Taguchi Loss Function in Intuitionistic Fuzzy Sets along with Personal Perceptions for the Sustainable Supplier Selection Problem
Abstract
:1. Introduction
- Compare theory and reality of sustainability.
- Investigate personal perceptions of decision makers to tackle negative effects on evaluations of suppliers using eight criteria related to personal perception.
- Find the best sustainable supplier considering six main criteria and seventeen sub-criteria determined by three decision makers.
- Provide an alternative way to calculate the distance between ideal positive and negative of intuitionistic fuzzy sets using the Taguchi loss function.
- Validate the proposed distance measurement approach, comparing Taguchi loss function with the intuitionistic fuzzy normalised Euclidean distance.
2. Background
2.1. Applications on Sustainable Supplier Selection
2.2. Applications on Personal Perception
3. Material and Methods
3.1. Intuitionistic Fuzzy Sets
3.2. Definition of Criteria
3.3. Problem Statement
- For the second scenario, in order to assign the weight of each decision maker, eight criteria related to the personal perception are used. The linguistic terms and their corresponding intuitionistic fuzzy numbers shown in Table 5 are used to calculate their weights. It is assumed that the importance of each criterion is equal and Equation (11) is applied to calculate the decision makers ‘weights for each criterion to achieve the mean score for each decision maker. These scores are averaged and are assigned as the weights of the decision makers.
- For the third scenario, it is assumed that the weights of all decision makers are equal to each other, and the sum of their weight is equal to 1.
3.4. Notations
4. Preliminary Experiments and Results
4.1. Application of the Method Proposed
- For the first scenario, the linguistic evaluation of decision makers is performed assigning ‘Very important’ (VI) for the first decision maker (DM1), ‘Important’ (I) for the second decision maker (DM2) and ‘Medium’ (M) for the third decision maker (DM3). Equation (7) is used to calculate their weights, and they are found to be 0.38, 0.35 and 0.27, respectively.
- For the second scenario, decision makers are examined in terms of eight criteria, as shown in Table 7. Decision makers’ weights are calculated using Equation (7) for each decision maker, and the mean value is taken as a weight for each decision maker. It is found that the weight of DM1 is 0.32, the weight of DM2 is 0.40, and the weight of DM3 is 0.29.
- For the third scenario, their weights are defined equally as 0.33, 0.33 and 0.33 in the same sequence.
4.2. Results and Comparative Analysis
5. Discussion
6. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Sectors | Methods |
---|---|
Electronics industry [16] | Analytic Network Process (ANP) |
Construction industry [17] | Fuzzy inference system |
Telecommunication industry [18] | Combination of Grey Relational Analysis and AHP |
Food packaging industry [19] | Multi-objective mathematical programming model along with TOPSIS |
