A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique
Abstract
:1. Introduction
2. Preliminaries
3. COMET Method with NIVTFNs
4. An Illustrative Example
5. Conclusions
- interval-valued intuitionistic fuzzy sets,
- hesitant fuzzy linguistic term sets,
- hesitant intuitionistic fuzzy linguistic term sets,
- etc.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Zadeh, L.A. Fuzzy Sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef] [Green Version]
- Bellman, R.E.; Zadeh, L.A. Decision-Making in a Fuzzy Environment. Manag. Sci. 1970, 17, B-141–B-273. [Google Scholar] [CrossRef]
- Masumpoor, S.; Yaghobi, H.; Ahmadieh Khanesar, M. Adaptive sliding-mode type-2 neuro-fuzzy control of an induction motor. Expert Syst. Appl. Int. J. 2015, 42, 6635–6647. [Google Scholar] [CrossRef]
- Jankowski, J.; Kazienko, P.; Wątróbski, J.; Lewandowska, A.; Ziemba, P.; Zioło, M. Fuzzy multi-objective modeling of effectiveness and user experience in online advertising. Expert Syst. Appl. 2016, 65, 315–331. [Google Scholar] [CrossRef]
- Chang, W.J.; Kuo, C.P.; Ku, C.C. Intelligent fuzzy control with imperfect premise matching concept for complex nonlinear multiplicative noised systems. Neurocomputing 2015, 154, 276–283. [Google Scholar] [CrossRef]
- Jankowski, J.; Lewandowska, A.; Watróbski, J.; Ziemba, P.; Salabun, W. Modeling the Perceptual Response from Effects Oriented Web Components Towards Lower Intrusiveness. In Proceedings of the 20th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES2016, York, UK, 5–7 September 2016; pp. 147–158. [Google Scholar]
- Al-Obeidat, F.; Al-Taani, A.T.; Belacel, N.; Feltrin, L.; Banerjee, N. A fuzzy decision tree for processing satellite images and landsat data. Procedia Comput. Sci. 2015, 52, 1192–1197. [Google Scholar] [CrossRef] [Green Version]
- Piegat, A.; Sałabun, W. Comparative analysis of MCDM methods for assessing the severity of chronic liver disease. In International Conference on Artificial Intelligence and Soft Computing; Springer: Cham, Switzerland, 2015; pp. 1–14. [Google Scholar]
- Deveci, M.; Demirel, N.Ç.; John, R.; Özcan, E. Fuzzy multi-criteria decision making for carbon dioxide geological storage in Turkey. J. Nat. Gas Sci. Eng. 2015, 27, 692–705. [Google Scholar] [CrossRef] [Green Version]
- Amin, F.; Fahmi, A.; Abdullah, S.; Ali, A.; Ahmad, R.; Ghani, F. Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. J. Intell. Fuzzy Syst. 2018, 34, 1–15. [Google Scholar] [CrossRef]
- Tseng, M.-L.; Lim, M.; Wu, K.-J.; Zhou, L.; Bui, D.T.D. A novel approach for enhancing green supply chain management using converged interval-valued triangular fuzzy numbers-grey relation analysis. Resour. Conserv. Recycl. 2018, 128, 122–133. [Google Scholar] [CrossRef]
- Tseng, M.L. Implementation and performance evaluation using the fuzzy network balanced scorecard. Comput. Educ. 2010, 55, 188–201. [Google Scholar] [CrossRef]
- Yu, D. Triangular Hesitant Fuzzy Set and Its Application to Teaching Quality Evaluation. J. Inf. Comput. Sci. 2013, 10, 1925–1934. [Google Scholar] [CrossRef]
- Faizi, S.; Rashid, T.; Sałabun, W.; Zafar, S.; Wątróbski, J. Decision making with uncertainty using hesitant fuzzy sets. Int. J. Fuzzy Syst. 2018, 20, 93–103. [Google Scholar] [CrossRef] [Green Version]
