# A Spherical Fuzzy Multi-Criteria Decision-Making Model for Industry 4.0 Performance Measurement

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Spherical Fuzzy Sets

#### 3.2. SF-AHP-WSM Methodology

**Step 1.**Creation of Hierarchical Structure: In this step, the hierarchical structure of the problem is created, as given in Figure 1. The goal, criteria, sub-criteria, and SMEs to be evaluated are determined. If there is a group decision, the decision-making group is selected at this stage.

**Step 2.**Creation of pairwise comparison matrices: Pairwise comparison matrices are evaluated by decision makers according to the linguistic measurements, which are given in Table 1.

**Step 3.**Calculation of the consistency ratio (CR): SI values are calculated by using Equation (15).

**Step 4.**Calculation of local fuzzy weights: SWAM operator, given in Equation (18), is used to calculate fuzzy weight values from pairwise comparison tables.

**Step 5.**Defuzzification of fuzzy weights: The defuzzification formula is given in Equation (19).

**Step 6.**Calculation of global weights: Global weights are obtained from defuzzified local weights.

**Step 7.**Evaluation of the Industry 4.0 performance score by using WSM: In the last step, the weighted performance score of the enterprise is calculated. This method allows researchers to evaluate and score more than one enterprise at the same time. If there is more than one candidate, the companies can be ranked.

