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An Improved Fuzzy MULTIMOORA Approach and Its Application in Welding Process Selection

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Abstract

In this article, an improved MULTIMOORA approach is proposed for multi-attribute decision making (MADM) using the fuzzy concept, best–worst method (BWM) and half-quadratic (HQ) theory. The fuzzy concept helps to capture the vague information derived from human judgement at different stages of decision making, while BWM helps to simplify the attribute weighing. The standard MULTIMOORA method uses three utility functions, namely the ratio system (RS) utility function, reference point (RP) utility function and full multiplicative form (FMF) utility function, for evaluating the alternatives and obtaining the ranking orders using each of the utility function scores, which are consolidated using dominance theory. However, the dominance theory in the existing MULTIMOORA method has limitations, like there is no way to ascertain the trust level of the consolidated ranking and the level of consensus among the three ranking orders. Also, there is a need for multiple comparisons during aggregation, difficulty in automation, and the problem of circular reasoning. To overcome the limitations of dominance theory, a new HQ theory-based aggregation procedure has been proposed in this paper, which also has two associated indices, one to ascertain the level of consensus from the three ranking orders from MULTIMOORA and the other to ascertain the trust level or reliability of the final ranking in the aggregated ranking. The new modification is expected to add to the trustworthiness of the MULTIMOORA decision tool. The applicability of the proposed approach has been demonstrated with cases on welding process selection.

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Abbreviations

~ (Tilde accent):

Fuzzy value

Ã = (l, m, u),:

The fuzzy set’s lower, middle and upper limits are represented by l, m, and u.

i = 1, 2,..., K :

Number of alternatives

j = 1, 2,... n :

Number of criteria

\(\tilde{V}_{B}\) :

Fuzzy best-to-others vector

\(\tilde{V}_{W}\) :

Fuzzy others-to-worst vector

\(\tilde{w}_{B}\) :

Best criterion fuzzy weight

\(\tilde{w}_{W}\) :

Worst criterion fuzzy weight

\(\tilde{\zeta }\) :

Objective function

:

Criteria fuzzy weights

:

Alternative fuzzy weights w.r.t. each criterion

\(\tilde{w}_{ij}^{a}\) :

Fuzzy decision matrix

\(\tilde{w}_{ij}^{a*}\) :

Normalized fuzzy decision matrix

\(\tilde{Q} = (\tilde{q}_{ij} ) = (l_{ij}^{q} ,m_{ij}^{q} ,u_{ij}^{q} )\) :

Fuzzy weighted normalized matrix

\(\tilde{y}_{i}\) :

Fuzzy ratio system utility value

\(\tilde{r}_{j}\) :

Optimum fuzzy reference point

\(h_{i}\) :

Fuzzy reference point utility value

\(\tilde{z}\) :

Fuzzy full multiplicative form utility value

\(\alpha_{g}\) :

Half-quadratic auxiliary

g = 1,..., G :

Number of utility functions

\(R^{g}\) :

Ranking obtained from gth utility function

\(w_{g}\) :

Weight for gth utility function

\(R^{*}\) :

Aggregate ranking of alternative

\(C(R^{*} )\) :

Consensus Index

\(T(R^{*} )\) :

Trust level

\(N_{\sigma }\) :

Probability density function

σ :

Standard deviation

\(q_{kg}\) :

The ratio of probability density function values for the error \((R^{g} - R^{*} )\) to the probability density function values for zero

References

  1. Boyacı, A.Ç., Tüzemen, M.Ç.: Multi-criteria decision-making approaches for aircraft-material selection problem. Int. J. Mater. Prod. Technol. 64, 45 (2022). https://doi.org/10.1504/IJMPT.2022.120246

    Article  Google Scholar 

  2. James, A.T., Vaidya, D., Sodawala, M., Verma, S.: Selection of bus chassis for large fleet operators in India: an AHP-TOPSIS approach. Expert Syst. Appl. 186, 115760 (2021). https://doi.org/10.1016/j.eswa.2021.115760