Dairy product manufacturer [20] | Integration of two methods: ANP and TOP-SIS |
Auto side parts manufacturer [21] | Interval Type-2 Fuzzy set |
Home appliance manufacturer [22] | Combined method of fuzzy best–worst method and fuzzy CoCoOn with Bonferroni |
Vehicle transmission industry [23] | Integration of rough-fuzzy and TOP-SIS-DEMATEL |
Textile industry [24] | Fuzzy multi-period multi-objective method |
Petrochemical industry [25] | Fuzzy best–worst method with the fuzzy inference system |
Producing transport vehicles [26] | Intuitionistic fuzzy dissimilarity measure |
Authors | Enviromental Criteria | Social Criteria | Economic Criteria |
---|---|---|---|
[18] |
|
|
|
[19] |
|
|
|
[17] |
|
|
|
[16] |
| NONE |
|
[20] |
| NONE |
|
[25] |
|
|
|
[27] |
|
|
|
[22] |
|
|
|
[21] |
|
|
|
Sectors | Authors | Methodology |
---|---|---|
Food safety | [28] | Survey to find out the risk perceptions of consumers during the COVID-19 pandemic. |
Organic food | [29] | Interviews to analyze credibility effect on organic food consumption. |
Battery-electric vehicle | [30] | Questionnaire to generate purchase intentions model under different hypotheses. |
Battery-electric vehicle | [31] | Survey to assess consumer awareness of a particular car brand. |
Buyer–supplier relationships | [32] | Survey to explore the role of similarity and likeability on buyer–supplier relationships. |
Buyer–supplier interactions | [14] | Interviews to analyze supply chain professionals’ behaviors under different scenarios. |
Buyer–supplier attraction | [33] | Interviews to explore how congruence in perceptions of attraction affects relationship success. |
Supply chain attributes | [34] | Survey to explore dyadic buyer–supplier relationships and how attributes differ based on relations. |
Criteria | Symbol | Sub-Criteria | Symbol |
---|---|---|---|
Quality | M1 | Quality control rejection rate; Customer rejection rate. | C1 C2 |
Delivery | M2 | Delivery lead time; Delivery flexibility. | C3 C4 |
Service Performance | M3 | Reliability; Empathy. | C5 C6 |
Cost | M4 | Product price; Logistic cost. | C7 C8 |
Environmental sustainability | M5 | Environmental efficiency; Green image; Pollution reduction; Green competencies. | C9 C10 C11 C12 |
Social sustainability | M6 | Having OHSAS 18001 certification; Rate of health and safety incidents; Employee rights; Forced child labour; Staff training. | C13 C14 C15 C16 C17 |
Linguistic Variables | IFNs (μ, ϑ, π) |
---|---|
Very important (VI) | (1, 0, 0) |
Important (I) | (0.75, 0.20, 0.05) |
Medium (M) | (0.50, 0.40, 0.10) |
Unimportant (U) | (0.25, 0.60, 0.15) |
Very unimportant (VU) | (0.10, 0.80, 0.10) |
Notation | Meaning |
---|---|
Pi | The ith criterion to evaluate personal perception of decision makers where i = {1,…,8}. |
Mj | The jth main criterion to evaluate suppliers where j = {1,…,6}. |
Ck | The kth sub-criterion to evaluate suppliers where k = {1,…,16}. |
The weight of the lth alternatives where where l = {1,2,3}. | |
DMm | The mth decision maker |
The global score of the kth sub-criterion where k = {1,…,17}. | |
Importance of the kth sub-criterion where k = {1,…,17}. | |
