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12620
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UniSZA
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[1] Aisbetta, J., Rickardb, J.T., and D. Morgenthaler, Multivariate modeling and type-2 fuzzy sets, Fuzzy Sets and Systems, vol.163, pp.78–95, 2011. [2] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.20, pp.87–96, 1986. [3] Atanassov, K., Intuitionistic fuzzy sets, VII ITKR's Session, pp.1677–1684, 1983. [4] Atanassova, L.C., Remark on the cardinality of the intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.75, pp.399–400, 1995. [5] Bana e Costa, C.A., Antao da Silva, P., and F. Nunes Correia, Multicriteria evaluation of flood control measures: the case of Ribeira do Livramento, Water Resources Management, vol.18, pp.263–283, 2004. [6] Boran, F.E., Genç, S., Kurt, M., and D. Akay, A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Systems with Applications, vol.36, pp.11363–11368, 2009. [7] Brouwer, R., and R. Van Ek, Integrated ecological, economic and social impact assessment of alternative flood control policies in the Netherlands, Ecological Economics, vol.50, pp.1–21, 2004. [8] Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Olagoitia, J., and P. Melo-Pinto, Contrast computing using Atanassov‘s intuitionistic fuzzy sets, 8th International FLINS Conference: Computational Intelligence in Decision and Control, pp.259–264, 2008. [9] Bustince, H., and P. Burillo, Short communication vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.79, pp.403–405, 1996. [10] Bustince, H., and P. Burillo, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, vol.78, pp.305–316, 1996. [11] Cattaneo, G., and D. Ciucci, Basic intuitionistic principles in fuzzy set theories and its extensions (A terminological debate on Atanassov IFS), Fuzzy Sets and Systems, vol.157, pp.3198–3219, 2006. [12] Chai, J., Liu, J.N.K., and Z. Xu, A new rule-based SIR approach to supplied selection under intuitionistic fuzzy environments, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.20, pp.451–471, 2012. [13] Chen, C.T., Extension of the TOPSIS for group decision making under fuzzy environment, Fuzzy Sets and Systems, vol.114, pp.1–9, 2000. [14] Chen, T.-Y., A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings, Information Sciences, vol.181, pp.3652–3676, 2011. [15] Chen, S.-M., and L.-W. Lee, Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method, Expert Systems with Application, vol.37, pp.2790–2798, 2010. [16] Chen, S.-M., and L.-W. Lee, Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets, Expert Systems with Applications, vol.37, pp.824–833, 2010. [17] Chen, T.-Y., and C-Y. Tsao, The interval-valued fuzzy TOPSIS method and experimental analysis, Fuzzy Sets and Systems, vol.159, pp.1410–1428, 2008. [18] Deschrijver, G., and E.E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and System, vol.133, pp.227–235, 2003. [19] Duboisa, D., Gottwaldb, S., Hajekc, P., Kacprzykd, J., and H. Pradea, Discussion terminological difficulties in fuzzy set theory—the case of ―intuitionistic fuzzy sets‖, Fuzzy Sets and Systems, vol.156, pp.485–491, 2005. [20] Gau, W.L., and D.J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybemetics, vol.23, pp.610–614, 1993. [21] Greenfield, S., Chiclana, F., Coupland, S., and R. John, The collapsing method of defuzzification for discretised interval type2 fuzzy sets, Information Sciences, vol.179, pp.2055–2069, 2009. [22] Gupta, B.L., Water Resources Engineering and Hydrology, Standard Publishers, New Delhi, 1979. [23] Harding, J., Walker, C., and E. Walker, The variety generated by the truth value algebra of type-2 fuzzy sets, Fuzzy Sets and Systems, vol.161, pp.735–749, 2010. [24] Hu, J., Zhang, Y., Chen, X., and Y. Liu, Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number, Journal of Knowledge-Based System, vol.43, pp.21–29, 2013. [25] Kamarouz, M., Szidarovszky, F., and B. Zahraie, Water Resources System Analysis, Lewis Publishers, Florida, 2003. [26] Lee, L.-W., and S.