An integrated picture fuzzy ANP-TODIM multi-criteria decision-making approach for tourism attraction recommendation
Abstract
In this paper, the picture fuzzy score and accuracy function are first defined. Then, a corresponding comparative method between two picture fuzzy numbers (PFNs) is developed. Next, a novel normalized picture fuzzy distance measure between two PFNs is disclosed, and part of the characteristics of the proposed distance measure are discussed. Afterwards, on the basis of the analytic network process (ANP) and an Acronym in Portuguese of Interactive and Multi-Criteria Decision-Making (TODIM) methods, an integrated ANP-TODIM approach is developed to resolve multi-criteria decision-making (MCDM) where the weights of the criteria are fully unknown. We use ANP approach to decide the weights of criteria on the basis of expert mean assessment method, and TODIM is utilized to obtain the ranking of alternatives. Finally, an illustrative example of an optimal tourism attraction recommendation is provided to testify applicability of the developed decision-making method and prove that its results are effective and reasonable.
First published online 3 December 2019
Keyword : multi-criteria decision-making, picture fuzzy numbers, ANP-TODIM, picture fuzzy distance
How to Cite
Tian, C., & Peng, J. (2020). An integrated picture fuzzy ANP-TODIM multi-criteria decision-making approach for tourism attraction recommendation. Technological and Economic Development of Economy, 26(2), 331-354. https://doi.org/10.3846/tede.2019.11412
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Barton, R. R., Nelson, B. L., & Xie, W. (2014). Quantifying input uncertainty via simulation confidence intervals. Informs Journal on Compuing, 26(1), 74-87 (in Chinese). https://doi.org/10.1287/ijoc.2013.0548
Chang, K. L., Liao, S. K., Tseng, T. W., & Liao, C. Y. (2015). An ANP based TOPSIS approach for Taiwanese service apartment location selection. Asia Pacific Management Review, 20(2), 49-55. https://doi.org/10.1016/j.apmrv.2014.12.007
Chatterjee, K., & Kar, S. (2018a). A multi-criteria decision making method for renewable energy selection using Z-number in uncertain environment. Technological and Economic Development of Economy, 24(2), 739-764. https://doi.org/10.3846/20294913.2016.1261375
Chatterjee, K., & Kar, S. (2018b). Supplier selection in telecom supply chain management: a fuzzy-rasch based COPRAS-G method. Technological and Economic Development of Economy, 24(2), 765-791. https://doi.org/10.3846/20294913.2017.1295289
Chen, J. Q., & Tang, T. (2014). Research on simulation credibility of train operation control system based on improved FAHP method. Journal of the China Railway Society, 36(3), 59-66 (in Chinese).
Cuong, B. C., & Kreinovich, V. (2013). Picture fuzzy sets-a new concept for computational intelligence problems. In Proceedings of 3rd World Congress on Information and Communication Technologies (WICT) (pp. 1-6), Hanoi, Vietnam. https://doi.org/10.1109/WICT.2013.7113099
Debnath, A., Bandyapadhyay, A., Roy, J., & Kar, S. (2018). Game theory based multi criteria decisionmaking problem under uncertainty: a case study on Indian tea industry. Journal of Business Economics and Management, 19(1), 154-175. https://doi.org/10.3846/16111699.2017.1401553
Debnath, A., Roy, J., & Kar, S. (2018). Measuring corporate social responsibility based on fuzzy analytic networking process-based balance scorecard model. International Journal of Information Technology & Decision Making, 17(4), 1203-1235. https://doi.org/10.1142/S0219622018500232
Gomes, L. F. A. M., & Lima, M. M. P. P. (1992a). TODIM: Basics and application to multicriteria ranking of projects with environmental impacts. Foundations of Computing and Decision science, 16(4), 113-127.
Gomes, L. F. A. M., & Lima, M. M. P. P. (1992b). From modeling individual preferences to multicriteria ranking of discrete alternatives: a look at prospect theory and the additive difference model. Foundations of Computing and Decision Sciences, 17, 171-184.
Hu, J. H., Zhang, X. H., Yang, Y., Liu, Y. M., & Chen, X. H. (2018). New doctors ranking system based on VIKOR method. International Transactions in Operational Research, 27(2), 1236-1261. https://doi.org/10.1111/itor.12569
Ji, P., Zhang, H. Y., & Wang, J. Q. (2018). A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Computing & Applications, 29(1), 221-234. https://doi.org/10.1007/s00521-016-2436-z
Joshi, R., Kumar, S., Gupta, D., & Kaur, H. (2017). A Jensen-a-norm dissimilarity measure for intuitionistic fuzzy sets and its applications in multiple attribute decision making. International Journal of Fuzzy Systems, 5, 1-15.
Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263-291. https://doi.org/10.2307/1914185
Li, D. F., & Cheng, C. T. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognition. Pattern Recognition Letters, 33, 221-225. https://doi.org/10.1016/S0167-8655(01)00110-6
Liu, H. W., & Wang, G. J. (2007). Multi-criteria methods based on intuitionistic fuzzy sets. European Journal Operational Research, 179(1), 220-233. https://doi.org/10.1016/j.ejor.2006.04.009
Mishra, A. R., Jain, D., & Hooda, D. S. (2017). Exponential intuitionistic fuzzy information measure with assessment of service quality. International Journal of Fuzzy Systems, 19(3), 788-798. https://doi.org/10.1007/s40815-016-0278-6
Ngan, R. T., Son, L. H., Cuong, B. C., & Ali, M. (2018). H-max distance measure of intuitionistic fuzzy sets in decision making. Applied Soft Computing, 69, 393-425. https://doi.org/10.1016/j.asoc.2018.04.036
Nguyen, V. D., & Nguyen, X. T. (2018). Some measures of picture fuzzy sets and their application in multi-attribute decision making. International Journal of Mathematical Sciences and Computing, 4(3), 23-41. https://doi.org/10.5815/ijmsc.2018.03.03
Peng, J. J., Wang, J. Q., & Wu, X. H. (2016). Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. International Journal of Information Technology & Decision Making, 15(03), 621-643. https://doi.org/10.1142/S0219622016500152
Pramanik, S., Dalapati, S., Alam, S., & Roy, T. K. (2018). NC-TODIM-based MAGDM under a neutrosophic cubic set environment. Information, 8(4), 149. https://doi.org/10.3390/info8040149
Saaty, T. L. (1996). Decision making with dependence and feedback: The analytic network process. International, 95(2), 129-157.
Shen, K. W., Li, L., & Wang, J. Q. (2019). Circular economy model for recycling waste resources under government participation: a case study in industrial waste water circulation in China. Technological and Economic Development of Economy.
Singh, P. (2015). Correlation coefficients for picture fuzzy sets. Journal of Intelligent & Fuzzy Systems, 28(2), 591-604.
Son, L. H. (2017). Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. Fuzzy Optimization & Decision Making, 16, 1-20. https://doi.org/10.1007/s10700-016-9249-5
Thong, P. H. (2016a). Picture fuzzy clustering for complex data. Engineering Applications of Artificial Intelligence, 56, 121-130. https://doi.org/10.1016/j.engappai.2016.08.009
Thong, P. H. (2016b). A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality. Knowledge-Based Systems, 109, 48-60. https://doi.org/10.1016/j.knosys.2016.06.023
Tian, C., Peng, J. J., Zhang, S., Zhang, W. Y., & Wang, J. Q. (2019). Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems. Computers & Industrial Engineering, 137, 106037. https://doi.org/10.1016/j.cie.2019.106037
Wang, J. Q., Han, Z. Q., & Zhang, H. Y. (2014). Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group Decision and Negotiation, 23, 715-733. https://doi.org/10.1007/s10726-012-9316-4
Wang, L., Peng, J. J., & Wang, J. Q. (2018). A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment. Journal of Cleaner Production, 191, 105-118. https://doi.org/10.1016/j.jclepro.2018.04.169
Wang, L., Wang, X. K., Peng, J. J., & Wang, J. Q. (2020). The differences in hotel selection among various types of travellers: A comparative analysis with a useful bounded rationality behavioural decision support model. Tourism Management, 76, 103961. https://doi.org/10.1016/j.tourman.2019.103961
Wang, L., Zhang, H. Y., Wang, J. Q., Wu, G. F. (2019). Picture fuzzy multi-criteria group decisionmaking method to hotel building energy efficiency retrofit project selection. RAIRO-Operations Research. https://doi.org/10.1051/ro/2019004
Wang, R., Wang, J., Gao, H., & Wei, G. W. (2019). Methods for MADM with picture fuzzy Muirhead mean operators and their application for evaluating the financial investment risk. Symmetry, 11(1), 6. https://doi.org/10.3390/sym11010006
Wang, W. Z., & Liu, X. W. (2012). Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Transactions on Fuzzy Systems, 20, 923-938. https://doi.org/10.1109/TFUZZ.2012.2189405
Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern Recognition Letters 26(13), 2063-2069. https://doi.org/10.1016/j.patrec.2005.03.018
Wei, G. W. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17(4), 491-502. https://doi.org/10.3846/16111699.2016.1197147
Wen, Y. M., Shi, Y. F., Cai, G. Y., Miao, Y. Q., & Long, G. (2014). A survey of personalized travel recommendation. Computer Science, Z11.