## 4. Application

## 5. Conclusions and Future Works

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Henning, K.; Wolfgang, W.; Johannes, H. Recommendations for Implementing the Strategic Initiative INDUSTRIE 4.0. Final. Rep. Ind.
**2013**, 4, 82. [Google Scholar] - Sung, T.K. Industry 4.0: A Korea Perspective. Technol. Forecast. Soc. Change
**2018**, 132, 40–45. [Google Scholar] [CrossRef] - Sevinc, E. A Novel Evolutionary Algorithm for Data Classification Problem with Extreme Learning Machines. IEEE Access
**2019**, 7, 122419–122427. [Google Scholar] [CrossRef] - Stock, T.; Seliger, G. Opportunities of Sustainable Manufacturing in Industry 4.0. Procedia CIRP
**2016**, 40, 536–541. [Google Scholar] [CrossRef] [Green Version] - Beltrami, M.; Orzes, G.; Sarkis, J.; Sartor, M. Industry 4.0 and Sustainability: Towards Conceptualization and Theory. J. Clean. Prod.
**2021**, 312, 127733. [Google Scholar] [CrossRef] - Liao, Y.; Deschamps, F.; de Loures, E.F.R.; Ramos, L.F.P. Past, Present and Future of Industry 4.0—A Systematic Literature Review and Research Agenda Proposal. Int. J. Prod. Res.
**2017**, 55, 3609–3629. [Google Scholar] [CrossRef] - Frederico, G.F.; Garza-Reyes, J.A.; Kumar, A.; Kumar, V. Performance Measurement for Supply Chains in the Industry 4.0 Era: A Balanced Scorecard Approach. Int. J. Product. Perform. Manag.
**2021**, 70, 789–807. [Google Scholar] [CrossRef] - Kamble, S.S.; Gunasekaran, A.; Ghadge, A.; Raut, R. A Performance Measurement System for Industry 4.0 Enabled Smart Manufacturing System in SMMEs—A Review and Empirical Investigation. Int. J. Prod. Econ.
**2020**, 229, 107853. [Google Scholar] [CrossRef] - Büyüközkan, G.; Feyzioğlu, O.; Havle, C.A. Analysis of Success Factors in Aviation 4.0 Using Integrated Intuitionistic Fuzzy MCDM Methods. In Proceedings of the Advances in Intelligent Systems and Computing; Springer: Berlin/Heidelberg, Germany, 2020; Volume 1029, pp. 598–606. [Google Scholar]
- Veza, I.; Celar, S.; Peronja, I. Competences-Based Comparison and Ranking of Industrial Enterprises Using PROMETHEE Method. Procedia Eng.
**2015**, 100, 445–449. [Google Scholar] [CrossRef] [Green Version] - Medic, N.; Marjanovic, U.; Zivlak, N.; Anisic, Z.; Lalic, B. Hybrid Fuzzy MCDM Method for Selection of Organizational Innovations in Manufacturing Companies. In Proceedings of the TEMS-ISIE 2018—1st Annual International Symposium on Innovation and Entrepreneurship of the IEEE Technology and Engineering Management Society, Beijing, China, 30 March–1 April 2018. [Google Scholar]
- Kazancoglu, Y.; Ozkan-Ozen, Y.D. Analyzing Workforce 4.0 in the Fourth Industrial Revolution and Proposing a Road Map from Operations Management Perspective with Fuzzy DEMATEL. J. Enterp. Inf. Manag.
**2018**, 31, 891–907. [Google Scholar] [CrossRef] - Hassanpour, M.; Pamučar, D. Evaluation of Iranian Household Appliance Industries Using MCDM Models. Oper. Res. Eng. Sci. Theory Appl.
**2019**, 2, 1–25. [Google Scholar] [CrossRef] - Ante, G.; Facchini, F.; Mossa, G.; Digiesi, S. Developing a Key Performance Indicators Tree for Lean and Smart Production Systems. IFAC-Pap.
**2018**, 51, 13–18. [Google Scholar] [CrossRef] - Lopes, M.A.; Martins, R.A. Mapping the Impacts of Industry 4.0 on Performance Measurement Systems. IEEE Lat. Am. Trans.
**2021**, 19, 1912–1923. [Google Scholar] [CrossRef] - Kloviene, L.; Uosyte, I. Development of Performance Measurement System in the Context of Industry 4.0: A Case Study. Eng. Econ.
**2019**, 30, 472–482. [Google Scholar] [CrossRef] [Green Version] - Xie, Y.; Yin, Y.; Xue, W.; Shi, H.; Chong, D. Intelligent Supply Chain Performance Measurement in Industry 4.0. Syst. Res. Behav. Sci.
**2020**, 37, 711–718. [Google Scholar] [CrossRef] - Yin, Y.; Qin, S.F. A Smart Performance Measurement Approach for Collaborative Design in Industry 4.0. Adv. Mech. Eng.
**2019**, 11, 1687814018822570. [Google Scholar] [CrossRef] [Green Version] - Sriram, R.M.; Vinodh, S. Analysis of Readiness Factors for Industry 4.0 Implementation in SMEs Using COPRAS. Int. J. Qual. Reliab. Manag.
**2021**, 38, 1178–1192. [Google Scholar] [CrossRef] - Vinodh, S.; Wankhede, V.A. Application of Fuzzy DEMATEL and Fuzzy CODAS for Analysis of Workforce Attributes Pertaining to Industry 4.0: A Case Study. Int. J. Qual. Reliab. Manag.
**2020**, 38, 1695–1721. [Google Scholar] [CrossRef] - Gupta, H.; Kumar, A.; Wasan, P. Industry 4.0, Cleaner Production and Circular Economy: An Integrative Framework for Evaluating Ethical and Sustainable Business Performance of Manufacturing Organizations. J. Clean. Prod.
**2021**, 295, 126253. [Google Scholar] [CrossRef] - Watróbski, J.; Sałabun, W. The Characteristic Objects Method: A New Intelligent Decision Support Tool for Sustainable Manufacturing. In Proceedings of the Smart Innovation, Systems and Technologies; Springer: Berlin/Heidelberg, Germany, 2016; Volume 52, pp. 349–359. [Google Scholar]
- Kizielewicz, B.; Shekhovtsov, A.; Sałabun, W. A New Approach to Eliminate Rank Reversal in the MCDA Problems. In Proceedings of the Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Springer: Berlin/Heidelberg, Germany, 2021; Volume 12742 LNCS, pp. 338–351. [Google Scholar]