    Article  Google Scholar 

  3. Kumar, V., Kalita, K., Chatterjee, P., Zavadskas, E.K., Chakraborty, S.: A SWARA-CoCoSo-based approach for spray painting robot selection. Informatica (2021). https://doi.org/10.15388/21-infor466

    Article  Google Scholar 

  4. Brauers, W.K.M., Zavadskas, E.K.: The MOORA method and its application to privatization in a transition economy by a new method: the MOORA method. Control Cybern. 35(2), 445–469 (2006)

    MATH  Google Scholar 

  5. Brauers, W.K.M., Zavadskas, E.K.: Project management by multimoora as an instrument for transition economies. Technol. Econ. Dev. Econ. 16(1), 5–24 (2010). https://doi.org/10.3846/tede.2010.01

    Article  Google Scholar 

  6. Chakraborty, S.: Applications of the MOORA method for decision making in manufacturing environment. Int. J. Adv. Manuf. Technol. 54, 1155–1166 (2011). https://doi.org/10.1007/s00170-010-2972-0

    Article  Google Scholar 

  7. Brauers, W.K.M., Baležentis, A., Baležentis, T.: Multimoora for the EU member states updated with fuzzy number theory. Technol. Econ. Dev. Econ. 17, 259–290 (2011). https://doi.org/10.3846/20294913.2011.580566

    Article  Google Scholar 

  8. Hafezalkotob, A., Hafezalkotob, A., Liao, H., Herrera, F.: An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Inf. Fusion 51, 145–177 (2019). https://doi.org/10.1016/j.inffus.2018.12.002

    Article  Google Scholar 

  9. Wu, X., Liao, H., Xu, Z., Hafezalkotob, A., Herrera, F.: Probabilistic linguistic MULTIMOORA: a multicriteria decision making method based on the probabilistic linguistic expectation function and the Improved Borda Rule. IEEE Trans. Fuzzy Syst. 26, 3688–3702 (2018). https://doi.org/10.1109/TFUZZ.2018.2843330

    Article  Google Scholar 

  10. Dahooie, J.H., Zavadskas, E.K., Firoozfar, H.R., Vanaki, A.S., Mohammadi, N., Brauers, W.K.M.: An improved fuzzy MULTIMOORA approach for multi-criteria decision making based on objective weighting method (CCSD) and its application to technological forecasting method selection. Eng. Appl. Artif. Intell. 79, 114–128 (2019). https://doi.org/10.1016/j.engappai.2018.12.008

    Article  Google Scholar 

  11. Asante, D., He, Z., Adjei, N.O., Asante, B.: Exploring the barriers to renewable energy adoption utilising MULTIMOORA- EDAS method. Energy Policy 142, 111479 (2020). https://doi.org/10.1016/j.enpol.2020.111479

    Article  Google Scholar 

  12. Hafezalkotob, A., Hafezalkotob, A., Liao, H., Herrera, F.: Interval MULTIMOORA method integrating interval borda rule and interval best-worst-method-based weighting model: case study on hybrid vehicle engine selection. IEEE Trans. Cybern. 50, 1157–1169 (2020). https://doi.org/10.1109/TCYB.2018.2889730

    Article  Google Scholar 

  13. Mohammadi, M., Rezaei, J.: Ensemble ranking: Aggregation of rankings produced by different multi-criteria decision-making methods. Omega 96, 102254 (2020). https://doi.org/10.1016/j.omega.2020.102254

    Article  Google Scholar 

  14. Løken, E.: Use of multicriteria decision analysis methods for energy planning problems. Renew. Sustain. Energy Rev. 11, 1584–1595 (2007). https://doi.org/10.1016/j.rser.2005.11.005

    Article  Google Scholar 

  15. Rezaei, J.: Best-worst multi-criteria decision-making method. Omega 53, 49–57 (2015). https://doi.org/10.1016/j.omega.2014.11.009

