Interval Type II Parametric Trapezoidal Fuzzy Number Approximation of Interval Type II Exponential Fuzzy Number Based on The Expected Interval

Year 2021, Volume: 6 Issue: 1, 21 - 32, 11.06.2021

Sinem Peker , Efendi Nasiboğlu

https://doi.org/10.33484/sinopfbd.817174

Abstract

Type I fuzzy numbers are used in some decision-making problems to handle the uncertainty. The membership degrees of Type I fuzzy numbers are crisp numbers. However, the events in which the membership degrees may be shown by fuzzy numbers may exist in the real life problems. In that cases, the Type II fuzzy numbers can be used. The usage of the simpler form of the fuzzy number is seen as an advantage for the avoiding of complex calculations in some studies. Considering this, the interval Type II parametric trapezoidal fuzzy number approximation of the interval Type II exponential fuzzy number has been found by a constrained optimization problem in which the equalities between expected intervals are used and the formulas have been given in this study.

Keywords

Type II fuzzy number, exponential fuzzy number, parametric trapezoidal fuzzy number, approximation, optimization

Beklenen Aralığa Dayanan Aralık Tip II Üssel Bulanık Sayının Aralık Tip II Parametrik Yamuk Bulanık Sayı Yakınsaması

Abstract

Tip I bulanık sayıları belirsizliği ele almak için bazı karar verme problemlerinde kullanılmaktadır. Tip I bulanık sayılarının üyelik dereceleri adi sayılardır. Ancak gerçek yaşam problemlerinde, üyelik derecelerinin bulanık sayılar ile gösterilebileceği olaylar var olabilir. Bu gibi durumlarda, Tip II bulanık sayıları kullanılabilir. Bulanık sayının daha basit bir formunun kullanılması bazı çalışmalarda karmaşık hesaplamalardan kaçınmak için bir avantaj olarak görülmektedir. Bu durum dikkate alınarak, bu çalışmada aralık Tip II üssel bulanık sayının aralık Tip II parametrik yamuk bulanık sayı yakınsaması, beklenen aralıkların eşitliklerinin kullanıldığı bir kısıtlı optimizasyon problemi ile bulunmuş ve formüller verilmiştir.

Keywords

Tip II bulanık sayı, üssel bulanık sayı, parametrik yamuk bulanık sayı, optimizasyon, yakınsama, optimizasyon

