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**Refractured well selection for multicriteria group decision making by integrating fuzzy AHP with fuzzy TOPSIS based on interval-typed fuzzy numbers.**
*(English)*
Zbl 1251.90264

Summary: Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems.

### MSC:

90B90 | Case-oriented studies in operations research |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C06 | Large-scale problems in mathematical programming |

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\textit{T. Li} et al., J. Appl. Math. 2012, Article ID 304287, 21 p. (2012; Zbl 1251.90264)

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### References:

[1] | S. T Chen and C. L. Hwang, Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer, Berlin, Germany, 1992. · Zbl 0768.90042 |

[2] | C. L. Hwang and K. Yoon, Multiple Attribute Decision Making Methods and Applications, Springer, Berlin, Germany, 1981. · Zbl 0453.90002 |

[3] | L. Duckstein and S. Opricovic, “Multiobjective optimization in river basin development,” Water Resources Research, vol. 16, no. 1, pp. 14-20, 1980. |

[4] | L. Bale\vzentien\De and A. U\vzupis, “Multi-criteria optimization for mitigation model of greenhouse gas emissions from abandoned grassland,” Journal of Food, Agriculture & Environment, vol. 10, pp. 859-865, 2012. |

[5] | F. Ye, “An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection,” Expert Systems with Applications, vol. 37, pp. 7050-7055, 2010. |

[6] | M. P. Amiri, “Project selection for oil-fields development by using the AHP and fuzzy TOPSIS methods,” Expert Systems with Applications, vol. 37, pp. 6218-6224, 2010. |

[7] | P. K. Dey, “Integrated project evaluation and selection using multiple-attribute decision-making technique,” International Journal of Production Economics, vol. 103, no. 1, pp. 90-103, 2006. |

[8] | B. Ashtiani, F. Haghighirad, A. Makui, and G. A. Montazer, “Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets,” Applied Soft Computing Journal, vol. 9, no. 2, pp. 457-461, 2009. · Zbl 05739045 |

[9] | A. Bale\vzentis and T. Bale\vzentis, “A novel method for group multi-attribute decision making with two-tuple linguistic computing: supplier evaluation under uncertainty,” Economic Computation and Economic Cybernetics Studies and Research, vol. 45, no. 4, pp. 5-30, 2011. |

[10] | A. Guitouni and J. M. Martel, “Tentative guidelines to help choosing an appropriate MCDA method,” European Journal of Operational Research, vol. 109, no. 2, pp. 501-521, 1998. · Zbl 0937.90042 |

[11] | M. S. Kuo and G. S. Liang, “A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers,” Applied Soft Computing, vol. 12, pp. 476-485, 2012. |

[12] | S. Opricovic, Multicriteria Optimization of Civil Engineering Systems, Faculy of Civil Engineering, Belgrade, Serbia, 1998. |

[13] | S. Opricovic and G. H. Tzeng, “Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS,” European Journal of Operational Research, vol. 156, no. 2, pp. 445-455, 2004. · Zbl 1056.90090 |

[14] | K. Peniwati, “Criteria for evaluating group decision-making methods,” Mathematical and Computer Modelling, vol. 46, no. 7-8, pp. 935-947, 2007. · Zbl 1173.91344 |

[15] | D. Bouyssou, “Some remarks on the notion of compensation in MCDM,” European Journal of Operational Research, vol. 26, no. 1, pp. 150-160, 1986. · Zbl 0598.90057 |

[16] | Y. J. Lai, T. Y. Liu, and C. L. Hwang, “TOPSIS for MODM,” European Journal of Operational Research, vol. 76, no. 3, pp. 486-500, 1994. · Zbl 0810.90078 |

[17] | L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338-353, 1965. · Zbl 0139.24606 |

[18] | R. E. Bellman and L. A. Zadeh, “Decision-making in a fuzzy environment,” Management Science, vol. 17, pp. 141-164, 1970. · Zbl 0224.90032 |

[19] | C. T. Chen, “Extensions of the TOPSIS for group decision-making under fuzzy environment,” Fuzzy Sets and Systems, vol. 114, no. 1, pp. 1-9, 2000. · Zbl 0963.91030 |

[20] | G. R. Jahanshahloo, F. H. Lotfi, and M. Izadikhah, “An algorithmic method to extend TOPSIS for decision-making problems with interval data,” Applied Mathematics and Computation, vol. 175, no. 2, pp. 1375-1384, 2006. · Zbl 1131.90386 |

[21] | L. Bale\vzentien\De and E. Klimas, “Multi-criteria evaluation of new humic fertilizers effectiveness and optimal rate on a basis of TOPSIS method,” Journal of Food, Agriculture & Environment, vol. 9, pp. 465-471, 2011. |

[22] | F. Wei-Guo and Z. Hong, “A multi-attribute group decision-making method approaching to group ideal solution,” in Proceedings of IEEE International Conference on Grey Systems and Intelligent Services (GSIS ’07), pp. 815-819, November 2007. |