- Faizi, S.; Sałabun, W.; Ullah, S.; Rashid, T.; Wieckowski, J. A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique. Symmetry
**2020**, 12, 516. [Google Scholar] [CrossRef] [Green Version] - Rehman, A.U.; Shekhovtsov, A.; Rehman, N.; Faizi, S.; Sałabun, W. On the Analytic Hierarchy Process Structure in Group Decision-Making Using Incomplete Fuzzy Information with Applications. Symmetry
**2021**, 13, 609. [Google Scholar] [CrossRef] - Saaty, T.L. The Analytic Hierarchy Process. Education
**1980**, 1–11. [Google Scholar] [CrossRef] - Eraslan, E. A Multi-Criteria Usability Assessment of Similar Types of Touch Screen Mobile Phones. J. Multi-Criteria Decis. Anal.
**2013**, 20, 185–195. [Google Scholar] [CrossRef] - Balaji, K.; Kumar, V.S.S. Multicriteria Inventory ABC Classification in an Automobile Rubber Components Manufacturing Industry. Procedia CIRP
**2014**, 17, 463–468. [Google Scholar] [CrossRef] [Green Version] - Vaidya, O.S.; Kumar, S. Analytic Hierarchy Process: An Overview of Applications. Eur. J. Oper. Res.
**2006**, 169, 1–29. [Google Scholar] [CrossRef] - Kahraman, C.; Onar, S.C.; Oztaysi, B. Fuzzy Multicriteria Decision-Making: A Literature Review. Int. J. Comput. Intell. Syst.
**2015**, 8, 637–666. [Google Scholar] [CrossRef] [Green Version] - Zadeh, L.A. Fuzzy Sets. Inf. Control.
**1965**, 8, 338–353. [Google Scholar] [CrossRef] [Green Version] - Zadeh, L.A. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning-I. Inf. Sci.
**1975**, 8, 199–249. [Google Scholar] [CrossRef] - Atanassov, K.T. Intuitionistic Fuzzy Sets. Fuzzy Sets Syst.
**1986**, 20, 87–96. [Google Scholar] [CrossRef] - Yager, R.R. On the Theory of Bags. Int. J. Gen. Syst.
**1986**, 13, 23–37. [Google Scholar] [CrossRef] - Atanassov, K.T. More on Intuitionistic Fuzzy Sets. Fuzzy Sets Syst.
**1989**, 33, 37–45. [Google Scholar] [CrossRef] - Smarandache, F. Neutrosophic Set—A Generalization of the Intuitionistic Fuzzy Set. In Proceedings of the 2006 IEEE International Conference on Granular Computing, Atlanta, GA, USA, 10–12 May 2006; pp. 38–42. [Google Scholar]
- Garibaldi, J.M.; Ozen, T. Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making. IEEE Trans. Fuzzy Syst.
**2007**, 15, 16–30. [Google Scholar] [CrossRef] - Torra, V. Hesitant Fuzzy Sets. Int. J. Intell. Syst.
**2010**, 25, 529–539. [Google Scholar] [CrossRef] - Yager, R.R. Pythagorean Membership Grades in Multicriteria Decision Making. IEEE Trans. Fuzzy Syst.
**2014**, 22, 958–965. [Google Scholar] [CrossRef] - Yager, R.R. Generalized Orthopair Fuzzy Sets. IEEE Trans. Fuzzy Syst.
**2017**, 25, 1222–1230. [Google Scholar] [CrossRef] - Gündoğdu, F.K.; Kahraman, C. Spherical Fuzzy Sets and Spherical Fuzzy TOPSIS Method. J. Intell. Fuzzy Syst.
**2019**, 36, 337–352. [Google Scholar] [CrossRef] - Mendel, J.M.; Wu, H. Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems. IEEE Trans. Fuzzy Syst.
**2006**, 14, 781–792. [Google Scholar] [CrossRef] - Rouyendegh, B.D.; Oztekin, A.; Ekong, J.; Dag, A. Measuring the Efficiency of Hospitals: A Fully-Ranking DEA–FAHP Approach. Ann. Oper. Res.
**2019**, 278, 361–378. [Google Scholar] [CrossRef] - Ashraf, S.; Abdullah, S.; Mahmood, T.; Ghani, F.; Mahmood, T. Spherical Fuzzy Sets and Their Applications in Multi-Attribute Decision Making Problems. J. Intell. Fuzzy Syst.
**2019**, 36, 2829–2844. [Google Scholar] [CrossRef] - Ayyildiz, E.; Taskin Gumus, A. A Novel Spherical Fuzzy AHP-Integrated Spherical WASPAS Methodology for Petrol Station Location Selection Problem: A Real Case Study for İstanbul. Environ. Sci. Pollut. Res.
**2020**, 27, 36109–36120. [Google Scholar] [CrossRef] - Gündoğdu, F.K.; Kahraman, C. Spherical Fuzzy Analytic Hierarchy Process (AHP) and Its Application to Industrial Robot Selection. In Proceedings of the Advances in Intelligent Systems and Computing; Springer: Berlin/Heidelberg, Germany, 2020. [Google Scholar]
- Gündoğdu, F.K.; Kahraman, C. A Novel Spherical Fuzzy Analytic Hierarchy Process and Its Renewable Energy Application. Soft Comput.
**2020**, 24, 4607–4621. [Google Scholar] [CrossRef] - Saaty, T.L. Decision Making with the Analytic Hierarchy Process. Int. J. Serv. Sci.
**2008**, 1, 83–98. [Google Scholar] [CrossRef] [Green Version] - Yildizbasi, A.; Erdebilli, B.; Barış, Ö.Z.E.N.; Özdemir, Y.S. Evaluation of Augmented Reality Tools Performance in Digital Supply Chain Management: A Group Decision Making Method. Eur. J. Sci. Technol.
**2021**, 149–162. [Google Scholar] [CrossRef] - Rodriguez, R.M.; Martinez, L.; Herrera, F. Hesitant Fuzzy Linguistic Term Sets for Decision Making. IEEE Trans. Fuzzy Syst.
**2012**, 20, 109–119. [Google Scholar] [CrossRef] - Yıldızbaşı, A.; Ünlü, V. Performance Evaluation of SMEs towards Industry 4.0 Using Fuzzy Group Decision Making Methods. SN Appl. Sci.
**2020**, 2, 355. [Google Scholar] [CrossRef] [Green Version]