    Article  Google Scholar 

  16. Rezaei, J.: Best-worst multi-criteria decision-making method: some properties and a linear model. Omega 64, 126–130 (2016). https://doi.org/10.1016/j.omega.2015.12.001

    Article  Google Scholar 

  17. Sofuoğlu, M.A.: Fuzzy applications of Best-Worst method in manufacturing environment. Soft Comput. 24, 647–659 (2020). https://doi.org/10.1007/s00500-019-04491-5

    Article  Google Scholar 

  18. Stević, Ž, Pamučar, D., Zavadskas, E.K., Ćirović, G., Prentkovskis, O.: The selection of wagons for the internal transport of a logistics company: a novel approach based on rough BWM and rough SAW methods. Symmetry 9, 264 (2017). https://doi.org/10.3390/sym9110264

    Article  Google Scholar 

  19. Hafezalkotob, A., Hami-Dindar, A., Rabie, N., Hafezalkotob, A.: A decision support system for agricultural machines and equipment selection: a case study on olive harvester machines. Comput. Electron. Agric. 148, 207–216 (2018). https://doi.org/10.1016/j.compag.2018.03.012

    Article  Google Scholar 

  20. Guo, S., Zhao, H.: Fuzzy best-worst multi-criteria decision-making method and its applications. Knowl.-Based Syst. 121, 23–31 (2017). https://doi.org/10.1016/j.knosys.2017.01.010

    Article  Google Scholar 

  21. Wu, Q., Zhou, L., Chen, Y., Chen, H.: An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods. Inf. Sci. 502, 394–417 (2019). https://doi.org/10.1016/j.ins.2019.06.049

    Article  Google Scholar 

  22. Brauers, W.K., Zavadskas, E.K.: Robustness of MULTIMOORA: a method for multi-objective optimization. Informatica 23, 1–25 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hafezalkotob, A., Hafezalkotob, A.: Interval MULTIMOORA method with target values of attributes based on interval distance and preference degree: biomaterials selection. J. Ind. Eng. Int. 13, 181–198 (2017). https://doi.org/10.1007/s40092-016-0176-4

    Article  MATH  Google Scholar 

  24. Zhao, H., You, J.X., Liu, H.C.: Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Comput. 21, 5355–5367 (2017). https://doi.org/10.1007/s00500-016-2118-x

    Article  Google Scholar 

  25. Liang, W., Zhao, G., Hong, C.: Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach. Neural Comput. Appl. 31, 5871–5886 (2019). https://doi.org/10.1007/s00521-018-3405-5

    Article  Google Scholar 

  26. Zavadskas, E.K., Bausys, R., Juodagalviene, B., Garnyte-Sapranaviciene, I.: Model for residential house element and material selection by neutrosophic MULTIMOORA method. Eng. Appl. Artif. Intell. 64, 315–324 (2017). https://doi.org/10.1016/j.engappai.2017.06.020

    Article  Google Scholar 

  27. Stević, Ž, Pamučar, D., Vasiljević, M., Stojić, G., Korica, S.: Novel integrated multi-criteria model for supplier selection: case study construction company. Symmetry 9, 279 (2017). https://doi.org/10.3390/sym9110279

    Article  Google Scholar 

  28. Stojić, G., Stević, Ž, Antuchevičiene, J., Pamučar, D., Vasiljević, M.: A novel rough WASPAS approach for supplier selection in a company manufacturing PVC carpentry products. Information 9, 121 (2018). https://doi.org/10.3390/info9050121

    Article  Google Scholar 

  29. Peng, H.G., Wang, J.Q.: A multicriteria group decision-making method based on the normal cloud model with Zadeh’s Z-numbers. IEEE Trans. Fuzzy Syst. 26, 3246–3260 (2018). https://doi.org/10.1109/TFUZZ.2018.2816909

