Sustainable method for tender selection using linear Diophantine multi-fuzzy soft set

Abstract

Tender selection is a fundamental issue for the success of construction projects since it contributes to the overall outline’s performance. In reallife problems, the decision-makers cannot express certain crisp data, so there is uncertainty and vagueness in the values. In this paper, a sustainable technique is proposed to find desirable tenderers coherently and fairly under the needed circumstances. This paper presents three methods of an algorithmic approach to evaluate the tendering process and rank the tenderers. The attributes are expressed as Linear Diophantine Multi-Fuzzy Soft numbers (LDMFSN) since the existence of reference parameters makes the DM freely choose their grade values. Some of the rudimentary properties of LDMFSN are presented. An illustrative example is demonstrated to validate our proposed method. The uniqueness of the result in all three algorithms shows the effectiveness of our proposed approach.

Keywords

• Linear Diophantine fuzzy
• tender selection
• threshold fuzzy
• comparision matrix
• score value

Thanks

This paper is presented in the Conference ICAMM-2023. The article has been written with the joint financial support of RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, Dt. 09.10.2018, DST-PURSE 2nd Phase programme vide letter No. SR/PURSE Phase 2/38 (G) Dt. 21.02.2017 and DST (FIST - level I) 657876570 vide letter No.SR/FIST/MS-I/2018/17 Dt. 20.12.2018.

References

1. Akcay, C., Manisali, E., Fuzzy decision support model for the selection of contractor in construction works, Revista de la Construction, 17 (2018), 258–266. DOI: 10.7764/RDLC.17.2.258
2. Atanassov K.T, Intuitionistic fuzzy sets, Fuzzy Set System, 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
3. Ayub, S., Shabir, M., Riaz, M., Aslam, M., Chinram, R., Linear Diophantine fuzzy relations and their algebraic properties with decision making, Symmetry, 13(6) (2021), 945. https://doi.org/10.3390/sym13060945
4. Al-Harbi, K.M.A.S., Application of the AHP in project management, International Journal of Project Management, 19(1) (2001), 19–27. https://doi.org/10.1016/S0263-7863(99)00038-1
5. Begam, S.S., Vimala, J., Application of lattice ordered multi-fuzzy soft set in forecasting process, Journal of Intelligent & Fuzzy Systems, 36(3) (2019), 2323–2331. 10.3233/JIFS-169943
6. Begam, S.S., Vimala, J., Preethi, D., A novel study on the algebraic applications of special class of lattice ordered multi-fuzzy soft sets, Journal of Discrete Mathematical Sciences and Cryptography, 22(5) (2019), 883–899. DOI: 10.1080/09720529.2019.1685239
7. Das, S., Kar, S., Intuitionistic Multi Fuzzy Soft Set and Its Application in Decision Making, International Conference on Pattern Recognition and Machine Intelligence, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2013, 587–592. https://doi.org/10.1007/978-3-642-45062-4-82
8. Deng, H., Multi-criteria analysis with fuzzy pairwise comparison, International Journal of Approximate Reasoning, 21(3) (1999), 215–231. https://doi.org/10.1016/S0888-613X(99)00025-0

