Extended fuzzy $ N $-Soft PROMETHEE method and its application in robot butler selection

Muhammad Akram; Maheen Sultan; José Carlos R. Alcantud; Mohammed M. Ali Al-Shamiri; Muhammad Akram; Maheen Sultan; José Carlos R. Alcantud; Mohammed M. Ali Al-Shamiri

doi:10.3934/mbe.2023081

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 1774-1800. doi: 10.3934/mbe.2023081

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Extended fuzzy $ N $-Soft PROMETHEE method and its application in robot butler selection

1.
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
2.
BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), Universidad de Salamanca, Salamanca 37007, Spain
3.
Department of Mathematics, Faculty of Science and Arts, Muhayl Asser, King Khalid University, K.S.A
4.
Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen

Academic Editor: Yang Kuang

Received: 14 July 2022 Revised: 12 September 2022 Accepted: 12 October 2022 Published: 07 November 2022

This paper extends the literature on fuzzy PROMETHEE, a well-known multi-criteria group decision-making technique. The PROMETHEE technique ranks alternatives by specifying an allowable preference function that measures their deviations from other alternatives in the presence of conflicting criteria. Its ambiguous variation helps to make an appropriate decision or choose the best option in the presence of some ambiguity. Here, we focus on the more general uncertainty in human decision-making, as we allow $ N $-grading in fuzzy parametric descriptions. In this setting, we propose a suitable fuzzy $ N $-soft PROMETHEE technique. We recommend using an Analytic Hierarchy Process to test the feasibility of standard weights before application. Then the fuzzy $ N $-soft PROMETHEE method is explained. It ranks the alternatives after some steps summarized in a detailed flowchart. Furthermore, its practicality and feasibility are demonstrated through an application that selects the best robot housekeepers. The comparison between the fuzzy PROMETHEE method and the technique proposed in this work demonstrates the confidence and accuracy of the latter method.
- analytic hierarchy process,
- ELECTRE method,
- outranked directed graph,
- score degree
Citation: Muhammad Akram, Maheen Sultan, José Carlos R. Alcantud, Mohammed M. Ali Al-Shamiri. Extended fuzzy $ N $-Soft PROMETHEE method and its application in robot butler selection[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 1774-1800. doi: 10.3934/mbe.2023081

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Abstract

This paper extends the literature on fuzzy PROMETHEE, a well-known multi-criteria group decision-making technique. The PROMETHEE technique ranks alternatives by specifying an allowable preference function that measures their deviations from other alternatives in the presence of conflicting criteria. Its ambiguous variation helps to make an appropriate decision or choose the best option in the presence of some ambiguity. Here, we focus on the more general uncertainty in human decision-making, as we allow $ N $-grading in fuzzy parametric descriptions. In this setting, we propose a suitable fuzzy $ N $-soft PROMETHEE technique. We recommend using an Analytic Hierarchy Process to test the feasibility of standard weights before application. Then the fuzzy $ N $-soft PROMETHEE method is explained. It ranks the alternatives after some steps summarized in a detailed flowchart. Furthermore, its practicality and feasibility are demonstrated through an application that selects the best robot housekeepers. The comparison between the fuzzy PROMETHEE method and the technique proposed in this work demonstrates the confidence and accuracy of the latter method.