Wu, Y. N., Zhang, B. Y., Xu, C. B., & Li, L. W. Y. (2018). Site selection decision framework using fuzzy ANP-VIKOR for large commercial rooftop PV system based on sustainability perspective. Sustainable Cities and Society, 40, 454-470. https://doi.org/10.1016/j.scs.2018.04.024
Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operations. IEEE Transactions on Fuzzy Systems, 15, 1179-1187. https://doi.org/10.1109/TFUZZ.2006.890678
Yang, L. Z., Gong, X. Y., Wang, X. J., & An, S. Q. (2014). Generalized exponential entropy on intuitionistic fuzzy sets. Applied Mechanics & Materials, 556-562, 4097-4102. https://doi.org/10.4028/www.scientific.net/AMM.556-562.4097
Yang, Y., Hu, J. H., Liu, Y. M., & Chen, X. H. (2018). Doctor recommendation based on an intuitionistic normal cloud model considering patient preferences. Cognitive Computation, 1-19. https://doi.org/10.1007/s12559-018-9616-3
Yu, S. M., Wang, J., & Wang, J. Q. (2018). An extended TODIM approach with intuitionistic linguistic numbers. International Transactions in Operational Research, 25(3), 781-805. https://doi.org/10.1111/itor.12363
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-356. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, G., Wang, J. Q., & Wang, T. L. (2019). Multi-criteria group decision-making method based on TODIM with probabilistic interval-valued hesitant fuzzy information. Expert Systems, 36(4), 12424. https://doi.org/10.1111/exsy.12424
Zhang, X. L., & Xu, Z. S. (2014). The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowledge-Based Systems, 61, 48-58. https://doi.org/10.1016/j.knosys.2014.02.006
Zhang, X. Y., Wang, J. Q., & Hu, J. H. (2018). On novel operational laws and aggregation operators of picture 2-tuple linguistic information for MCDM problems. International Journal of Fuzzy Systems, 20(3), 958-969. https://doi.org/10.1007/s40815-017-0441-8
Zhang, Y. P., Wang, Y. H., & Yang, N. (2018). On the risk assessment method of balise system based on the ANP and fuzzy evidence theory. Journal of Safety and Environment, 18(2), 434-440 (in Chinese).
Barton, R. R., Nelson, B. L., & Xie, W. (2014). Quantifying input uncertainty via simulation confidence intervals. Informs Journal on Compuing, 26(1), 74-87 (in Chinese). https://doi.org/10.1287/ijoc.2013.0548
Chang, K. L., Liao, S. K., Tseng, T. W., & Liao, C. Y. (2015). An ANP based TOPSIS approach for Taiwanese service apartment location selection. Asia Pacific Management Review, 20(2), 49-55. https://doi.org/10.1016/j.apmrv.2014.12.007
Chatterjee, K., & Kar, S. (2018a). A multi-criteria decision making method for renewable energy selection using Z-number in uncertain environment. Technological and Economic Development of Economy, 24(2), 739-764. https://doi.org/10.3846/20294913.2016.1261375
Chatterjee, K., & Kar, S. (2018b). Supplier selection in telecom supply chain management: a fuzzy-rasch based COPRAS-G method. Technological and Economic Development of Economy, 24(2), 765-791. https://doi.org/10.3846/20294913.2017.1295289
Chen, J. Q., & Tang, T. (2014). Research on simulation credibility of train operation control system based on improved FAHP method. Journal of the China Railway Society, 36(3), 59-66 (in Chinese).