- Montes, R.; Sanchez, A.M.; Villar, P.; Herrera, F. Teranga Go!: Carpooling Collaborative Consumption Community with multi-criteria hesitant fuzzy linguistic term set opinions to build confidence and trust. Appl. Soft Comput. 2018, 67, 941–952. [Google Scholar] [CrossRef]
- Rodríguez, R.M.; Martínez, L.; Torra, V.; Xu, Z.S.; Herrera, F. Hesitant Fuzzy Sets: State of the Art and Future Directions. Int. J. Intell. Syst. 2014, 29, 495–524. [Google Scholar] [CrossRef]
- Torra, V. Hesitant Fuzzy Sets. Int. J. Intell. Syst. 2010, 25, 529–539. [Google Scholar] [CrossRef]
- Rashid, T.; Husnine, S.M. Multicriteria group decision making by using trapezoidal valued hesitant fuzzy sets. Sci. World J. 2014, 2014, 304834. [Google Scholar] [CrossRef]
- Ngan, S.C. A unified representation of intuitionistic fuzzy sets, hesitant fuzzy sets and generalized hesitant fuzzy sets based on their u-maps. Expert Syst. Appl. 2017, 69, 257–276. [Google Scholar] [CrossRef]
- Qian, G.; Wang, H.; Feng, X. Generalized hesitant fuzzy sets and their application in decision support system. Knowl. -Based Syst. 2013, 37, 357–365. [Google Scholar] [CrossRef]
- Atanassov, K.; Gargov, G. Interval valued intutionistic fuzzy sets. Fuzzy Sets Syst. 1989, 31, 343–349. [Google Scholar] [CrossRef]
- Deveci, M.; Öner, S.C.; Canıtez, F.; Öner, M. Evaluation of service quality in public bus transportation using interval-valued intuitionistic fuzzy QFD methodology. Res. Transp. Bus. Manag. 2019, 2019, 100387. [Google Scholar] [CrossRef]
- Zhou, H.; Wang, J.; Li, X.; Wang, J.Q. Intuitionistic hesitant linguistic sets and their application in multi-criteria decision making problems. Int. J. Oper. Res. 2016, 16, 131–160. [Google Scholar] [CrossRef]
- Karczmarczyk, A.; Jankowski, J.; Sałabun, W. Linguistic Query Based Quality Evaluation of Selected Image Search Engines. Procedia Comput. Sci. 2017, 112, 1809–1818. [Google Scholar] [CrossRef]
- Wang, J.Q.; Wu, J.T.; Wang, J.; Zhang, H.Y.; Chen, X.H. Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf. Sci. 2014, 288, 55–72. [Google Scholar] [CrossRef]
- Zadeh, L.A. The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 1975, 8, 199–249. [Google Scholar] [CrossRef]
- Shih, H.S.; Shyur, H.J.; Lee, E.S. An extension of TOPSIS for group decision making. Math. Comput. Model. 2007, 45, 801–813. [Google Scholar] [CrossRef]
- Yoon, K.P.; Kim, W.K. The behavioral TOPSIS. Expert Syst. Appl. 2017, 89, 266–272. [Google Scholar] [CrossRef]
- Ziemba, P.; Wątróbski, J.; Zioło, M.; Karczmarczyk, A. Using the PROSA method in offshore wind farm location problems. Energies 2017, 10, 1755. [Google Scholar] [CrossRef] [Green Version]
- Ayhan, M.B. A Fuzzy AHP Approach for Supplier Selection Problem: A Case Study in a Gearmotor Company. arXiv 2013, arXiv:1311.2886. [Google Scholar] [CrossRef]
- Bayazit, O. Use of AHP in decision-making for flexible manufacturing systems. J. Manuf. Technol. Manag. 2005, 16, 808–819. [Google Scholar] [CrossRef] [Green Version]
- Gholipour, R.; Jandaghi, G.; Rajaei, R. Contractor selection in MCDM context using fuzzy AHP. Iran. J. Manag. Stud. 2014, 7, 151–173. [Google Scholar]
- Sałabun, W.; Ziemba, P.; Wątróbski, J. The rank reversals paradox in management decisions: The comparison of the AHP and COMET methods. Smart Innov. Syst. Technol. 2016, 56, 181–191. [Google Scholar]