**Table 1.**SF-AHP preference scale for pairwise comparisons [47].

Linguistic Measurement | $\left(\mathit{\mu},\mathit{v},\mathit{\pi}\right)$ | Score Index (SI) |
---|---|---|

Absolutely More Important (AMI) | (0.9, 0.1, 0.0) | 9 |

Very High Important (VHI) | (0.8, 0.2, 0.1) | 7 |

High Important (HI) | (0.7, 0.3, 0.2) | 5 |

Slightly More Important (SMI) | (0.6, 0.4, 0.3) | 3 |

Equally Important (EI) | (0.5, 0.4, 0.4) | 1 |

Slightly Low Important (SLI) | (0.4, 0.6, 0.3) | 1/3 |

Low Important (LI) | (0.3, 0.7, 0.2) | 1/5 |

Very Low Important (VLI) | (0.2, 0.8, 0.1) | 1/7 |

Absolutely Low Important (ALI) | (0.1, 0.9, 0.0) | 1/9 |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|

0.00 | 0.00 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |

Main Criteria | Sub Criteria | Explanation |
---|---|---|

C1—Software | C11—ERP Software | Efficiency of Enterprise Resource Planning (ERP) software implementation. |

C12—Cyber Security | Taking cybersecurity measures. | |

C13—Cloud Computing | Cloud and cloud computing applications used in the operations. | |

C14—Software Solutions | Using software solutions for specific requirements. | |

C2—Production | C21—Process Simulation | Simulation usage in the production processes. |

C22—IoT | IoT device usage in the production line. | |

C23—Autonomous Robots | Autonomous robot usage in the production line. | |

C24—Information Share | ERP software package utilized to share information between different functional areas. | |

C3—External Stakeholders | C31—Customer Relations | Using software for Customer Relationship Management (CRM). |

C32—Public Relations | Using the internet or digital platforms for communication with public institutions. | |

C33—Digital Supply Chain | Sharing supply chain management information with software. | |