    Article  Google Scholar 

  30. Wu, S.M., You, X.Y., Liu, H.C., Wang, L.E.: Improving quality function deployment analysis with the cloud MULTIMOORA method. Int. Trans. Oper. Res. 27, 1600–1621 (2020). https://doi.org/10.1111/itor.12484

    Article  MathSciNet  Google Scholar 

  31. Rani, P., Mishra, A.R.: Fermatean fuzzy Einstein aggregation operators-based MULTIMOORA method for electric vehicle charging station selection. Expert Syst. Appl. 182, 115267 (2021). https://doi.org/10.1016/j.eswa.2021.115267

    Article  Google Scholar 

  32. Omrani, H., Alizadeh, A., Amini, M.: A new approach based on BWM and MULTIMOORA methods for calculating semi-human development index: an application for provinces of Iran. Socioecon. Plann. Sci. 70, 100689 (2020). https://doi.org/10.1016/j.seps.2019.02.004

    Article  Google Scholar 

  33. Eghbali-Zarch, M., Tavakkoli-Moghaddam, R., Esfahanian, F., Sepehri, M.M., Azaron, A.: Pharmacological therapy selection of type 2 diabetes based on the SWARA and modified MULTIMOORA methods under a fuzzy environment. Artif. Intell. Med. 87, 20–33 (2018). https://doi.org/10.1016/j.artmed.2018.03.003

    Article  Google Scholar 

  34. Shang, Z., Yang, X., Barnes, D., Wu, C.: Supplier selection in sustainable supply chains: using the integrated BWM, fuzzy Shannon entropy, and fuzzy MULTIMOORA methods. Expert Syst. Appl. 195, 116567 (2022). https://doi.org/10.1016/j.eswa.2022.116567

    Article  Google Scholar 

  35. Elshaboury, N., Marzouk, M.: Optimizing construction and demolition waste transportation for sustainable construction projects. Eng. Constr. Archit. Manag. (2020). https://doi.org/10.1108/ECAM-08-2020-0636

    Article  Google Scholar 

  36. Balasubramanian, V., Guha, B., Swamidas, A.S.J., Seshadri, R.: Selection of welding process to fabricate cruciform joints using analytic hierarchic process based on qualitative factors. Sci. Technol. Weld. Join. 5, 203–207 (2000). https://doi.org/10.1179/136217100101538218

    Article  Google Scholar 

  37. Ravisankar, V., Balasubramanian, V., Muralidharan, C.: Selection of welding process to fabricate butt joints of high strength aluminium alloys using analytic hierarchic process. Mater. Des. 27, 373–380 (2006). https://doi.org/10.1016/j.matdes.2004.11.008

    Article  Google Scholar 

  38. Balasubramanian, V., Varahamoorthy, R., Ramachandran, C.S., Muralidharan, C.: Selection of welding process for hardfacing on carbon steels based on quantitative and qualitative factors. Int. J. Adv. Manuf. Technol. 40, 887–897 (2009). https://doi.org/10.1007/s00170-008-1406-8

    Article  Google Scholar 

  39. Saluja, R.S., Singh, V.: Subjective factors consideration in the selection of welding technique for welded tube manufacturing. In: Narayanan, R.G., Joshi, S.N., Dixit, U.S. (eds.) Advances in Computational Methods in Manufacturing, pp. 205–213. Springer, Singapore (2019)

    Chapter  Google Scholar 

  40. Saluja, R.S., Singh, V.: MADM-Based Approach for Selection of Welding Process for Aluminum Tube Manufacturing (2020)

  41. Saad, M.H., Darras, B.M., Nazzal, M.A.: Evaluation of welding processes based on multi-dimensional sustainability assessment model. J. Precis. Eng. Manuf.-Green Technol. Int. (2020). https://doi.org/10.1007/s40684-019-00184-4