- Bayazit, O. Use of analytic network process in vendor selection decisions. Benchmarking Int. J. 2006, 13, 566–579. [Google Scholar] [CrossRef]
- Bayazit, O.; Karpak, B. An analytical network process-based framework for successful total quality management (TQM): An assessment of Turkish manufacturing industry readiness. Int. J. Prod. Econ. 2007, 105, 79–96. [Google Scholar] [CrossRef]
- Büyüközkan, G.; Güleryüz, S.; Karpak, B. A new combined IF-DEMATEL and IF-ANP approach for CRM partner Evaluation. Int. J. Prod. Econ. 2017, 191, 194–206. [Google Scholar] [CrossRef]
- Piegat, A.; Sałabun, W. Identification of a Multicriteria Decision—Making Model Using the Characteristic Objects Method. Appl. Comput. Intell. Soft Comput. 2014, 2014, 536492. [Google Scholar] [CrossRef] [Green Version]
- Sałabun, W. The Characteristic Objects Method: A new distance based approach to multi-criteria decision-making problems. J. Multi Criteria Decis. Anal. 2015, 22, 37–50. [Google Scholar] [CrossRef]
- Sałabun, W. The Characteristic Objects Method: A new approach to Identify a multi-criteria group decision-making problems. Int. J. Comput. Appl. Technol. 2014, 5, 1597–1602. [Google Scholar]
- Sałabun, W.; Karczmarczyk, A.; Wątróbski, J.; Jankowski, J. Handling Data Uncertainty in Decision Making with COMET. In Proceedings of the 2018 IEEE Symposium Series on Computational Intelligence (SSCI), Bangalore, India, 18–21 November 2018; pp. 1478–1484. [Google Scholar]
- Sałabun, W.; Karczmarczyk, A.; Wątróbski, J. Decision-Making using the Hesitant Fuzzy Sets COMET Method: An Empirical Study of the Electric City Buses Selection. In Proceedings of the 2018 IEEE Symposium Series on Computational Intelligence (SSCI), Bangalore, India, 18–21 November 2018; pp. 1485–1492. [Google Scholar]
- Wang, J.Q.; Wang, J.; Chen, Q.H.; Zhang, H.Y.; Chen, X.H. An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf. Sci. 2014, 280, 338–351. [Google Scholar] [CrossRef]
- Figueira, J.R.; Mousseau, V.; Roy, B. ELECTRE methods. Int. Ser. Oper. Res. Manag. Sci. 2016, 233, 155–185. [Google Scholar]
- Mousavi, M.; Gitinavard, H.; Mousavi, S.M. A soft computing based-modified ELECTRE model for renewable energy policy selection with unknown information. Renew. Sustain. Energy Rev. 2017, 68, 774–787. [Google Scholar] [CrossRef]
- Brans, J.P.; Mareschal, B.; Vincke, P. PROMETHEE: A New Family of Outranking Methods in Multicriteria Analysis. Oper. Res. 1984, 3, 477–490. [Google Scholar]
- Brans, J.P.; de Smet, Y. PROMETHEE methods. In Multiple Criteria Decision Analysis; Springer: New York, NY, USA, 2016; pp. 187–219. [Google Scholar]
- Wu, Y.; Wang, Y.; Chen, K.; Xu, C.; Li, L. Social sustainability assessment of small hydropower with hesitant PROMETHEE method. Sustain. Cities Soc. 2017, 35, 522–537. [Google Scholar] [CrossRef]
- Ziemba, P. NEAT F-PROMETHEE—A new fuzzy multiple criteria decision making method based on the adjustment of mapping trapezoidal fuzzy numbers. Expert Syst. Appl. 2018, 110, 363–380. [Google Scholar] [CrossRef]
- Soares De Mello, J.C.C.B.; Fernandes, J.E.M.; Gomes, L.F.A.M. Multicriteria selection of an aircraft with NAIADE. In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems (ICORES-2012), Vilamoura, Portugal, 2–6 February 2012; pp. 427–431. [Google Scholar]
- Pastijn, H.; Leysen, J. Constructing an outranking relation with ORESTE. Int. Ser. Mod. Appl. Math. Comput. Sci. 1989, 1255–1268. [Google Scholar] [CrossRef]