-M. Chen, A new method for fuzzy multiple attribute group decision-making based on the arithmetic operations of interval type-2 fuzzy sets, Proceedings of the 2008 international conference on machine learning and cybernetics, pp.3084–3089, 2008. [27] Levy, J.K., Multiple criteria decision making and decision support systems for flood risk management, Stochastic Environmental Research Risk Assessment, vol.19, pp.438–447, 2005. [28] Li, D.-F., Wang, L.-L., and G.-H. Chen, Group decision making methodology based on the Atanassov‘s intuitionistic fuzzy set generalized OWA operator, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.18, pp.801–817, 2010. [29] Maragoudaki, R, and G. Tsakiris, Flood mitigation planning using PROMETHEE, European Water, vol.9, pp.51–58, 2005. [30] Mendel, J.M., Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, Prentice-Hall, Upper Saddle River, NJ, 2001. [31] Mendel, J.M., Type-2 fuzzy sets: some questions and answers, IEEE Neural Networks Society, pp.10–13, 2013. [32] Mendel, J.M., and R.I. John, Type-2 fuzzy sets made simple, IEEE Transactions on Fuzzy Systems, vol.10, pp.117–127, 2012. [33] Mendel, J.M., John, R.I., and F.L. Liu, Interval type-2 fuzzy logical systems made simple, IEEE Transactions on Fuzzy Systems, vol.14, pp.808–821, 2006. [34] Mendel, J.M., and Q. Liang, Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters, IEEE Transactions on Fuzzy Systems,, vol.8, pp.551–563, 2000. [35] Mokhtarian, M.N., A new fuzzy weighted average (FWA) method based on left and right scores: an application for determining a suitable location for a gas oil station, Computers and Mathematics with Application, vol.61, pp.3136–3145, 2001. [36] Pei, Z., and L. Zheng, A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets, Expert Systems with Applications, vol.39, pp.2560–2566, 2012. [37] Su, Z.-X., Chen, M.-Y., Xia, G.-P., and L. Wang, An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making, Expert Systems with Applications, vol.38, pp.15286–15295, 2011. [38] Van Duivendijk, J., Assessment of Flood Management Options, Contributing papers to the World Commission on Dams, 2005. [39] Wang, W., Liu, X., and Y. Qin, Multi-attribute group decision making models under interval type-2 fuzzy environment, Knowledge-Based Systems, vol.30, pp.121–128, 2012. [40] Ward, R., Floods, The Macmillan Press Ltd, London, 1978. [41] Willett, K., and R. Sharda, Using the analytic hierarchy process in water resources planning: selection of flood control projects, Socioeconomic Planning, vol.25, pp.103–112, 1991. [42] Wu, D.R., and J.M. Mendel, Aggregation using the linguistic weighted average and interval type-2 fuzzy sets, IEEE Transactions on Fuzzy System, vol.15, pp.1145–1161, 2007. [43] Wu, D.R., and J.M. Mendel, Corrections to ―aggregation using the linguistic weighted average and interval type-2 fuzzy sets‖, IEEE Transactions on Fuzzy System, vol.16, pp.1664–1666, 2008. [44] Ye, F., 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. [45] Yue, Z., and Y. Jia, A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making, Applied Soft Computing, vol.13, pp.2304–2317, 2013. [46] Yue, Z., Jia, Y., and G. Ye, An approach for multiple attribute group decision making based on intuitionistic fuzzy information, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.17, pp.317–332, 2009. [47] Zadeh, L.A., Fuzzy sets and systems, Proceedings of the Symposium on Systems Theory, pp.29–37, 1965. [48] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, vol.8, pp.199–249, 1975. [49] Zhang, Z., On characterization of generalized interval type-2 fuzzy rough sets, Information Sciences, vol.219, pp.124–150, 2013. [50] Zhang, Z., and S. Zhang, A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets, Applied Mathematical Modelling, vol.37, pp.4948–4971, 2013. [51] Zhou, H., Li, W., and C. Zhang, Optimizing schemes of flood control and disaster reduction engineering based on variable fuzzy sets theory, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (IEEE), vol.2, pp.598–603, 2007.
