本論文旨在根據我們所提之非線性規劃法、得分矩陣中之得分值之間的距 離、及我們所提之區間直覺模糊值之新的得分函數提出一個作多屬性決策之新方法，其中我們所提之非線性規劃法被用於獲得各屬性之最佳權重。首先，我們提出一個區間直覺模糊值之新的得分函數，以克服目前已存在之區間直覺模糊值之得分函數的缺點。然後，我們根據所提之得分函數和決策者提供之決策矩陣以構建分數矩陣。然後，根據構建的分數矩陣中的得分值之間的距離、決策者提供之各屬性的區間直覺模糊值權重、偏差變量的概念、及每個屬性之最大區間直覺模糊權重之範圍，我們提出一個非線性規劃法以獲得各屬性之最佳權重。然後，我們根據所得之分數矩陣及各屬性的最佳權重計算每一個方案的加權分數。最後，我們根據每一個方案的加權分數以對所有的方案進行排序以獲得所有的方案之偏好順序。我們所提之新的多屬性決策方法能夠克服目前已存在之多屬性決策方法的缺點。

In this thesis, we propose a new multiple attribute decision making method based on the proposed nonlinear programming model, the distance between the score values appeared in the constructed score matrix, and the proposed score function of interval-valued intuitionistic fuzzy values, where the nonlinear programming model is used to obtain the optimal weights of the attributes. Firstly, we propose a new score function to overcome the drawbacks of the existing score functions of interval-valued intuitionistic fuzzy values. Then, we use the proposed score function to build the score matrix from the decision matrix provided by the decision maker. Then, we propose a nonlinear programming model to get the optimal weights of the attributes based on the distance between the score values appeared in the constructed score matrix, the interval-valued intuitionistic fuzzy weights of the attributes given by the decision maker, the concept of deviation variables, and the largest range of the interval-valued intuitionistic fuzzy weight of each attribute. Then, we compute the weighted score of each alternative based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, we rank the alternatives based on the weighted scores of the alternatives to get the preference order of the alternatives. The proposed multiple attribute decision making method can overcome the drawbacks of the existing multiple attribute decision making methods.

[1] M. Akram, A. Sattar, and A. B. Saeid, “Competition graphs with complex intuitionistic fuzzy information,” Granular Computing, vol. 7, no. 1, pp. 25-47, 2022.
[2] S. Askari, “Noise-resistant fuzzy clustering algorithm,” Granular Computing, vol. 6, no. 4, pp. 815-828, 2021.
[3] K. Atanassov and G. Gargov, “Interval valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 31 no. 3, pp. 343-349, 1989.
[4] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
[5] Z. Y. Bai, “An interval-valued intuitionistic fuzzy TOPSIS method based on an improved score function,” The Scientific World Journal, vol. 2013, Article ID 879089, 6 pages, 2013 (https://doi.org/10.1155/2013/879089).
[6] E. Bas and E. Egrioglu, “A fuzzy regression functions approach based on Gustafson-Kessel Clustering Algorithm,” Information Sciences, vol. 592, pp. 206-214, 2022.
[7] D. Bishop and K. Mogford, “Language development in exceptional circumstances,” Psychology Press, New York, U.S.A., pp. 8, 2013.
[8] P.S. Bullen, Handbook of Means and Their Inequalities, pp. 399-401, 2003.
[9] S. M. Chen and C. H. Chiou, “Multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques, and evidential reasoning methodology,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 6, pp. 1905-1916, 2015.
[10] S. M. Chen and Y. C. Chu, “Multiattribute decision making based on U-quadratic distribution of intervals and the transformed matrix in interval-valued intuitionistic fuzzy environments,” Information Sciences, vol. 537, pp. 30-45, 2020.
[11] S. M. Chen and H. L. Deng, “Multiattribute decision making based on nonlinear programming methodology and novel score function of interval-valued intuitionistic fuzzy values,” Information Sciences, vol. 607, pp. 1348-1371, 2022.
[12] S. M. Chen and K. Y. Fan, “Multiattribute decision making based on probability density functions and the variances and standard deviations of largest ranges of evaluating interval-valued intuitionistic fuzzy values,” Information Sciences, vol. 490, pp. 329-343, 2019.
[13] S. M. Chen and W. H. Han, “A new multiattribute decision making method based on multiplication operations of interval-valued intuitionistic fuzzy values and linear programming methodology,” Information Sciences, vol. 429, pp. 421-432, 2018.
