# 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

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**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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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