Soft Decision-Making Methods Employing Multiple ifpifs-Matrices and Their Application
Abstract
The concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) is a mathematical tool coming to the forefront with its ability to model problems containing intuitionistic fuzzy uncertainties or multiple fuzzy uncertainties. The present study continues the paper entitled “Generalisations of SDM Methods in fpfs-Matrices Space to Render Them Operable in ifpifs-Matrices Space and Their Application to Performance Ranking of the Noise-Removal Filters”. It generalizes 36 soft decision-making (SDM) methods employing multiple fuzzy parameterized fuzzy soft matrices (fpfs-matrices) to operable in the ifpifs-matrices space. Afterward, this study proposes three ifpifs-matrices for each test case in the above-mentioned paper and determines SDM methods producing successful results in these test cases by using the proposed ifpifs-matrices. Moreover, it applies the determined SDM methods to a performance-based value assignment (PVA) to seven well-known salt-and-pepper noise removal filters used in digital images. Finally, this study discusses SDM methods’ applications and the need for further research.
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References
Arslan, B., Aydın, T., Memiş, S., Enginoğlu, S.: Generalisations of SDM methods in fpfs-matrices space to render them operable in ifpifs-matrices space and their application to performance ranking of the noise-removal filters. J New Theory (36), 88–116 (2021)
Arslan, B., Enginoğlu, S.: Algebraic operations of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application to a performance-based value assignment problem. In: Özkan, A., Biroğul, S., Güngör, Ö., Of, M., Taşdemirci, Ç. (eds) International Marmara Sciences Congress IMASCON–Autumn. Turkiye, Kocaeli, pp 127–137 (2020)
Atanassov, K. T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1), 87–96 (1986)
Aydın, T., Enginoğlu, S.: Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making. J Ambient Intell Humaniz Comput 12, 1541–1558 (2021)
Aydın, T., Enginoğlu, S.: Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft matrices and their application to performance-based value assignment to noise removal filters. Comput Appl Math 41, Article number: 192 (2022)
Cuong, B. C.: Picture fuzzy sets. J Comput Sci Cybern 30(4), 409–420 (2014)
Enginoğlu, S., Arslan, B.: Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making. Comput Appl Math 39, Article number: 325 (2020)
Enginoğlu, S., Ay, M., Çağman, N., Tolun, V.: Classification of the monolithic columns produced in Troad and Mysia region ancient granite quarries in northwestern Anatolia via soft decision-making. Bilgesci 3(Special Issue), 21–34 (2019)
Enginoğlu, S., Aydın, T., Memiş, S., Arslan, B.: Operability-oriented configurations of the soft decision-making methods proposed between 2013 and 2016 and their comparisons. J New Theory (34), 82–114 (2021)
Enginoğlu, S., Aydın, T., Memiş, S., Arslan, B.: SDM methods’ configurations (2017-2019) and their application to a performance-based value assignment problem: A follow up study. Ann Optim Theory Pract 4(1), 41–85 (2021)
Enginoğlu, S., Çağman, N.: Fuzzy parameterized fuzzy soft matrices and their an application in decision-making. TWMS J Appl Eng Math 10(4), 1105–1115 (2020)
Enginoğlu, S., Erkan, U., Memiş, S.: Pixel similarity-based adaptive Riesz mean filter for salt-and-pepper noise removal. Multimed Tools Appl 78, 35401–35418 (2019)
Enginoğlu, S., Memiş, S.: A configuration of some soft decision-making algorithms via fpfs-matrices. Cumhur Sci J 39(4), 871–881 (2018)
Enginoğlu, S., Memiş, S.: A review on an application of fuzzy soft set in multicriteria decision making problem [P. K. Das, R. Borgohain, International Journal of Computer Applications 38(12) (2012) 33–37]. In: Akgül, M., Yılmaz, İ., İpek, A. (eds) International Conference on Mathematical Studies and Applications. Turkiye, Karaman, pp 173–178 (2018)
Enginoğlu, S., Memiş, S.: A new approach to the criteria-weighted fuzzy soft max-min decision-making method and its application to a performance-based value assignment problem. J New Results in Sci 9(1), 19–36 (2020)
Enginoğlu, S., Memiş, S., Arslan, B.: A fast and simple soft decision-making algorithm: EMA18an. In: Akgül, M., Yılmaz, İ., İpek, A. (eds) International Conference on Mathematical Studies and Applications. Turkiye, Karaman, pp 428–436 (2018)
Enginoğlu, S., Memiş, S., Arslan, B.: Comment (2) on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848–855]. J New Theory (25), 84–102 (2018)