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12620 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=12620 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal image/jpeg inches 96 96 norman 1420 776 45 45 2015-12-30 14:57:43 1420x776 6927-01-FH02-FIK-15-04685.jpg UniSZA Private Access A new intuitionistic preference scale based on interval type-2 fuzzy set for MCDM problems Journal of Uncertain Systems Interval Type-2 Fuzzy TOPSIS (IT2FTOPSIS) is a useful way to handle Fuzzy Multiple Attribute Decision Making (FMADM) problems in a more flexible and intelligent manner. It is very useful due to the fact that it uses Type-2 Fuzzy Sets (T2FSs) rather than Type-1 Fuzzy Sets (T1FSs) to represent the evaluating values and the weights of attributes. Besides, all the linguistic terms are pointed in Type-1 Fuzzy Numbers (T1FNs) rather than Fuzzy TOPSIS (FTOPSIS), using crisps numbers. However, IT2FTOPSIS only focuses on the membership degree without considering the non-membership degree. In real life situation, evaluation becomes more comprehensive if non-membership degree is considered concurrently. Preference is expected to be more effective when considering both membership and non-membership degree due to the effectiveness of fuzziness taken from the hesitation degree. Therefore, the aim of this paper is to introduce a new preference scale that considers both membership and non-membership degree in IT2FTOPSIS. Both membership and non-membership degree of Intuitionistic Fuzzy Sets (IFSs) are developed under Interval Type-2 FMADM environment. Then, this new method is tested using five illustrative examples. Finally, this new method is applied to a case study on selecting the best of flood control project and the results demonstrate the feasibility. This paper has been proven able to measure human being decision making progress to solve the incomplete information and becomes a new way to deal with the vagueness and uncertainty. 9 4 World Academic Union World Academic Union 251-273 [1] Aisbetta, J., Rickardb, J.T., and D. Morgenthaler, Multivariate modeling and type-2 fuzzy sets, Fuzzy Sets and Systems, vol.163, pp.78–95, 2011. [2] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.20, pp.87–96, 1986. [3] Atanassov, K., Intuitionistic fuzzy sets, VII ITKR's Session, pp.1677–1684, 1983. [4] Atanassova, L.C., Remark on the cardinality of the intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.75, pp.399–400, 1995. [5] Bana e Costa, C.A., Antao da Silva, P., and F. Nunes Correia, Multicriteria evaluation of flood control measures: the case of Ribeira do Livramento, Water Resources Management, vol.18, pp.263–283, 2004. [6] Boran, F.E., Genç, S., Kurt, M., and D. Akay, A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Systems with Applications, vol.36, pp.11363–11368, 2009. [7] Brouwer, R., and R. Van Ek, Integrated ecological, economic and social impact assessment of alternative flood control policies in the Netherlands, Ecological Economics, vol.50, pp.1–21, 2004. [8] Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Olagoitia, J., and P. Melo-Pinto, Contrast computing using Atanassov‘s intuitionistic fuzzy sets, 8th International FLINS Conference: Computational Intelligence in Decision and Control, pp.259–264, 2008. [9] Bustince, H., and P. Burillo, Short communication vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.79, pp.403–405, 1996. [10] Bustince, H., and P. Burillo, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, vol.78, pp.305–316, 1996. [11] Cattaneo, G., and D. Ciucci, Basic intuitionistic principles in fuzzy set theories and its extensions (A terminological debate on Atanassov IFS), Fuzzy Sets and Systems, vol.157, pp.3198–3219, 2006. [12] Chai, J., Liu, J.N.K., and Z. Xu, A new rule-based SIR approach to supplied selection under intuitionistic fuzzy environments, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.20, pp.451–471, 2012. [13] Chen, C.T., Extension of the TOPSIS for group decision making under fuzzy environment, Fuzzy Sets and Systems, vol.114, pp.1–9, 2000. [14] Chen, T.-Y., A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings, Information Sciences, vol.181, pp.3652–3676, 2011. [15] Chen, S.