Cuong, B. C., & Kreinovich, V. (2013). Picture fuzzy sets-a new concept for computational intelligence problems. In Proceedings of 3rd World Congress on Information and Communication Technologies (WICT) (pp. 1-6), Hanoi, Vietnam. https://doi.org/10.1109/WICT.2013.7113099
Debnath, A., Bandyapadhyay, A., Roy, J., & Kar, S. (2018). Game theory based multi criteria decisionmaking problem under uncertainty: a case study on Indian tea industry. Journal of Business Economics and Management, 19(1), 154-175. https://doi.org/10.3846/16111699.2017.1401553
Debnath, A., Roy, J., & Kar, S. (2018). Measuring corporate social responsibility based on fuzzy analytic networking process-based balance scorecard model. International Journal of Information Technology & Decision Making, 17(4), 1203-1235. https://doi.org/10.1142/S0219622018500232
Gomes, L. F. A. M., & Lima, M. M. P. P. (1992a). TODIM: Basics and application to multicriteria ranking of projects with environmental impacts. Foundations of Computing and Decision science, 16(4), 113-127.
Gomes, L. F. A. M., & Lima, M. M. P. P. (1992b). From modeling individual preferences to multicriteria ranking of discrete alternatives: a look at prospect theory and the additive difference model. Foundations of Computing and Decision Sciences, 17, 171-184.
Hu, J. H., Zhang, X. H., Yang, Y., Liu, Y. M., & Chen, X. H. (2018). New doctors ranking system based on VIKOR method. International Transactions in Operational Research, 27(2), 1236-1261. https://doi.org/10.1111/itor.12569
Ji, P., Zhang, H. Y., & Wang, J. Q. (2018). A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Computing & Applications, 29(1), 221-234. https://doi.org/10.1007/s00521-016-2436-z
Joshi, R., Kumar, S., Gupta, D., & Kaur, H. (2017). A Jensen-a-norm dissimilarity measure for intuitionistic fuzzy sets and its applications in multiple attribute decision making. International Journal of Fuzzy Systems, 5, 1-15.
Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263-291. https://doi.org/10.2307/1914185
Li, D. F., & Cheng, C. T. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognition. Pattern Recognition Letters, 33, 221-225. https://doi.org/10.1016/S0167-8655(01)00110-6
Liu, H. W., & Wang, G. J. (2007). Multi-criteria methods based on intuitionistic fuzzy sets. European Journal Operational Research, 179(1), 220-233. https://doi.org/10.1016/j.ejor.2006.04.009
Mishra, A. R., Jain, D., & Hooda, D. S. (2017). Exponential intuitionistic fuzzy information measure with assessment of service quality. International Journal of Fuzzy Systems, 19(3), 788-798. https://doi.org/10.1007/s40815-016-0278-6
Ngan, R. T., Son, L. H., Cuong, B. C., & Ali, M. (2018). H-max distance measure of intuitionistic fuzzy sets in decision making. Applied Soft Computing, 69, 393-425. https://doi.org/10.1016/j.asoc.2018.04.036
Nguyen, V. D., & Nguyen, X. T. (2018). Some measures of picture fuzzy sets and their application in multi-attribute decision making. International Journal of Mathematical Sciences and Computing, 4(3), 23-41. https://doi.org/10.5815/ijmsc.2018.03.03
Peng, J. J., Wang, J. Q., & Wu, X. H. (2016). Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. International Journal of Information Technology & Decision Making, 15(03), 621-643. https://doi.org/10.1142/S0219622016500152
Pramanik, S., Dalapati, S., Alam, S., & Roy, T. K. (2018). NC-TODIM-based MAGDM under a neutrosophic cubic set environment. Information, 8(4), 149. https://doi.org/10.3390/info8040149
Saaty, T. L. (1996). Decision making with dependence and feedback: The analytic network process. International, 95(2), 129-157.
Shen, K. W., Li, L., & Wang, J. Q. (2019). Circular economy model for recycling waste resources under government participation: a case study in industrial waste water circulation in China. Technological and Economic Development of Economy.
Singh, P. (2015). Correlation coefficients for picture fuzzy sets. Journal of Intelligent & Fuzzy Systems, 28(2), 591-604.