Enginoğlu, S., Memiş, S., Çağman, N.: A generalisation of fuzzy soft max-min decision-making method and its application to a performance-based value assignment in image denoising. El-Cezerî J Sci Eng 6(3), 466–481 (2019)
Enginoğlu, S., Memiş, S., Karaaslan, F.: A new approach to group decision-making method based on TOPSIS under fuzzy soft environment. J New Results in Sci 8(2), 42–52 (2019)
Enginoğlu, S., Memiş, S., Öngel, T.: A fast and simple soft decision-making algorithm: EMO18o. In: Akgül, M., Yılmaz, İ., İpek, A. (eds) International Conference on Mathematical Studies and Applications. Turkiye, Karaman, pp 179–187 (2018)
Enginoğlu, S., Memiş, S., Öngel, T.: Comment on soft set theory and uni-int decision making [European Journal of Operational Research, (2010) 207, 848–855]. J New Results in Sci 7(3), 28–43 (2018)
Enginoğlu, S., Öngel, T.: Configurations of several soft decision-making methods to operate in fuzzy parameterized fuzzy soft matrices space. Eskişehir Technical University J Sci and Tech A-Appl Sci Eng 21(1), 58–71 (2020)
Erkan, U., Gökrem, L.: A new method based on pixel density in salt and pepper noise removal. Turk J Electr Eng Comput Sci 26(1), 162–171 (2018)
Erkan, U., Gökrem, L., Enginoğlu, S.: Different applied median filter in salt and pepper noise. Comput Electr Eng 70, 789–798 (2018)
Esakkirajan, S., Veerakumar, T., Subramanyam, A. N., PremChand, C. H.: Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter. IEEE Signal Process Lett 18(5), 287–290 (2011)
Memiş, S.: A study on picture fuzzy sets. In: Çuvalcıoğlu, G. (ed) 7th IFS and Contemporary Mathematics Conference. Turkiye, Mersin, pp 125–132 (2021)
Memiş, S., Arslan, B., Aydın, T., Enginoğlu, S., Camcı, Ç.: A classification method based on Hamming pseudo-similarity of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices. J New Results in Sci 10(2), 59–76 (2021)
Memiş, S., Enginoğlu, S.: An application of fuzzy parameterized fuzzy soft matrices in data classification. In: Kılıç, M., Özkan, K., Karaboyacı, M., Taşdelen, K., Kandemir, H., Beram, A. (eds) International Conferences on Science and Technology, Natural Science and Technology. Kosovo, Prizren, pp 68–77 (2019)
Memiş, S., Enginoğlu, S., Erkan, U.: A data classification method in machine learning based on normalised Hamming pseudo-similarity of fuzzy parameterized fuzzy soft matrices. Bilgesci 3(Special Issue), 1–8 (2019)
Memiş, S., Enginoğlu, S., Erkan, U.: Numerical data classification via distance-based similarity measures of fuzzy parameterized fuzzy soft matrices. IEEE Access 9, 88583–88601 (2021)
Molodtsov, D.: Soft set theory-first results. Comput Math Appl 37(4-5), 19–31 (1999)
Sheikh, H. R., Bovik, A. C.: Image information and visual quality. IEEE Trans Image Process 15(2), 430–444 (2006)
Srinivasan, K. S., Ebenezer, D.: A new fast and efficient decision-based algorithm for removal of high-density impulse noises, IEEE Signal Process. Lett. 14(3), 189–192 (2007).
Tang, Z., Yang, Z., Liu, K., Pei, Z.: A new adaptive weighted mean filter for removing high density impulse noise. In: Falco, C. M., Jiang, X. (eds) 8th International Conference on Digital Image Processing, Series in International Society for Optics and Photonics, Vol. 10033 (SPIE - International Society for Optics and Photonics). China, Chengu, pp 1003353/1–5 (2016)
Toh, K. K. V., Isa, N. A. M.: Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction. IEEE Signal Process Lett 17(3), 281–284 (2010)
Wang, Z., Bovik, A. C., Sheikh, H. R., Simoncelli, E. P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans Image Process 13(4), 600–612 (2004)
Zadeh, L. A.: Fuzzy sets, Inf Control 8(3), 338–353 (1965)
Arslan, B., Enginoğlu, S.: Algebraic operations of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application to a performance-based value assignment problem. In: Özkan, A., Biroğul, S., Güngör, Ö., Of, M., Taşdemirci, Ç. (eds) International Marmara Sciences Congress IMASCON–Autumn. Turkiye, Kocaeli, pp 127–137 (2020)
Atanassov, K. T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1), 87–96 (1986)
Aydın, T., Enginoğlu, S.: Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making. J Ambient Intell Humaniz Comput 12, 1541–1558 (2021)
Aydın, T., Enginoğlu, S.: Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft matrices and their application to performance-based value assignment to noise removal filters. Comput Appl Math 41, Article number: 192 (2022)
Cuong, B. C.: Picture fuzzy sets. J Comput Sci Cybern 30(4), 409–420 (2014)