References

[1]	L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
[2]	F. Fatimah, D. Rosadi, R. Hakim, J. Alcantud, $N$-soft sets and their decision making algorithms, Soft Comput., 22 (2018), 3829–3842. https://doi.org/10.1007/s00500-017-2838-6 doi: 10.1007/s00500-017-2838-6
[3]	D. Molodtsov, Soft set theory - First results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
[4]	J. Alcantud, The semantics of $N$-soft sets, their applications, and a coda about three-way decision, Symmetry, 606 (2022), 837–852. https://doi.org/10.1016/j.ins.2022.05.084 doi: 10.1016/j.ins.2022.05.084
[5]	J. Alcantud, G. Santos-García, M. Akram, OWA aggregation operators and multi-agent decisions with $N$-soft sets, Expert Syst. Appl., 203 (2022), 117430. https://doi.org/10.1016/j.eswa.2022.117430 doi: 10.1016/j.eswa.2022.117430
[6]	P. Maji, A. Roy, R. Biswas, Fuzzy soft sets, J. Fuzzy Math., 9 (2001), 589–602.
[7]	P. Maji, A. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077–1083. https://doi.org/10.1016/S0898-1221(02)00216-X doi: 10.1016/S0898-1221(02)00216-X
[8]	J. Alcantud, S. Rambaud, M. J. M. Torrecillas, Valuation fuzzy soft sets: a flexible fuzzy soft set based decision making procedure for the valuation of assets, Symmetry, 9 (2017), 253. https://doi.org/10.3390/sym9110253 doi: 10.3390/sym9110253
[9]	M. El Sayed, A. Al Qubati, M. El-Bably, Soft pre-rough sets and its applications in decision making, Math. Biosci. Eng., 17 (2020), 6045–6063. https://doi.org/10.3934/mbe.2020321 doi: 10.3934/mbe.2020321
[10]	M. Akram, A. Adeel, J. Alcantud, Fuzzy $N$-soft sets: a novel model with applications, J. Int. Fuzzy Syst., 35 (2018), 4757–4771. https://doi.org/10.3233/JIFS-18244 doi: 10.3233/JIFS-18244
[11]	M. Akram, A. Adeel, J. Alcantud, Hesitant fuzzy $N$-soft sets: a new model with applications in decision-making, J. Int. Fuzzy Syst., 36 (2019), 6113–6127. https://doi.org/10.3233/JIFS-181972 doi: 10.3233/JIFS-181972
[12]	D. Zhang, P. Li, S. An, $N$-soft rough sets and its applications, J. Int. Fuzzy Syst., 40 (2021), 565–573. https://doi.org/10.3233/JIFS-200338 doi: 10.3233/JIFS-200338
[13]	J. Alcantud, F. Feng, R. Yager, An $N$-soft set approach to rough sets, IEEE Trans. Fuzzy Syst., 28 (2020), 2996–3007. https://doi.org/10.1109/TFUZZ.2019.2946526 doi: 10.1109/TFUZZ.2019.2946526
[14]	F. Fatimah, J. Alcantud, The multi-fuzzy $N$-soft set and its applications to decision-making, Neural Comput. Appl., 33 (2021), 11437–11446. https://doi.org/10.1007/s00521-020-05647-3 doi: 10.1007/s00521-020-05647-3
[15]	T. Mahmood, U. ur Rehman, Z. Ali, A novel complex fuzzy $N$-soft sets and their decision-making algorithm, Complex Intell. Syst., 7 (2021), 2255–2280. https://doi.org/10.1007/s40747-021-00373-2 doi: 10.1007/s40747-021-00373-2
[16]	U. Rehman, T. Mahmood, Picture fuzzy $N$-soft sets and their applications in decision-making problems, Fuzzy Inf. Eng., 13 (2021), 335–367. https://doi.org/10.1080/16168658.2021.1943187 doi: 10.1080/16168658.2021.1943187
[17]	C. L. Hwang, K. Yoon, Multiple attribute decision making: methods and applications- A State-of-the-Art Survey, Springer, Berlin, 1981.
[18]	R. Benayoun, B. Roy, B. Sussman, ELECTRE: Une méthode pour guider le choix en présence de points de vue multiples, Note de travail, 49, SEMA-METRA International, Direction Scientifique, 1966.