-M., and L.-W. Lee, Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method, Expert Systems with Application, vol.37, pp.2790–2798, 2010. [16] Chen, S.-M., and L.-W. Lee, Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets, Expert Systems with Applications, vol.37, pp.824–833, 2010. [17] Chen, T.-Y., and C-Y. Tsao, The interval-valued fuzzy TOPSIS method and experimental analysis, Fuzzy Sets and Systems, vol.159, pp.1410–1428, 2008. [18] Deschrijver, G., and E.E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and System, vol.133, pp.227–235, 2003. [19] Duboisa, D., Gottwaldb, S., Hajekc, P., Kacprzykd, J., and H. Pradea, Discussion terminological difficulties in fuzzy set theory—the case of ―intuitionistic fuzzy sets‖, Fuzzy Sets and Systems, vol.156, pp.485–491, 2005. [20] Gau, W.L., and D.J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybemetics, vol.23, pp.610–614, 1993. [21] Greenfield, S., Chiclana, F., Coupland, S., and R. John, The collapsing method of defuzzification for discretised interval type2 fuzzy sets, Information Sciences, vol.179, pp.2055–2069, 2009. [22] Gupta, B.L., Water Resources Engineering and Hydrology, Standard Publishers, New Delhi, 1979. [23] Harding, J., Walker, C., and E. Walker, The variety generated by the truth value algebra of type-2 fuzzy sets, Fuzzy Sets and Systems, vol.161, pp.735–749, 2010. [24] Hu, J., Zhang, Y., Chen, X., and Y. Liu, Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number, Journal of Knowledge-Based System, vol.43, pp.21–29, 2013. [25] Kamarouz, M., Szidarovszky, F., and B. Zahraie, Water Resources System Analysis, Lewis Publishers, Florida, 2003. [26] Lee, L.-W., and S.-M. Chen, A new method for fuzzy multiple attribute group decision-making based on the arithmetic operations of interval type-2 fuzzy sets, Proceedings of the 2008 international conference on machine learning and cybernetics, pp.3084–3089, 2008. [27] Levy, J.K., Multiple criteria decision making and decision support systems for flood risk management, Stochastic Environmental Research Risk Assessment, vol.19, pp.438–447, 2005. [28] Li, D.-F., Wang, L.-L., and G.-H. Chen, Group decision making methodology based on the Atanassov‘s intuitionistic fuzzy set generalized OWA operator, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.18, pp.801–817, 2010. [29] Maragoudaki, R, and G. Tsakiris, Flood mitigation planning using PROMETHEE, European Water, vol.9, pp.51–58, 2005. [30] Mendel, J.M., Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, Prentice-Hall, Upper Saddle River, NJ, 2001. [31] Mendel, J.M., Type-2 fuzzy sets: some questions and answers, IEEE Neural Networks Society, pp.10–13, 2013. [32] Mendel, J.M., and R.I. John, Type-2 fuzzy sets made simple, IEEE Transactions on Fuzzy Systems, vol.10, pp.117–127, 2012. [33] Mendel, J.M., John, R.I., and F.L. Liu, Interval type-2 fuzzy logical systems made simple, IEEE Transactions on Fuzzy Systems, vol.14, pp.808–821, 2006. [34] Mendel, J.M., and Q. Liang, Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters, IEEE Transactions on Fuzzy Systems,, vol.8, pp.551–563, 2000. [35] Mokhtarian, M.N., A new fuzzy weighted average (FWA) method based on left and right scores: an application for determining a suitable location for a gas oil station, Computers and Mathematics with Application, vol.61, pp.3136–3145, 2001. [36] Pei, Z., and L. Zheng, A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets, Expert Systems with Applications, vol.39, pp.2560–2566, 2012. [37] Su, Z.-X., Chen, M.-Y., Xia, G.-P., and L. Wang, An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making, Expert Systems with Applications, vol.38, pp.15286–15295, 2011. [38] Van Duivendijk, J., Assessment of Flood Management Options, Contributing papers to the World Commission on Dams, 2005. [39] Wang, W., Liu, X., and Y. Qin, Multi-attribute group decision making models under interval type-2 fuzzy environment, Knowledge-Based Systems, vol.30, pp.121–128, 2012. [40] Ward, R., Floods, The Macmillan Press Ltd, London, 1978. [41] Willett, K., and R. Sharda, Using the analytic hierarchy process in water resources planning: selection of flood control projects, Socioeconomic Planning, vol.25, pp.103–112, 