References

• Ban, A. I., Coroianu, L., & Khastan, A. (2016). Conditioned weighted L–R approximations of fuzzy numbers. Fuzzy Sets and Systems, 283, 56-82. https://doi.org/10.1016/j.fss.2015.03.012
• Nasibov, E. N., & Peker, S. (2008). On the nearest parametric approximation of a fuzzy number. Fuzzy Sets and Systems, 159(11), 1365-1375. https://doi.org/10.1016/j.fss.2007.08.005
• Hao, Z., Xu, Z., Zhao, H., & Zhang, R. (2021). The context-based distance measure for intuitionistic fuzzy set with application in marine energy transportation route decision making. Applied Soft Computing, 101, Article 107044. https://doi.org/10.1016/j.asoc.2020.107044
• Krawczak, M., & Szkatuła, G. (2020). On matching of intuitionistic fuzzy sets. Information Sciences, 517, 254-274. https://doi.org/10.1016/j.ins.2019.11.050
• Alcantud, J. C. R., Khameneh, A. Z., & Kilicman, A. (2020). Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Information Sciences, 514, 106-117. https://doi.org/10.1016/j.ins.2019.12.008
• Sodenkamp, M. A., Tavana, M., & Di Caprio, D. (2018). An aggregation method for solving group multi-criteria decision-making problems with single-valued neutrosophic sets. Applied Soft Computing, 71, 715-727. https://doi.org/10.1016/j.asoc.2018.07.020
• Grzegorzewski, P. (2002). Nearest interval approximation of a fuzzy number. Fuzzy Sets and systems, 130(3), 321-330. https://doi.org/10.1016/S0165-0114(02)00098-2
• Hai, S., Gong, Z., & Chen, Z. (2020). Weighted pseudometric approximation of 2-dimensional fuzzy numbers by fuzzy 2-cell prismoid numbers preserving the centroid. Fuzzy Sets and Systems, 387, 158-173. https://doi.org/10.1016/j.fss.2018.12.013
• Liu, X., & Lin, H. (2007). Parameterized approximation of fuzzy number with minimum variance weighting functions. Mathematical and computer modelling, 46(11-12), 1398-1409. https://doi.org/10.1016/j.mcm.2007.01.011
• Coroianu, L., & Stefanini, L. (2016). General approximation of fuzzy numbers by F-transform. Fuzzy Sets and Systems, 288, 46-74. https://doi.org/10.1016/j.fss.2015.03.015
• Chanas, S. (2001). On the interval approximation of a fuzzy number. Fuzzy Sets and Systems, 122(2), 353-356. https://doi.org/10.1016/S0165-0114(00)00080-4
• Coroianu, L., Gagolewski, M., & Grzegorzewski, P. (2013). Nearest piecewise linear approximation of fuzzy numbers. Fuzzy Sets and Systems, 233, 26-51. https://doi.org/10.1016/j.fss.2013.02.005
• Yeh, C. T., & Chu, H. M. (2014). Approximations by LR-type fuzzy numbers. Fuzzy Sets and Systems, 257, 23-40. https://doi.org/10.1016/j.fss.2013.09.004
• Huang, H., Wu, C., Xie, J., & Zhang, D. (2017). Approximation of fuzzy numbers using the convolution method. Fuzzy Sets and Systems, 310, 14-46. https://doi.org/10.1016/j.fss.2016.06.010
• Ban, A. (2008). Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets and Systems, 159(11), 1327-1344. https://doi.org/10.1016/j.fss.2007.09.008
• Ban, A. I., & Coroianu, L. (2015). Existence, uniqueness, calculus and properties of triangular approximations of fuzzy numbers under a general condition. International Journal of Approximate Reasoning, 62, 1-26. https://doi.org/10.1016/j.ijar.2015.05.004
• Grzegorzewski, P., & Pasternak-Winiarska, K. (2014). Natural trapezoidal approximations of fuzzy numbers. Fuzzy Sets and Systems, 250, 90-109. https://doi.org/10.1016/j.fss.2014.03.003
• Wang, G., & Li, J. (2017). Approximations of fuzzy numbers by step type fuzzy numbers. Fuzzy sets and systems, 310, 47-59. https://doi.org/10.1016/j.fss.2016.08.003
• Zhou, J., Miao, D., Gao, C., Lai, Z., & Yue, X. (2019). Constrained three-way approximations of fuzzy sets: From the perspective of minimal distance. Information Sciences, 502, 247-267. https://doi.org/10.1016/j.ins.2019.06.004
• Ban, A. I., & Coroianu, L. (2012). Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity. International Journal of Approximate Reasoning, 53(5), 805-836.
• Peker, S., & Nasibov, E. (2019). Tip II genelleştirilmiş çan şekilli bulanık sayısının Tip II parametrik yamuk bulanık sayı yakınsanması. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(1), 163-169. https://doi.org/10.19113/sdufenbed.466901
• Huang, S., Zhao, G., & Chen, M. (2018). A fast analytical approximation type-reduction method for a class of spiked concave type-2 fuzzy sets. International Journal of Approximate Reasoning, 103, 212-226. https://doi.org/10.1016/j.ijar.2018.10.002
• Wang, C. Y., & Wan, L. (2018). Type-2 fuzzy implications and fuzzy-valued approximation reasoning. International Journal of Approximate Reasoning, 102, 108-122. https://doi.org/10.1016/j.ijar.2018.08.004
• Dutta, P., & Limboo, B. (2017). Bell-shaped fuzzy soft sets and their application in medical diagnosis. Fuzzy Information and Engineering, 9(1), 67-91. https://doi.org/10.1016/j.fiae.2017.03.004