[23] | R. A. Krohling and V. C. Campanharo, “Fuzzy TOPSIS for group decision making: a case study for accidents with oil spill in the sea,” Expert Systems with Applications, vol. 38, no. 4, pp. 4190-4197, 2011. |

[24] | T. L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, NY, USA, 1980. · Zbl 0587.90002 |

[25] | M. Da\vgdeviren and I. Yüksel, “Developing a fuzzy analytic hierarchy process (AHP) model for behavior-based safety management,” Information Sciences, vol. 178, no. 6, pp. 1717-1733, 2008. · Zbl 05248570 |

[26] | S. M. Miri Lavasani, Z. Yang, J. Finlay, and J. Wang, “Fuzzy risk assessment of oil and gas offshore wells,” Process Safety and Environmental Protection, vol. 89, pp. 277-294, 2011. |

[27] | Y. B. Ju and A. H. Wang, “Emergency alternative evaluation under group decision makers: a method of incorporating DS/AHP with extended TOPSIS,” Expert Systems with Applications, vol. 39, pp. 1315-1323, 2012. |

[28] | T. L. Saaty and L. T. Tran, “On the invalidity of fuzzifying numerical judgments in the analytic hierarchy process,” Mathematical and Computer Modelling, vol. 46, no. 7-8, pp. 962-975, 2007. · Zbl 1173.91345 |

[29] | C. C. Sun, “A performance evaluation model by integrating fuzzy AHP and fuzzy TOPSIS methods,” Expert Systems with Applications, vol. 37, no. 12, pp. 7745-7754, 2010. |

[30] | A. T. Gumus, “Evaluation of hazardous waste transportation firms by using a two step fuzzy-AHP and TOPSIS methodology,” Expert Systems with Applications, vol. 36, no. 2, pp. 4067-4074, 2009. |

[31] | F. Torfi, R. Z. Farahani, and S. Rezapour, “Fuzzy AHP to determine the relative weights of evaluation criteria and Fuzzy TOPSIS to rank the alternatives,” Applied Soft Computing Journal, vol. 10, no. 2, pp. 520-528, 2010. · Zbl 05739803 |

[32] | G. Büyüközkan and G. Cifci, “A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry,” Expert Systems with Applications, vol. 39, pp. 2341-2354, 2012. |

[33] | T.-Y. Chen and C.-Y. Tsao, “The interval-valued fuzzy TOPSIS method and experimental analysis,” Fuzzy Sets and Systems, vol. 159, no. 11, pp. 1410-1428, 2008. · Zbl 1178.90179 |

[34] | P. Liu, “A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers,” Expert Systems with Applications, vol. 38, no. 1, pp. 1053-1060, 2011. |

[35] | P. Liu, “An extended TOPSIS method for multiple attribute group decision making based on generalized interval-valued trapezoidal fuzzy numbers,” Informatica, vol. 35, no. 2, pp. 185-196, 2011. · Zbl 1242.68335 |

[36] | P. Liu and F. Jin, “A multi-attribute group decision-making method based on weighted geometric aggragation operators of interval-valued trapezoidal fuzzy numbers,” Applied Mathematical Modelling, vol. 36, pp. 2498-2509, 2012. · Zbl 1246.91034 |

[37] | G. Wang and X. Li, “Correlation and information energy of interval-valued fuzzy numbers,” Fuzzy Sets and Systems, vol. 103, no. 1, pp. 169-175, 1999. · Zbl 1017.94034 |

[38] | S. H. Wei and S. M. Chen, “Fuzzy risk analysis based on interval-valued fuzzy numbers,” Expert Systems with Applications, vol. 36, no. 2, pp. 2285-2299, 2009. |

[39] | R.-C. Tsaur, “Decision risk analysis for an interval TOPSIS method,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4295-4304, 2011. · Zbl 1239.90074 |

[40] | C. Kahraman, T. Ertay, and G. Büyüközkan, “A fuzzy optimization model for QFD planning process using analytic network approach,” European Journal of Operational Research, vol. 171, no. 2, pp. 390-411, 2006. · Zbl 1090.90016 |

[41] | E. Tolga, M. L. Demircan, and C. Kahraman, “Operating system selection using fuzzy replacement analysis and analytic hierarchy process,” International Journal of Production Economics, vol. 97, no. 1, pp. 89-117, 2005. |

[42] | L. Mikhailov, “A fuzzy approach to deriving priorities from interval pairwise comparison judgements,” European Journal of Operational Research, vol. 159, no. 3, pp. 687-704, 2004. · Zbl 1065.90523 |

[43] | M. T. Tang, G. H. Tzeng, and S. W. Wang, “A hierarchy fuzzy MCDM method for studying electronic marketing strategies in the information service industry,” Journal of International Information Management, vol. 8, pp. 1-22, 2000. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.