[14] S. M. Chen and W. H. Han, “An improved multiattribute decision making method using interval-valued intuitionistic fuzzy values,” Information Sciences, vol. 467, pp. 489-505, 2018.
[15] S. M. Chen and Z. C. Huang, “Multiattribute decision making based on interval-valued intuitionistic fuzzy values and linear programming methodology,” Information Sciences, vol. 381, pp. 341-351, 2017.
[16] S. M. Chen and W. T. Liao, “Multiple attribute decision making using Beta distribution of intervals, expected values of intervals, and new score function of interval-valued intuitionistic fuzzy values,” Information Sciences, vol. 579, pp. 863-887, 2021.
[17] S. M. Chen and G. L. Lu, “Multiple attribute decision making based on novel nonlinear programming model, the distance between score values, and novel score function of interval-valued intuitionistic fuzzy values,” Information Sciences, vol.654, 119338, 2023.
[18] S. M. Chen and B. D. Phuong, “Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors,” Knowledge-Based Systems, vol. 118, pp. 204-216, 2017.
[19] S. M. Chen and C. A. Tsai, “Multiattribute decision making using novel score function of interval-valued intuitionistic fuzzy values and the means and the variances of score matrices,” Information Sciences, vol. 577, pp. 748-768, 2021..
[20] S. M. Chen and K. Y. Tsai, “Multiattribute decision making based on new score function of interval-valued intuitionistic fuzzy values and normalized score matrices,” Information Sciences, vol. 575, pp. 714-731, 2021.
[21] S. M. Chen and C. H. Wang, “Fuzzy risk analysis based on ranking fuzzy numbers using α-cuts, belief features and signal/noise ratios,” Expert Systems with Applications, vol. 36, no. 3, pp. 5576-5581, 2009.
[22] S. M. Chen and S. H. Yu, “Multiattribute decision making based on novel score function and the power operator of interval-valued intuitionistic fuzzy values,” Information Sciences, vol. 606, pp. 763-785, 2022.
[23] T. Y. Chen, “A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings,” Information Sciences, vol. 181, no. 17, pp. 3652-3676, 2011.
[24] S. Dick, R. R. Yager and O. Yazdanbakhsh, "On Pythagorean and Complex Fuzzy Set Operations," IEEE Transactions on Fuzzy Systems, vol. 24, no. 5, pp. 1009-1021, 2016.
[25] J. Dong, S. Wan, and S. M. Chen, “Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making,” Information Sciences, vol. 547, pp. 1080-1104, 2021.
[26] P. Dutta, “Multi-criteria decision making under uncertainty via the operations of generalized intuitionistic fuzzy numbers,” Granular Computing, vol. 6, no. 2, pp. 321-337, 2021.
[27] P. Dutta and D. Doley, “Fuzzy decision making for medical diagnosis using arithmetic of generalised parabolic fuzzy numbers,” Granular Computing, vol. 6, no. 2, pp. 377-388, 2021.
[28] P. Dutta and B. Saikia, “Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making,” Granular Computing, vol. 6, no. 1, pp. 163-179, 2021.
[29] E. Egrioglu, R. Fildes, and E. Baş, “Recurrent fuzzy time series functions approaches for forecasting,” Granular Computing, vol. 7, no. 1, pp. 163-170, 2022.
[30] R. Gupta and S. Kumar, “Intuitionistic fuzzy scale-invariant entropy with correlation coefficients-based VIKOR approach for multi-criteria decision-making,” Granular Computing, vol. 7, no. 1, pp. 77-93, 2022.
[31] Y. T. İç and M. Yurdakul, “Development of a new trapezoidal fuzzy AHP-TOPSIS hybrid approach for manufacturing firm performance measurement,” Granular Computing, vol. 6, no. 4, pp. 915-929, 2021.
[32] R. Joshi, “Multi-criteria decision-making based on bi-parametric exponential fuzzy information measures and weighted correlation coefficients,” Granular Computing, vol. 7, no. 1, pp. 49-62, 2022.
[33] R. Kadian and S. Kumar, “A novel intuitionistic Renyi’s-Tsallis discriminant information measure and its applications in decision-making,” Granular Computing, vol. 6, no. 4, pp. 901-913, 2021.
[34] M. Kaushal and Q. M. Lohani, “Generalized intuitionistic fuzzy c-means clustering algorithm using an adaptive intuitionistic fuzzification technique,” Granular Computing, vol. 7, no. 1, pp. 183-195, 2022.
[35] K. Kumar and S. M. Chen, “Multiattribute decision making based on converted decision matrices, probability density functions, and interval-valued intuitionistic fuzzy values,” Information Sciences, vol. 554, pp 313-324, 2021.