[19]	J. Brans, P. Vincke, A preference ranking organisation method : The PROMETHEE method for multiple criteria decision making, Manage. Sci., 31 (1985), 647–656. https://doi.org/10.1287/mnsc.31.6.647 doi: 10.1287/mnsc.31.6.647
[20]	T. Saaty, Axiomatic foundation of the analytic hierarchy process, Manage. Sci., 32 (1986), 841–855. https://doi.org/10.1287/mnsc.32.7.841 doi: 10.1287/mnsc.32.7.841
[21]	R. Bellman, L. Zadeh, Decision-making in a fuzzy environment, Manage. Sci., 17 (1970), 141–164. https://doi.org/10.1287/mnsc.17.4.B141 doi: 10.1287/mnsc.17.4.B141
[22]	M. Akram, Shumaiza, J. Alcantud, An $m$-polar fuzzy PROMETHEE approach for AHP-assisted group decision-making, Math. Comput. Appl., 25 (2020), 26. https://doi.org/10.3390/mca25020026 doi: 10.3390/mca25020026
[23]	F. Feng, Z. Xu, H. Fujita, M. Liang, Enhancing PROMETHEE method with intuitionistic fuzzy soft sets, Int. J. Int. Syst., 35 (2020), 1071–1104. https://doi.org/10.1002/int.22235 doi: 10.1002/int.22235
[24]	M. Sevkli, An application of the fuzzy ELECTRE method for supplier selection, Int. J. Prod. Res., 48 (2010), 3393–3405. https://doi.org/10.1080/00207540902814355 doi: 10.1080/00207540902814355
[25]	M. Akram, C. Kahraman and K. Zahid, Extension of TOPSIS model to the decision-making under complex spherical fuzzy information, Soft Comput., 25 (2021), 10771–10795. https://doi.org/10.1007/s00500-021-05945-5 doi: 10.1007/s00500-021-05945-5
[26]	M. Goumas, V. Lygerou, An extension of the PROMETHEE method for decision making in fuzzy environment: Ranking of alternative energy exploitation projects, Eur. J. Oper. Res., 123 (2000), 606–613. https://doi.org/10.1016/S0377-2217(99)00093-4 doi: 10.1016/S0377-2217(99)00093-4
[27]	F. Lolli, A. Ishizaka, R. Gamberini, B. Rimini, A. Ferrari, S. Marinelli, et al., Waste treatment: an environmental, economic and social analysis with a new group fuzzy PROMETHEE approach, Clean Technol. Environ. Policy, 18 (2016), 1317–1332. https://doi.org/10.1007/s10098-015-1087-6 doi: 10.1007/s10098-015-1087-6
[28]	Y. Chen, T. Wang, C.Y. Wu, Strategic decisions using the fuzzy PROMETHEE for IS outsourcing, Expert Syst. Appl., 38 (2011), 13216–13222. https://doi.org/10.1016/j.eswa.2011.04.137 doi: 10.1016/j.eswa.2011.04.137
[29]	R. Krishankumar, K. Ravichandran, A. Saeid, A new extension to PROMETHEE under intuitionistic fuzzy environment for solving supplier selection problem with linguistic preferences, Appl. Soft Comput., 60 (2017), 564–576. https://doi.org/10.1016/j.asoc.2017.07.028 doi: 10.1016/j.asoc.2017.07.028
[30]	H. Wu, J. Wang, S. Liu, T. Yang, Research on decision-making of emergency plan for waterlogging disaster in subway station project based on linguistic intuitionistic fuzzy set and TOPSIS, Math. Biosci. Eng., 17 (2020), 4825–4851. https://doi.org/10.3934/mbe.2020263 doi: 10.3934/mbe.2020263
[31]	B. Sun, M. Wei, W. Wu, B. Jing, A novel group decision making method for airport operational risk management, Math. Biosci. Eng., 17 (2020), 2402–2417. https://doi.org/10.3934/mbe.2020130 doi: 10.3934/mbe.2020130
[32]	P. Ziemba, NEAT F-PROMETHEE-A new fuzzy multiple criteria decision making method based on the adjustment of mapping trapezoidal fuzzy numbers, Expert Syst. Appl., 110 (2018), 363–380. https://doi.org/10.1016/j.eswa.2018.06.008 doi: 10.1016/j.eswa.2018.06.008