Performance of alternative m for the kth sub-criterion. | |
Sn | The nth alternative (supplier). |
The nth supplier for Scenario x. |
Criterion | DM1 | DM2 | DM3 | Criterion | DM1 | DM2 | DM3 |
---|---|---|---|---|---|---|---|
P1 | VI | I | M | P5 | M | M | VI |
P2 | VI | I | M | P6 | VI | I | VI |
P3 | I | I | I | P7 | VI | M | M |
P4 | VI | VI | VI | P8 | I | I | VI |
Criterion | DM1 | DM2 | DM3 | Criterion | DM1 | DM2 | DM3 | Criterion | DM1 | DM2 | DM3 |
---|---|---|---|---|---|---|---|---|---|---|---|
M1 | VI | VI | M | C3 | M | M | M | C11 | M | VI | I |
M2 | VI | M | M | C4 | M | M | M | C12 | M | M | M |
M3 | M | VI | M | C5 | VI | M | M | C13 | M | VI | U |
M4 | VI | M | U | C6 | M | M | M | C14 | M | VI | VI |
M5 | M | VI | M | C7 | VI | M | U | C15 | M | M | VI |
M6 | M | M | M | C8 | VI | M | U | C16 | M | M | VI |
C1 | M | VI | I | C9 | M | VI | M | C17 | M | M | VI |
C2 | M | VI | I | C10 | M | M | M | - | - | - | - |
Importance of Criteria | DM1 | DM2 | DM3 | ||||||
---|---|---|---|---|---|---|---|---|---|
μ | ϑ | π | μ | ϑ | π | μ | ϑ | π | |
C1G | 0.50 | 0.40 | 0.10 | 1.00 | 0.00 | 0.00 | 0.38 | 0.52 | 0.11 |
C2G | 0.50 | 0.40 | 0.10 | 1.00 | 0.00 | 0.00 | 0.38 | 0.52 | 0.11 |
C3G | 0.50 | 0.40 | 0.10 | 0.25 | 0.64 | 0.11 | 0.25 | 0.64 | 0.11 |
C4G | 0.50 | 0.40 | 0.10 | 0.25 | 0.64 | 0.11 | 0.25 | 0.64 | 0.11 |
C5G | 0.50 | 0.40 | 0.10 | 0.50 | 0.40 | 0.10 | 0.25 | 0.64 | 0.11 |
C6G | 0.25 | 0.64 | 0.11 | 0.50 | 0.40 | 0.10 | 0.25 | 0.64 | 0.11 |
C7G | 1.00 | 0.00 | 0.00 | 0.25 | 0.64 | 0.11 | 0.06 | 0.84 | 0.10 |
C8G | 1.00 | 0.00 | 0.00 | 0.25 | 0.64 | 0.11 | 0.06 | 0.84 | 0.10 |
C9G | 0.25 | 0.64 | 0.11 | 1.00 | 0.00 | 0.00 | 0.25 | 0.64 | 0.11 |
C10G | 0.25 | 0.64 | 0.11 | 0.50 | 0.40 | 0.10 | 0.25 | 0.64 | 0.11 |
C11G | 0.25 | 0.64 | 0.11 | 1.00 | 0.00 | 0.00 | 0.38 | 0.52 | 0.11 |
C12G | 0.25 | 0.64 | 0.11 | 0.50 | 0.40 | 0.10 | 0.25 | 0.64 | 0.11 |
C13G | 0.75 | 0.20 | 0.05 | 0.50 | 0.40 | 0.10 | 0.13 | 0.76 | 0.12 |
C14G | 0.25 | 0.64 | 0.11 | 0.50 | 0.40 | 0.10 | 0.50 | 0.40 | 0.10 |
C15G | 0.25 | 0.64 | 0.11 | 0.25 | 0.64 | 0.11 | 0.50 | 0.40 | 0.10 |
C16G | 0.25 | 0.64 | 0.11 | 0.25 | 0.64 | 0.11 | 0.50 | 0.40 | 0.10 |
C17G | 0.25 | 0.64 | 0.11 | 0.25 | 0.64 | 0.11 | 0.50 | 0.40 | 0.10 |
Criteria | DM1 | DM2 | DM3 | ||||||
---|---|---|---|---|---|---|---|---|---|
S1 | S2 | S3 | S1 | S2 | S3 | S1 | S2 | S3 | |
M1 | VH | MH | MH | VH | MH | MH | VH | H | VH |
M2 | H | H | MH | H | MH | VH | H | H | MH |
M3 | VH | MH | VH | MH | MH | H | H | H | H |
M4 | MH | MH | VH | MH | MH | VH | H | H | H |
M5 | MH | H | H | MH | H | H | H | H | H |
M6 | H | H | H | H | H | H | MH | H | H |
C1 | H | VH | MH | MH | VH | VH | VH | VH | MH |
C2 | VH | MH | MH | VH | VH | VH | VH | MH | MH |
C3 | MH | H | VH | MH | H | VH | H | H | H |
C4 | MH | H | VH | MH | H | VH | H | H | H |
C5 | VH | VH | MH | MH | VH | H | H | H | H |
C6 | MH | MH | MH | MH | MH | H | H | H | H |
C7 | VH | MH | VH | MH | MH | VH | H | H | H |
C8 | VH | MH | VH | MH | MH | VH | H | H | H |
C9 | MH | H | H | MH | H | H | H | H | ML |
C10 | H | H | H | H | H | H | MH | H | H |