[36] K. Kumar and S. M. Chen, “Multiattribute decision making based on interval-valued intuitionistic fuzzy values, score function of connection numbers, and the set pair analysis theory,” Information Sciences, vol. 551, pp. 100-112, 2021.
[37] K. Kumar and S. M. Chen, “Multiattribute decision making based on the improved intuitionistic fuzzy Einstein weighted averaging operator of intuitionistic fuzzy values,” Information Sciences, vol. 568, pp. 369-383, 2021.
[38] C. S. Lee, M. H. Wang and S. T. Lan, "Adaptive Personalized Diet Linguistic Recommendation Mechanism Based on Type-2 Fuzzy Sets and Genetic Fuzzy Markup Language," IEEE Transactions on Fuzzy Systems, vol. 23, no. 5, pp. 1777-1802, 2015
[39] D. F. Li, “TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 2, pp. 299-311, 2010.
[40] H. Liu, J. Tu, and C. Sun, “Improved possibility degree method for intuitionistic fuzzy multi-attribute decision making and application in aircraft cockpit display ergonomic evaluation,” IEEE Access, vol. 8, pp. 202540-202554, 2020.
[41] Y. Mu, J. Wang, W. Wei, H. Guo, L. Wang, and X. Liu, “Information granulation-based fuzzy partition in decision tree induction,” Information Sciences, vol. 608, pp. 1651-1674, 2022.
[42] Muneeza, S. Abdullah, M. Qiyas, and M. A. Khan, “Multi-criteria decision making based on intuitionistic cubic fuzzy numbers,” Granular Computing, vol. 7, no. 1, pp. 217-227, 2022.
[43] M. Pant and S. Kumar, “Particle swarm optimization and intuitionistic fuzzy set-based novel method for fuzzy time Series forecasting,” Granular Computing, vol. 7, no. 2, pp. 285-303, 2022.
[44] K. Patra, “Fuzzy risk analysis using a new technique of ranking of generalized trapezoidal fuzzy numbers,” Granular Computing, vol. 7, no. 1, pp. 127-140, 2022.
[45] G. Ruiz-García, H. Hagras, H. Pomares and I. R. Ruiz, "Toward a Fuzzy Logic System Based on General Forms of Interval Type-2 Fuzzy Sets," IEEE Transactions on Fuzzy Systems, vol. 27, no. 12, pp. 2381-2395, 2019.
[46] S. Sen, K. Patra, and S. K. Mondal, “A new approach to similarity measure for generalized trapezoidal fuzzy numbers and its application to fuzzy risk analysis,” Granular Computing, vol. 6, no. 3, pp. 705-718, 2021.
[47] S. H. Tsai and Y. W. Chen, "A Novel Interval Type-2 Fuzzy System Identification Method Based on the Modified Fuzzy C-Regression Model," IEEE Transactions on Cybernetics, vol. 52, no. 9, pp. 9834-9845, 2022.
[48] S. Wan, J. Dong, and S. M. Chen, “Fuzzy best-worst method based on generalized interval-valued trapezoidal fuzzy numbers for multi-criteria decision-making,” Information Sciences, vol. 573, pp. 493-518, 2021.
[49] Z. S. Xu, “Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making,” Control and Decision, vol. 22, no. 2, pp. 215-219, 2007. (in Chinese)
[50] C. Yang, Q. Wang, W. Peng, J. Zhang, and J. Zhu, “A normal wiggly Pythagorean hesitant fuzzy bidirectional projection method and its application in EV Power Battery Recycling Mode Selection,” IEEE Access, vol. 8, pp. 62164-62180, 2020.
[51] Z. Yang and J. Chang, “Interval-valued pythagorean normal fuzzy information aggregation operators for multi-attribute decision making,” IEEE Access, vol. 8, pp. 51295-51314, 2020.
[52] Dejian Yu and Yingyu Wu, “Interval-valued intuitionistic fuzzy Heronian mean operators and their application in multi-criteria decision making,” African Journal of Business Management, vol. 6, no. 11, pp. 4158-4168, 2012.
[53] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
[54] Z. Zhitao and Z. Yingjun, “Multiple attribute decision making method in the frame of interval-valued intuitionistic fuzzy sets,” in: Proceedings of the 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery, Shanghai, China, 2011, pp. 192-196.
[55] A. Ziqan, S. Ibrahim, M. Marabeh, and A. Qarariyah, “Fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers,” Granular Computing, vol. 7, no. 2, pp. 229-238, 2022.