[33]	J. Alcantud, A. Biondo, A. Giarlotta, Fuzzy politics I: The genesis of parties, Fuzzy Sets Syst., 349 (2018), 71–98. https://doi.org/10.1016/j.fss.2018.01.015 doi: 10.1016/j.fss.2018.01.015
[34]	L. Abdullah, W. Chan and A. Afshari, Application of PROMETHEE method for green supplier selection: A comparative result based on preference functions, J. Ind. Eng. Int., 15 (2019), 271–285. https://doi.org/10.1007/s40092-018-0289-z doi: 10.1007/s40092-018-0289-z
[35]	J. Brans, P. Vincke, B. Mareschal, How to select and how to rank projects: The PROMETHEE method, Eur. J. Oper. Res., 24 (1986), 228–238. https://doi.org/10.1016/0377-2217(86)90044-5 doi: 10.1016/0377-2217(86)90044-5
[36]	H. Zhao, Y. Peng, W. Li, Revised PROMETHEE II for improving efficiency in emergency response, Procedia Comput. Sci., 17 (2013), 181–188. https://doi.org/10.1016/j.procs.2013.05.025 doi: 10.1016/j.procs.2013.05.025
[37]	D. Ozsahin, B. Uzun, M. Musa, N. Sentürk, F. Nurçin, I. Ozsahin, Evaluating nuclear medicine imaging devices using fuzzy PROMETHEE method, Procedia Comput. Sci., 120 (2017), 699–705. https://doi.org/10.1016/j.procs.2017.11.298 doi: 10.1016/j.procs.2017.11.298
[38]	M. Behzadian, R. Kazemzadeh, A. Albadvi, M. Aghdasi, PROMETHEE: A comprehensive literature review on methodologies and applications, Eur. J. Oper. Res., 200 (2010), 198–215. https://doi.org/10.1016/j.ejor.2009.01.021 doi: 10.1016/j.ejor.2009.01.021
[39]	K. Govindan, M. Kadzinski, R. Sivakumar, Application of a novel PROMETHEE-based method for construction of a group compromise ranking to prioritization of green suppliers in food supply chain, Omega, 71 (2017), 129–145. https://doi.org/10.1016/j.omega.2016.10.004 doi: 10.1016/j.omega.2016.10.004
[40]	I. Ozsahin, T. Sharif, D. U. Ozsahin and B. Uzun, Evaluation of solid-state detectors in medical imaging with fuzzy PROMETHEE, J. Instrum., 14 (2019). https://doi.org/10.1088/1748-0221/14/01/C01019
[41]	M. Maisaini, B. Uzun, I. Ozsahin, D. Uzun, Evaluating lung cancer treatment techniques using fuzzy PROMETHEE approach, In International Conference on Theory and Applications of Fuzzy Systems and Soft Computing, (2018), 209–215. https://doi.org/10.1007/978-3-030-04164-9_29
[42]	M. Gul, E. Celik, A. Gumus, A. F. Guneri, A fuzzy logic based PROMETHEE method for material selection problems, Beni-Suef Univ. J. Basic Appl. Sci., 7 (2018), 68–79. https://doi.org/10.1016/j.bjbas.2017.07.002 doi: 10.1016/j.bjbas.2017.07.002
[43]	T. Amaral, A. P. Costa, Improving decision-making and management of hospital resources: An application of the PROMETHEE II method in an Emergency Department, Oper. Res. Health Care, 3 (2014), 1–6. https://doi.org/10.1016/j.orhc.2013.10.002 doi: 10.1016/j.orhc.2013.10.002
[44]	M. Molla, B. Giri, P. Biswas, Extended PROMETHEE method with Pythagorean fuzzy sets for medical diagnosis problems, Soft Comput., 25 (2021), 4503–4512. https://doi.org/10.1007/s00500-020-05458-7 doi: 10.1007/s00500-020-05458-7
[45]	F. Samanlioglu, Z. Ayag, A fuzzy AHP-PROMETHEE II approach for evaluation of solar power plant location alternatives in Turkey, J. Intell. Fuzzy Syst., 33 (2017), 859–871. https://doi.org/10.3233/JIFS-162122 doi: 10.3233/JIFS-162122

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