1991. [42] Wu, D.R., and J.M. Mendel, Aggregation using the linguistic weighted average and interval type-2 fuzzy sets, IEEE Transactions on Fuzzy System, vol.15, pp.1145–1161, 2007. [43] Wu, D.R., and J.M. Mendel, Corrections to ―aggregation using the linguistic weighted average and interval type-2 fuzzy sets‖, IEEE Transactions on Fuzzy System, vol.16, pp.1664–1666, 2008. [44] Ye, F., 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. [45] Yue, Z., and Y. Jia, A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making, Applied Soft Computing, vol.13, pp.2304–2317, 2013. [46] Yue, Z., Jia, Y., and G. Ye, An approach for multiple attribute group decision making based on intuitionistic fuzzy information, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.17, pp.317–332, 2009. [47] Zadeh, L.A., Fuzzy sets and systems, Proceedings of the Symposium on Systems Theory, pp.29–37, 1965. [48] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, vol.8, pp.199–249, 1975. [49] Zhang, Z., On characterization of generalized interval type-2 fuzzy rough sets, Information Sciences, vol.219, pp.124–150, 2013. [50] Zhang, Z., and S. Zhang, A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets, Applied Mathematical Modelling, vol.37, pp.4948–4971, 2013. [51] Zhou, H., Li, W., and C. Zhang, Optimizing schemes of flood control and disaster reduction engineering based on variable fuzzy sets theory, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (IEEE), vol.2, pp.598–603, 2007.
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A new intuitionistic preference scale based on interval type-2 fuzzy set for MCDM problems
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| summary |
Interval Type-2 Fuzzy TOPSIS (IT2FTOPSIS) is a useful way to handle Fuzzy Multiple Attribute Decision Making (FMADM) problems in a more flexible and intelligent manner. It is very useful due to the fact that it uses Type-2 Fuzzy Sets (T2FSs) rather than Type-1 Fuzzy Sets (T1FSs) to represent the evaluating values and the weights of attributes. Besides, all the linguistic terms are pointed in Type-1 Fuzzy Numbers (T1FNs) rather than Fuzzy TOPSIS (FTOPSIS), using crisps numbers. However, IT2FTOPSIS only focuses on the membership degree without considering the non-membership degree. In real life situation, evaluation becomes more comprehensive if non-membership degree is considered concurrently. Preference is expected to be more effective when considering both membership and non-membership degree due to the effectiveness of fuzziness taken from the hesitation degree. Therefore, the aim of this paper is to introduce a new preference scale that considers both membership and non-membership degree in IT2FTOPSIS. Both membership and non-membership degree of Intuitionistic Fuzzy Sets (IFSs) are developed under Interval Type-2 FMADM environment. Then, this new method is tested using five illustrative examples. Finally, this new method is applied to a case study on selecting the best of flood control project and the results demonstrate the feasibility. This paper has been proven able to measure human being decision making progress to solve the incomplete information and becomes a new way to deal with the vagueness and uncertainty.
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| title |
A new intuitionistic preference scale based on interval type-2 fuzzy set for MCDM problems
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| title_full |
A new intuitionistic preference scale based on interval type-2 fuzzy set for MCDM problems
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| title_fullStr |
A new intuitionistic preference scale based on interval type-2 fuzzy set for MCDM problems
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| title_full_unstemmed |
A new intuitionistic preference scale based on interval type-2 fuzzy set for MCDM problems
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| title_short |
A new intuitionistic preference scale based on interval type-2 fuzzy set for MCDM problems
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| title_sort |
new intuitionistic preference scale based on interval type-2 fuzzy set for mcdm problems
|