Son, L. H. (2017). Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. Fuzzy Optimization & Decision Making, 16, 1-20. https://doi.org/10.1007/s10700-016-9249-5
Thong, P. H. (2016a). Picture fuzzy clustering for complex data. Engineering Applications of Artificial Intelligence, 56, 121-130. https://doi.org/10.1016/j.engappai.2016.08.009
Thong, P. H. (2016b). A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality. Knowledge-Based Systems, 109, 48-60. https://doi.org/10.1016/j.knosys.2016.06.023
Tian, C., Peng, J. J., Zhang, S., Zhang, W. Y., & Wang, J. Q. (2019). Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems. Computers & Industrial Engineering, 137, 106037. https://doi.org/10.1016/j.cie.2019.106037
Wang, J. Q., Han, Z. Q., & Zhang, H. Y. (2014). Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group Decision and Negotiation, 23, 715-733. https://doi.org/10.1007/s10726-012-9316-4
Wang, L., Peng, J. J., & Wang, J. Q. (2018). A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment. Journal of Cleaner Production, 191, 105-118. https://doi.org/10.1016/j.jclepro.2018.04.169
Wang, L., Wang, X. K., Peng, J. J., & Wang, J. Q. (2020). The differences in hotel selection among various types of travellers: A comparative analysis with a useful bounded rationality behavioural decision support model. Tourism Management, 76, 103961. https://doi.org/10.1016/j.tourman.2019.103961
Wang, L., Zhang, H. Y., Wang, J. Q., Wu, G. F. (2019). Picture fuzzy multi-criteria group decisionmaking method to hotel building energy efficiency retrofit project selection. RAIRO-Operations Research. https://doi.org/10.1051/ro/2019004
Wang, R., Wang, J., Gao, H., & Wei, G. W. (2019). Methods for MADM with picture fuzzy Muirhead mean operators and their application for evaluating the financial investment risk. Symmetry, 11(1), 6. https://doi.org/10.3390/sym11010006
Wang, W. Z., & Liu, X. W. (2012). Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Transactions on Fuzzy Systems, 20, 923-938. https://doi.org/10.1109/TFUZZ.2012.2189405
Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern Recognition Letters 26(13), 2063-2069. https://doi.org/10.1016/j.patrec.2005.03.018
Wei, G. W. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17(4), 491-502. https://doi.org/10.3846/16111699.2016.1197147
Wen, Y. M., Shi, Y. F., Cai, G. Y., Miao, Y. Q., & Long, G. (2014). A survey of personalized travel recommendation. Computer Science, Z11.
Wu, Y. N., Zhang, B. Y., Xu, C. B., & Li, L. W. Y. (2018). Site selection decision framework using fuzzy ANP-VIKOR for large commercial rooftop PV system based on sustainability perspective. Sustainable Cities and Society, 40, 454-470. https://doi.org/10.1016/j.scs.2018.04.024
Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operations. IEEE Transactions on Fuzzy Systems, 15, 1179-1187. https://doi.org/10.1109/TFUZZ.2006.890678
Yang, L. Z., Gong, X. Y., Wang, X. J., & An, S. Q. (2014). Generalized exponential entropy on intuitionistic fuzzy sets. Applied Mechanics & Materials, 556-562, 4097-4102. https://doi.org/10.4028/www.scientific.net/AMM.556-562.4097
Yang, Y., Hu, J. H., Liu, Y. M., & Chen, X. H. (2018). Doctor recommendation based on an intuitionistic normal cloud model considering patient preferences. Cognitive Computation, 1-19. https://doi.org/10.1007/s12559-018-9616-3
Yu, S. M., Wang, J., & Wang, J. Q. (2018). An extended TODIM approach with intuitionistic linguistic numbers. International Transactions in Operational Research, 25(3), 781-805. https://doi.org/10.1111/itor.12363
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-356. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, G., Wang, J. Q., & Wang, T. L. (2019). Multi-criteria group decision-making method based on TODIM with probabilistic interval-valued hesitant fuzzy information. Expert Systems, 36(4), 12424. https://doi.org/10.1111/exsy.12424
Zhang, X. L., & Xu, Z. S. (2014). The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowledge-Based Systems, 61, 48-58. https://doi.org/10.1016/j.knosys.2014.02.006
Zhang, X. Y., Wang, J. Q., & Hu, J. H. (2018). On novel operational laws and aggregation operators of picture 2-tuple linguistic information for MCDM problems. International Journal of Fuzzy Systems, 20(3), 958-969. https://doi.org/10.1007/s40815-017-0441-8
Zhang, Y. P., Wang, Y. H., & Yang, N. (2018). On the risk assessment method of balise system based on the ANP and fuzzy evidence theory. Journal of Safety and Environment, 18(2), 434-440 (in Chinese).