the V. Vij  = wj* rij

4. In the 3rd step, we have to determine the ideal solution matrix of both the positive ideal and negative ideal [5]. The formula is as follows:

, i = 1, 2, … m

, i = 1, 2, … m

5. In this step, the separation is calculated [6].

Ideal separation:

Negative separation:

6. The positive ideal solution is calculated with the following formula [7, 8]:

7. In the final step, we have to rank the solution. The solution with the highest value of CCi  is the best solution.

8. Acceptance criteria (table 3).

Table 3

Acceptance criteria

Closeness Coefficient (CCi)

Evaluation

Not recommended

Recommended with high risk

Recommended with low risk

Acceptable

Accepted and preferred

Practical example. In this example, we are going to consider server selection problem 9 criteria and 5 alternatives.

C1-Price (AZN)

C2- RAM capacity (GB)

C3-Processor speed (GHz)

C4-Number of cores

C5-Hard disk capacity (TB)

C6-Reliability

C7-Security

C8-Scalability

C9-Quality of services

1. Representation of linguistic decision matrix (table 4).

Table 4

Linguistic decision matrix

 

A1

A2

A3

A4

A5

C1

L

M

H

L

VH

C2

M

H

VH

VL

H

C3

H

M

M

H

VH

C4

M

VH

H

M

VH

C5

L

M

VH

M

VH

C6

VL

H

M

L

VH

C7

M

VL

H

M

H

C8

H

M

L

M

L

C9

M

H

VH

H

M

The weight importance vector is: w=(H,VH,M,L,H,M,VH,L,H)

2. Convert linguistic variables into triangular fuzzy numbers (table 5).

Table 5

Triangular fuzzy numbers presentation 

 

A1

A2

A3

A4

A5

C1

(1,1,3)

(3,5,7)

(5,7,9)

(1,3,5)

(7,9,9)

C2

(3,5,7)

(5,7,9)

(7,9,9)

(1,1,3)

(5,7,9)

C3

(5,7,9)

(3,5,7)

(3,5,7)

(5,7,9)

(7,9,9)

C4

(3,5,7)

(7,9,9)

(5,7,9)

(3,5,7)

(7,9,9)

C5

(1,3,5)

(3,5,7)

(7,9,9)

(3,5,7)

(7,9,9)

C6

(1,1,3)

(5,7,9)

(3,5,7)

(1,3,5)

(7,9,9)

C7

(3,5,7)

(1,1,3)

(5,7,9)

(3,5,7)

(5,7,9)

C8

(5,7,9)

(3,5,7)

(1,3,5)

(3,5,7)

(1,3,5)

C9

(3,5,7)

(5,7,9)

(7,9,9)

(5,7,9)

(3,5,7)

3. Normalized fuzzy decision-matrix is calculated by the given formula (table 6).

Table 6

Normalized fuzzy decision-matrix

 

A1

A2

A3

A4

A5

C1

(0.33,1,1)

(0.14,0.2,0.33)

(0.11,0.14,0.2)

(0.2,0.33,1)

(0.11,0.11,0.14)

C2

(0.33,0.56,0.78)

(0.56,0.78,1)

(0.78,1,1)

(0.11,0.11,0.33)

(0.56,0.78,1)

C3

(0.56,0.78,1)

(0.33,0.56,0.78)

(0.33,0.56,0.78)

(0.56,0.78,1)

(0.78,1,1)

C4

(0.33,0.56,0.78)

(0.78,1,1)

(0.56,0.78,1)

(0.33,0.56,0.78)

(0.78,1,1)

C5

(0.11,0.33,0.56)

(0.33,0.56,0.78)

(0.78,1,1)

(0.33,0.56,0.78)

(0.78,1,1)

C6

(0.11,0.11,0.33)

(0.56,0.78,1)

(0.33,0.56,0.78)

(0.11,0.33,0.56)

(0.78,1,1)

C7

(0.33,0.56,0.78)

(0.11,0.11,0.33)

(0.56,0.78,1)

(0.33,0.56,0.78)

(0.56,0.78,1)

C8

(0.56,0.78,1)

(0.33,0.56,0.78)

(0.11,0.33,0.56)

(0.33,0.56,0.78)

(0.11,0.33,0.56)

C9

(0.33,0.56,0.78)

(0.56,0.78,1)

(0.78,1,1)

(0.56,0.78,1)

(0.33,0.56,0.78)

4. The weighted normalized decision matrix is calculated (table 7).

Table 7

Weighted normalized decision matrix

 

A1

A2

A3

A4

A5

C1

(0.17,0.7,0.9)

(0.07,0.14,0.3)

(0.06,0.1,0.18)

(0.1,0.23,0.9)

(0.06,0.08,0.13)

C2

(0.23,0.5,0.7)

(0.39,0.7,0.9)

(0.54,0.9,0.9)

(0.08,0.1,0.3)

(0.39,0.7,0.9)

C3

(0.17,0.39,0.7)

(0.1,0.28,0.54)

(0.1,0.28,0.54)

(0.17,0.39,0.7)

(0.23,0.5,0.7)

C4

(0.03,0.17,0.39)

(0.08,0.3,0.5)

(0.06,0.23,0.5)

(0.03,0.17,0.39)

(0.08,0.3,0.5)

C5

(0.06,0.23,0.5)

(0.17,0.39,0.7)

(0.39,0.7,0.9)