C11 | H | H | H | MH | H | H | MH | H | M |
C12 | H | H | H | H | H | H | MH | H | M |
C13 | VH | H | H | VH | H | MH | VH | H | H |
C14 | H | H | H | H | H | H | H | MH | H |
C15 | H | H | H | H | H | H | H | H | H |
C16 | H | H | H | H | H | H | H | H | H |
C17 | H | H | H | H | H | H | H | H | H |
Decision Maker | S1 | S2 |
---|---|---|
DM1 | (0.64, 0.24, 0.13) | (0.55, 0.33, 0.12) |
DM2 | (0.55, 0.33, 0.12) | (0.55, 0.33, 0.12) |
DM3 | (0.72, 0.19, 0.09) | (0.64, 0.24, 0.13) |
The Expert-Based Model | ||||||||
---|---|---|---|---|---|---|---|---|
Euclidean Distance | Taguchi Loss Function | |||||||
Suppliers | Pos. Ideal | Neg. Ideal | Closeness Coefficent | Rank | Pos. İdeal | Neg. Ideal | Closeness Coefficent | Rank |
S1Scenario1 | 0.73 | 0.29 | 0.2872 | 2 | 46.50 | 8.68 | 0.1573 | 2 |
S2Scenario1 | 0.74 | 0.29 | 0.2849 | 3 | 45.97 | 8.57 | 0.1572 | 3 |
S3Scenario1 | 0.72 | 0.31 | 0.2986 | 1 | 48.24 | 0.38 | 0.1628 | 1 |
S1Scenario2 | 0.73 | 0.29 | 0.2864 | 3 | 46.40 | 8.63 | 0.1568 | 3 |
S2Scenario2 | 0.73 | 0.30 | 0.2876 | 2 | 46.37 | 8.74 | 0.1586 | 2 |
S3Scenario2 | 0.72 | 0.31 | 0.2992 | 1 | 48.32 | 9.42 | 0.1632 | 1 |
S1Scenario3 | 0.74 | 0.29 | 0.2792 | 3 | 45.33 | 8.20 | 0.1532 | 3 |
S2Scenario3 | 0.74 | 0.29 | 0.2803 | 2 | 45.25 | 8.30 | 0.1550 | 2 |
S3Scenario3 | 0.73 | 0.30 | 0.2906 | 1 | 47.04 | 8.89 | 0.1589 | 1 |
The Theorical-Based Model | ||||||||
Euclidean Distance | Taguchi Loss Function | |||||||
Suppliers | Pos. Ideal | Neg. Ideal | Closeness Coefficent | Rank | Pos. İdeal | Neg. Ideal | Closeness Coefficent | Rank |
S1Scenario1 | 0.35 | 0.67 | 0.662 | 1 | 88.0 | 45.7 | 0.342 | 1 |
S2Scenario1 | 0.45 | 0.58 | 0.568 | 2 | 80.2 | 34.1 | 0.298 | 2 |
S3Scenario1 | 0.49 | 0.53 | 0.518 | 3 | 75.7 | 28.1 | 0.271 | 3 |
S1Scenario2 | 0.34 | 0.67 | 0.665 | 1 | 88.40 | 46.0 | 0.342 | 1 |
S2Scenario2 | 0.45 | 0.58 | 0.563 | 2 | 79.90 | 33. 4 | 0.295 | 2 |
S3Scenario2 | 0.49 | 0.51 | 0.502 | 3 | 74.20 | 26. 2 | 0.261 | 3 |
S1Scenario3 | 0.34 | 0.68 | 0.666 | 1 | 88.4 | 46.24 | 0.344 | 1 |
S2Scenario3 | 0.45 | 0.58 | 0.564 | 2 | 79.9 | 33.73 | 0.297 | 2 |
S3Scenario3 | 0.51 | 0.52 | 0.505 | 3 | 74. 4 | 26.66 | 0.264 | 3 |
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Turk, S. Taguchi Loss Function in Intuitionistic Fuzzy Sets along with Personal Perceptions for the Sustainable Supplier Selection Problem. Sustainability 2022, 14, 6178. https://doi.org/10.3390/su14106178
Turk S. Taguchi Loss Function in Intuitionistic Fuzzy Sets along with Personal Perceptions for the Sustainable Supplier Selection Problem. Sustainability. 2022; 14(10):6178. https://doi.org/10.3390/su14106178
Chicago/Turabian StyleTurk, Seda. 2022. "Taguchi Loss Function in Intuitionistic Fuzzy Sets along with Personal Perceptions for the Sustainable Supplier Selection Problem" Sustainability 14, no. 10: 6178. https://doi.org/10.3390/su14106178
APA StyleTurk, S. (2022). Taguchi Loss Function in Intuitionistic Fuzzy Sets along with Personal Perceptions for the Sustainable Supplier Selection Problem. Sustainability, 14(10), 6178. https://doi.org/10.3390/su14106178