9. Hatush, Z., Skitmore, M., Contractor selection using multi-criteria utility theory: An additive model, Building and Environment, 33(23) (1998), 105–115. https://doi.org/10.1016/S0360-1323(97)00016-4
10. Hussain, A., Ali, M.I., Mahmood, T., Munir, M., q-Rung orthopair fuzzy soft average aggregation operators and their application in multi-criteria decision-making, International Journal of Intelligent Systems, 35(4) (2020), 571–599. https://doi.org/10.1002/int.22217
11. Hashmi, M.R., Tehrim, S.T., Riaz, M., Pamucar, D, Cirovic G, Spherical linear Diophantine fuzzy soft rough sets with multi-criteria decision making, Axioms, 10(185) (2021). https://doi.org/10.3390/axioms10030185
12. Iampan, A., Garcia, G.S., Riaz, M., Athar Farid, H.M., Chinram, R., Linear Diophantine fuzzy Einstein aggregation operators for multi-criteria decision-making problems, Journal of Mathematics, 2021 (2021), 1–31. https://doi.org/10.1155/2021/5548033
13. Jamili, A., Tender participation selection problem with fuzzy approach, Advances in Industrial Engineering, 54(4) (2020), 355–364. 10.22059/JIENG.2021.325197.1772
14. Kamaci, H., Linear Diophantine fuzzy algebraic structures, J Ambient Intell Human Comput, 12 (2021), 10353–10373. https://doi.org/10.1007/s12652-020-02826-x
15. Kannan, J., Garg, H., Jayakumar, V., Hananf, A., Aty, A., Haleem, A., Linear Diophantine multi-fuzzy aggregation operators and its application in digital transformation, Journal of Intelligent & Fuzzy Systems, 45(2) (2023), 3097–3107. DOI: 10.3233/JIFS-223844
16. Lambropoulos, S., The use of time and cost utility for construction contract award under European Union Legislation, Building and Environment, 42(1) (2007), 452–463. https://doi.org/10.1016/j.buildenv.2005.08.002
17. Lai, K.K., Liu, S.L., Wang, S.Y., A method used for evaluating bids in the Chinese construction industry, International Journal of Project Management, 22 (2004), 193-201. https://doi.org/10.1016/S0263-7863(03)00009-7
18. Liu, B., Huo, T., Wang, X., Shen, G.Q., Chen, Y., The decision model of the intuitionistic fuzzy group bid evaluation for urban infrastructure projects considering social costs, Canadian Journal of Civil Engineering, 40(3) (2013), 263-273. 10.1139/cjce-2012-0283
19. Maji, P.K., Biswas, R., Roy, A.R., Fuzzy soft sets, J. Fuzzy Math., 9(3) (2001), 589–602.
20. Padhi, S.S., Mohapatra, P.K.J., Contractor selection in government procurement auctions: A case study, European Journal of Industrial Engineering, 3(2) (2009), 170–186. DOI:10.1504/EJIE.2009.023604
21. Peng X.A., Yang, Y., Song, J., Pythagoren fuzzy soft set and its application, Computer Engineering, 41 (2015), 224-229. https://doi.org/10.1016/j.jksuci.2021.08.010
22. Reeta, A.J., Vimala, J., A study on distributive and modular lattice ordered fuzzy soft group and its duality, Appl. Math. J. Chin. Univ., 31 (2016), 491-502.
23. Riaz, M., Farid, H.M.A., Aslam, M., Pamucar, D., Bozanic, D., Novel approach for thirdparty reverse logistic provider selection process under linear Diophantine fuzzy prioritized aggregation operators, Symmetry, 13 (2021), 1152. https://doi.org/10.3390/sym13071152
24. Riaz, M., Hashmi, M.R., Masooma, R., Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems, Journal of Intelligent and Fuzzy Systems, 37 (2019), 5417–5439. https://doi.org/10.3233/JIFS-190550
25. Riaz, M., Hashmi, M.R., Kalsoom, H., Pamucar, D., Chu, M., Linear Diophantine fuzzy soft rough sets for the selection of sustainable material handling equipment, Symmetry, 12 (2020), 1215. https://doi.org/10.3390/sym12081215
26. Rajareega, S., Vimala, J., Operations on complex intuitionistic fuzzy soft lattice ordered group and CIFS-COPRAS method for equipment selection process, Journal of Intelligent & Fuzzy Systems, 41(5) (2021), 5709–5718. DOI: 10.3233/JIFS-189890
27. Sebastian, S., Multi-fuzzy sets, International Mathematical Forum, 5 (2010), 2471–2476.
28. Vimala, J., Garg, H., Jeevitha, K., Prognostication of myocardial infarction using lattice ordered linear Diophantine multi-fuzzy soft set, Intelligent Journal of Fuzzy System, (2023). https://doi.org/10.1007/s40815-023-01574-2
29. Wang, Y., Xi, C., Zhang, S., Zhang, W., Yu, D., Combined approach for government etendering using GA and TOPSIS with intuitionistic fuzzy information, PloS One, 10 (2015), e0130767. 10.1371/journal.pone.0130767
30. Yang, Y., Tan, X., Meng, C., The multi-fuzzy soft set and its application in decision making, Applied Mathematical Modelling, 37 (2013), 4915–4923. https://doi.org/10.1016/j.apm.2012.10.015
31. Yager, R.R., Generalized orthopair fuzzy sets, IEEE Transactions on Fuzzy Systems, 25(5) (2017), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005
32. Yager, R.R, Pythagorean membership grades in multicriteria decision making, IEEE Transactions on Fuzzy Systems, 22(4) (2014), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989
33. Zadeh, L.A., Fuzzy sets, Information Controls, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X