(0.17,0.39,0.7)

(0.39,0.7,0.9)

C6

(0.03,0.06,0.23)

(0.17,0.39,0.7)

(0.1,0.28,0.54)

(0.03,0.17,0.39)

(0.23,0.5,0.7)

C7

(0.23,0.5,0.7)

(0.08,0.1,0.3)

(0.39,0.7,0.9)

(0.23,0.5,0.7)

(0.39,0.7,0.9)

C8

(0.06,0.23,0.5)

(0.03,0.17,0.39)

(0.01,0.1,0.28)

(0.03,0.17,0.39)

(0.01,0.1,0.28)

C9

(0.17,0.39,0.7)

(0.28,0.54,0.9)

(0.39,0.7,0.9)

(0.28,0.54,0.9)

(0.17,0.39,0.7)

5. The distance between the decisions is calculated (table 8).

Table 8

Distance between the decisions

 

C1

C2

C3

C4

C5

d(A1,A+)

0.44

0.46

0.36

0.34

0.66

d(A2,A+)

0.74

0.32

0.43

0.27

0.53

d(A3,A+)

0.79

0.21

0.43

0.30

0.32

d(A4,A+)

0.60

0.75

0.36

0.34

0.53

d(A5,A+)

0.81

0.32

0.29

0.27

0.32

d(A1,A-)

0.62

0.44

0.39

0.22

0.28

d(A2,A-)

0.15

0.62

0.28

0.31

0.42

d(A3,A-)

0.08

0.72

0.28

0.29

0.64

d(A4,A-)

0.50

0.13

0.39

0.22

0.42

d(A5,A-)

0.04

0.62

0.42

0.31

0.64

 

C6

C7

C8

C9

d(A1,A+)

0.60

0.46

0.30

0.53

d(A2,A+)

0.36

0.75

0.34

0.41

d(A3,A+)

0.43

0.32

0.39

0.32

d(A4,A+)

0.52

0.46

0.34

0.41

d(A5,A+)

0.29

0.32

0.39

0.53

d(A1,A-)

0.12

0.44

0.31

0.33

d(A2,A-)

0.44

0.13

0.24

0.48

d(A3,A-)

0.33

0.62

0.16

0.54

d(A4,A-)

0.22

0.44

0.24

0.48

d(A5,A-)

0.48

0.62

0.16

0.33

As the final step, the closeness coefficient is calculated by the given formula (table 9.)

Table 9

Closeness coefficients

 

CCi

Ranking

A1

4.15

3.15

0.431

3

A2

4.14

3.07

0.426

4

A3

3.50

3.66

0.512

2

A4

4.31

3.04

0.413

5

A5

3.54

3.64

0.508

1

According to the acceptance criteria  A5 is the optimal decision.

Conclusion

The topic of MCDM for server selection is the focus of this essay. In today’s environment, companies need to choose the right server among many decisions. The right server is a server that has the lowest price and the best quality. The selection process is complex because there are uncertainties as the decision-makers are individuals. An examination of known strategies for resolving this challenge is provided. The fuzzy TOPSIS approach is utilized to solve this problem. The challenges of the actual application of this approach are thoroughly examined. The server selection problem with 9 criteria and 5 choices is viewed as a practical challenge. The criteria were price, ram capacity, processor speed, number of cores, hard disk capacity, reliability, security, scalability, and quality of service. After the closeness coefficient is calculated, it shows that A5 is the best alternative among other given alternatives. For that reason, it is recommended for small businesses to choose that alternative. The solution’s findings at each stage are provided.

Текст статьи
  1. A comprehensive literature review on methodologies and applications. European Journal Operational Research, 200, 198–215.
  2. Behzadian, M., Khanmohammadi Otaghsara, S., Yazdani, M., & Ignatius, J. (2012).
  3. Čančer, V. Why and how to deal with complexity by quantitative computer-supported methods. In 17th International Conference on Information and Intelligent Systems, Conference Proceedings, pages 147-153, Faculty of Organisation and Informatics, Varaždin, 2010.
  4. Čančer, V. A-Frame Procedure for Multi-criteria Decision-making: Formulation and Applications. KOI 2008 Proceedings, Croatian Operational Research Society, Pula, Zagreb, forthcoming.
  5. Sridhar, P., Madni, A. M., Jamshidi, M. Multi-Criteria Decision Making in Sensor Networks. IEEE Instrumentation & Measurement Magazine, February: 24-29, 2010.
  6. Interactive TOPSIS algorithms for solving multi-level non-linear multi-objective decision-making problems.Applied Mathematical Modelling, 38, 1417–1433.Baky, I. & Abo-Sinna, M. A. (2013)
  7. An integrated multi-criteria decision-making methodology for outsourcing management.Computers & Operations Research, 34,3738–3756.Ataei, M., Shahsavany, H., & Mikaeil, R. (2013).
  8. Kelemenis, A. and Askounis, D. (2010). A New TOPSIS-Based Multi-Criteria Approach To Personel Selection, Expert Systems with Applications, 37(7), 4999-5008
  9. Seyedmohammadi, J., Sarmadian, F., Jafarzadeh, AA, Ghorban i, MA, & Shahbazi, F. Application of SAW, TOPSIS and fuzzy TOPSIS models in cultivation priority planning for maize, rapeseed and soybean crops. Geoderma, 310, 178-190, 2018.
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