C34—Online Orders | Receive orders online. |

Main Criteria | Software | Production | External Stakeholders |
---|---|---|---|

Software | EI | EI | SMI |

Production | EI | EI | SMI |

External Stakeholders | SLI | SLI | EI |

Main Criteria | $\mu $ | $v$ | $\pi $ | Weight |
---|---|---|---|---|

Software | 0.5372 | 0.4000 | 0.3675 | 0.3638 |

Production | 0.5111 | 0.4309 | 0.3667 | 0.3442 |

External Stakeholders | 0.4372 | 0.5241 | 0.3413 | 0.2920 |

Software | $\mu $ | $v$ | $\pi $ | Local Weight |
---|---|---|---|---|

ERP Software | 0.5284 | 0.4000 | 0.3756 | 0.2626 |

Cyber Security | 0.5715 | 0.3936 | 0.3254 | 0.2930 |

Cloud Computing | 0.4870 | 0.4681 | 0.3536 | 0.2422 |

Software Solutions | 0.4086 | 0.5635 | 0.3162 | 0.2022 |

Production | $\mu $ | $v$ | $\pi $ | Local Weight |
---|---|---|---|---|

Process Simulation | 0.4362 | 0.5091 | 0.3456 | 0.2078 |

IoT | 0.6621 | 0.3224 | 0.2532 | 0.3409 |

Autonomous Robots | 0.5224 | 0.4601 | 0.3153 | 0.2582 |

Information Share | 0.4086 | 0.5384 | 0.3431 | 0.1930 |

External Stakeholders | $\mu $ | $v$ | $\pi $ | Local Weight |
---|---|---|---|---|

Customer Relations | 0.5877 | 0.3722 | 0.3269 | 0.2939 |

Public Relations | 0.5471 | 0.4120 | 0.3298 | 0.2713 |

Digital Supply Chain | 0.5284 | 0.4162 | 0.3498 | 0.2588 |

Online Orders | 0.3646 | 0.6086 | 0.2785 | 0.1760 |

Sub Criteria | Global Weight | SME1 | SME2 | SME3 | SME4 | SME5 |
---|---|---|---|---|---|---|

ERP Software | 0.0955 | 0.8284 | 0.7329 | 0.8915 | 0.8599 | 0.7959 |

Cyber Security | 0.1066 | 0.8176 | 0.7110 | 0.9594 | 0.8528 | 0.9242 |

Cloud Computing | 0.0881 | 0.4697 | 0.6169 | 0.6759 | 0.5578 | 0.7341 |

Software Solutions | 0.0736 | 0.4171 | 0.5642 | 0.6128 | 0.5149 | 0.6620 |

Process Simulation | 0.0715 | 0.4291 | 0.5957 | 0.5721 | 0.5485 | 0.4055 |

IoT | 0.1173 | 0.8601 | 0.8214 | 0.9387 | 0.9774 | 0.9000 |

Autonomous Robots | 0.0889 | 0.5626 | 0.3848 | 0.8292 | 0.8594 | 0.3848 |

Information Share | 0.0664 | 0.4651 | 0.5760 | 0.5760 | 0.6424 | 0.4205 |

Customer Relations | 0.0858 | 0.6865 | 0.7723 | 0.5432 | 0.8006 | 0.5432 |

Public Relations | 0.0792 | 0.7393 | 0.6600 | 0.7131 | 0.2908 | 0.4754 |

Digital Supply Chain | 0.0756 | 0.5539 | 0.5796 | 0.6295 | 0.4285 | 0.6801 |

Online Orders | 0.0514 | 0.4455 | 0.4281 | 0.4625 | 0.3767 | 0.4111 |

Industry 4.0 Performance Score: | 7.2748 | 7.4429 | 8.4038 | 7.7099 | 7.3369 |

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**MDPI and ACS Style**

Ozdemir, Y.S.
A Spherical Fuzzy Multi-Criteria Decision-Making Model for Industry 4.0 Performance Measurement. *Axioms* **2022**, *11*, 325.
https://doi.org/10.3390/axioms11070325

**AMA Style**

Ozdemir YS.
A Spherical Fuzzy Multi-Criteria Decision-Making Model for Industry 4.0 Performance Measurement. *Axioms*. 2022; 11(7):325.
https://doi.org/10.3390/axioms11070325

**Chicago/Turabian Style**

Ozdemir, Yavuz Selim.
2022. "A Spherical Fuzzy Multi-Criteria Decision-Making Model for Industry 4.0 Performance Measurement" *Axioms* 11, no. 7: 325.
https://doi.org/10.3390/axioms11070325