- Guitouni, A.; Martel, J.-M.; Bélanger, M.; Hunter, C. Multiple criteria courses of action selection. Mil. Oper. Res. 2008, 13, 35–50. [Google Scholar] [CrossRef]
- Wątróbski, J.; Jankowski, J.; Ziemba, P.; Karczmarczyk, A.; Zioło, M. Generalised framework for multi-criteria method selection. Omega 2019, 86, 107–124. [Google Scholar] [CrossRef]
- Farhadinia, B. Distance and similarity measures for higher order hesitant fuzzy sets. Knowl. Based Syst. 2014, 55, 43–48. [Google Scholar] [CrossRef]
- Wang, J.; Wang, J.-Q.; Zhang, H.-Y.; Chen, X.-H. Distance-Based Multi-Criteria Group Decision-Making Approaches with Multi-Hesitant Fuzzy Linguistic Information. Int. J. Inf. Technol. Decis. Mak. 2017, 16, 1069–1099. [Google Scholar] [CrossRef]
- Van der Helm, P.A. Weber-Fechner behavior in symmetry perception? Atten. Percept. Psychophys. 2010, 72, 1854–1864. [Google Scholar] [CrossRef] [Green Version]
- Gitinavard, H.; Mousavi, S.M.; Vahdani, B. Soft computing-based new interval-valued hesitant fuzzy multi-criteria group assessment method with last aggregation to industrial decision problems. Soft Comput. 2017, 21, 3247–3265. [Google Scholar] [CrossRef]
- Gorzalczany, M.B. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 1987, 21, 1–17. [Google Scholar] [CrossRef]
- Lee, C.-S.; Chung, C.-C.; Lee, H.-S.; Gan, G.-Y.; Chou, M.-T. An interval-valued fuzzy number approach for supplier selection. J. Mar. Sci. Technol. 2016, 24, 384–389. [Google Scholar]
- Yao, J.S.; Lin, F.T. Constructing a fuzzy flow-shop sequencing model based on statistical data. Int. J. Approx. Reason. 2002, 29, 215–234. [Google Scholar] [CrossRef] [Green Version]
- Dubois, D.; Prade, H. Operations on fuzzy Numbers. Int. J. Syst. Sci. 1978, 9, 613–626. [Google Scholar] [CrossRef]
- Piegat, A.; Landowski, M. Is an interval the right result of arithmetic operations on intervals? Int. J. Appl. Math. Comput. Sci. 2017, 27, 575–590. [Google Scholar] [CrossRef] [Green Version]
Alternatives | Reference Ranking | |||
---|---|---|---|---|
FP | BM | EP | ||
84 | 8 | 3 | 2 | |
65 | 7 | 8 | ||
73 | 6 | 7 | ||
76 | 8 | 6 | ||
80 | 7 | 4 | ||
61 | 6 | 9 | ||
80 | 5 | |||
85 | 8 | 1 | ||
59 | 6 | 10 | ||
79 | 8 | 4 | 3 |
Sr. No | Variable | Value |
---|---|---|
1 | ||
2 | ||
3 | ||
4 | ||
5 |
Alternatives | Preference Intervals | Rank | ||||
---|---|---|---|---|---|---|
2 | 0.8469 | 2 | 2 | |||
8 | 0.6521 | 8 | 8 | |||
7 | 0.7321 | 7 | 7 | |||
4 | 0.7655 | 6 | 6 | |||
5 | 0.8052 | 3 | 4 | |||
9 | 0.6106 | 9 | 9 | |||
6 | 0.8043 | 4 | 5 | |||
1 | 0.8584 | 1 | 1 | |||
10 | 0.5904 | 10 | 10 | |||
3 | 0.7963 | 5 | 3 |
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Faizi, S.; Sałabun, W.; Ullah, S.; Rashid, T.; Więckowski, J. A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique. Symmetry 2020, 12, 516. https://doi.org/10.3390/sym12040516
Faizi S, Sałabun W, Ullah S, Rashid T, Więckowski J. A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique. Symmetry. 2020; 12(4):516. https://doi.org/10.3390/sym12040516
Chicago/Turabian StyleFaizi, Shahzad, Wojciech Sałabun, Samee Ullah, Tabasam Rashid, and Jakub Więckowski. 2020. "A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique" Symmetry 12, no. 4: 516. https://doi.org/10.3390/sym12040516