    Article  Google Scholar 

  42. Mirhedayatian, S.M., Vahdat, S.E., Jelodar, M.J., Saen, R.F.: Welding process selection for repairing nodular cast iron engine block by integrated fuzzy data envelopment analysis and TOPSIS approaches. Mater. Des. 43, 272–282 (2013). https://doi.org/10.1016/j.matdes.2012.07.010

    Article  Google Scholar 

  43. Jafarian, M., Vahdat, S.E.: A fuzzy multi-attribute approach to select the welding process at high pressure vessel manufacturing. J. Manuf. Process. 14, 250–256 (2012). https://doi.org/10.1016/j.jmapro.2011.10.006

    Article  Google Scholar 

  44. Saluja, R.S., Singh, V.: A fuzzy multi-attribute decision making model for selection of welding process for grey cast iron. Mater. Today Proc. 28, 1194–1199 (2020). https://doi.org/10.1016/j.matpr.2020.01.108

    Article  Google Scholar 

  45. Sánchez-Lozano, J.M., Meseguer-Valdenebro, J.L., Portoles, A.: Assessment of arc welding process through the combination of TOPSIS–AHP methods with fuzzy logic. Trans. Indian Inst. Met. 70, 935–946 (2017). https://doi.org/10.1007/s12666-016-0884-x

    Article  Google Scholar 

  46. Omar, M., Soltan, H.: A framework for welding process selection. SN Appl. Sci. 2, 1–12 (2020). https://doi.org/10.1007/s42452-020-2144-2

    Article  Google Scholar 

  47. Omar, M., Janada, K., Soltan, H.: FAQT: A precise system for welding process selection. Int. J. Fuzzy Syst. 1–14 (2022)

  48. Mathew, M., Patanwar, S.K., Gupta, S., Sachdev, T.: Performance evaluation of arc welding processes for the manufacturing of pressure vessel using novel hybrid MCDM technique. Int. J. Inf. Decis. Sci. 13, 235–253 (2021)

    Google Scholar 

  49. Zadeh, L.A.: Information and control. Fuzzy Sets 8, 338–353 (1965)

    Google Scholar 

  50. Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), B-141 (1970)

    Article  MathSciNet  Google Scholar 

  51. Fattahi, R., Khalilzadeh, M.: Risk evaluation using a novel hybrid method based on FMEA, extended MULTIMOORA, and AHP methods under fuzzy environment. Saf. Sci. 102, 290–300 (2018). https://doi.org/10.1016/j.ssci.2017.10.018

    Article  Google Scholar 

  52. AyaAkk, G., Turanoğlu, B., Öztaş, S.: An integrated fuzzy AHP and fuzzy MOORA approach to the problem of industrial engineering sector choosing. Expert Syst. Appl. 42, 9565–9573 (2015). https://doi.org/10.1016/j.eswa.2015.07.061

    Article  Google Scholar 

  53. Kannan, D., Khodaverdi, R., Olfat, L., Jafarian, A., Diabat, A.: Integrated fuzzy multi criteria decision making method and multiobjective programming approach for supplier selection and order allocation in a green supply chain. J. Clean. Prod. 47, 355–367 (2013). https://doi.org/10.1016/j.jclepro.2013.02.010

    Article  Google Scholar 

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  1. Department of Mechanical Engineering, K. K. Birla Goa Campus, BITS Pilani, Zuarinagar, Goa, India

    Ravindra Singh Saluja & Varinder Singh

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  1. Ravindra Singh Saluja
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  2. Varinder Singh
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RSS contributed to the problem conceptualization, data curation, formal analysis, investigation, methodology, validation, visualization and writing—original draft. VS was involved in the resources, supervision, visualization and writing—review and editing.

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Correspondence to Ravindra Singh Saluja.

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Saluja, R.S., Singh, V. An Improved Fuzzy MULTIMOORA Approach and Its Application in Welding Process Selection. Int. J. Fuzzy Syst. 25, 1707–1726 (2023). https://doi.org/10.1007/s40815-023-01472-7

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