Enginoğlu, S., Arslan, B.: Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making. Comput Appl Math 39, Article number: 325 (2020)
Enginoğlu, S., Ay, M., Çağman, N., Tolun, V.: Classification of the monolithic columns produced in Troad and Mysia region ancient granite quarries in northwestern Anatolia via soft decision-making. Bilgesci 3(Special Issue), 21–34 (2019)
Enginoğlu, S., Aydın, T., Memiş, S., Arslan, B.: Operability-oriented configurations of the soft decision-making methods proposed between 2013 and 2016 and their comparisons. J New Theory (34), 82–114 (2021)
Enginoğlu, S., Aydın, T., Memiş, S., Arslan, B.: SDM methods’ configurations (2017-2019) and their application to a performance-based value assignment problem: A follow up study. Ann Optim Theory Pract 4(1), 41–85 (2021)
Enginoğlu, S., Çağman, N.: Fuzzy parameterized fuzzy soft matrices and their an application in decision-making. TWMS J Appl Eng Math 10(4), 1105–1115 (2020)
Enginoğlu, S., Erkan, U., Memiş, S.: Pixel similarity-based adaptive Riesz mean filter for salt-and-pepper noise removal. Multimed Tools Appl 78, 35401–35418 (2019)
Enginoğlu, S., Memiş, S.: A configuration of some soft decision-making algorithms via fpfs-matrices. Cumhur Sci J 39(4), 871–881 (2018)
Enginoğlu, S., Memiş, S.: A review on an application of fuzzy soft set in multicriteria decision making problem [P. K. Das, R. Borgohain, International Journal of Computer Applications 38(12) (2012) 33–37]. In: Akgül, M., Yılmaz, İ., İpek, A. (eds) International Conference on Mathematical Studies and Applications. Turkiye, Karaman, pp 173–178 (2018)
Enginoğlu, S., Memiş, S.: A new approach to the criteria-weighted fuzzy soft max-min decision-making method and its application to a performance-based value assignment problem. J New Results in Sci 9(1), 19–36 (2020)
Enginoğlu, S., Memiş, S., Arslan, B.: A fast and simple soft decision-making algorithm: EMA18an. In: Akgül, M., Yılmaz, İ., İpek, A. (eds) International Conference on Mathematical Studies and Applications. Turkiye, Karaman, pp 428–436 (2018)
Enginoğlu, S., Memiş, S., Arslan, B.: Comment (2) on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848–855]. J New Theory (25), 84–102 (2018)
Enginoğlu, S., Memiş, S., Çağman, N.: A generalisation of fuzzy soft max-min decision-making method and its application to a performance-based value assignment in image denoising. El-Cezerî J Sci Eng 6(3), 466–481 (2019)
Enginoğlu, S., Memiş, S., Karaaslan, F.: A new approach to group decision-making method based on TOPSIS under fuzzy soft environment. J New Results in Sci 8(2), 42–52 (2019)
Enginoğlu, S., Memiş, S., Öngel, T.: A fast and simple soft decision-making algorithm: EMO18o. In: Akgül, M., Yılmaz, İ., İpek, A. (eds) International Conference on Mathematical Studies and Applications. Turkiye, Karaman, pp 179–187 (2018)
Enginoğlu, S., Memiş, S., Öngel, T.: Comment on soft set theory and uni-int decision making [European Journal of Operational Research, (2010) 207, 848–855]. J New Results in Sci 7(3), 28–43 (2018)
Enginoğlu, S., Öngel, T.: Configurations of several soft decision-making methods to operate in fuzzy parameterized fuzzy soft matrices space. Eskişehir Technical University J Sci and Tech A-Appl Sci Eng 21(1), 58–71 (2020)
Erkan, U., Gökrem, L.: A new method based on pixel density in salt and pepper noise removal. Turk J Electr Eng Comput Sci 26(1), 162–171 (2018)
Erkan, U., Gökrem, L., Enginoğlu, S.: Different applied median filter in salt and pepper noise. Comput Electr Eng 70, 789–798 (2018)
Esakkirajan, S., Veerakumar, T., Subramanyam, A. N., PremChand, C. H.: Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter. IEEE Signal Process Lett 18(5), 287–290 (2011)
Memiş, S.: A study on picture fuzzy sets. In: Çuvalcıoğlu, G. (ed) 7th IFS and Contemporary Mathematics Conference. Turkiye, Mersin, pp 125–132 (2021)
Memiş, S., Arslan, B., Aydın, T., Enginoğlu, S., Camcı, Ç.: A classification method based on Hamming pseudo-similarity of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices. J New Results in Sci 10(2), 59–76 (2021)
Memiş, S., Enginoğlu, S.: An application of fuzzy parameterized fuzzy soft matrices in data classification. In: Kılıç, M., Özkan, K., Karaboyacı, M., Taşdelen, K., Kandemir, H., Beram, A. (eds) International Conferences on Science and Technology, Natural Science and Technology. Kosovo, Prizren, pp 68–77 (2019)
Memiş, S., Enginoğlu, S., Erkan, U.: A data classification method in machine learning based on normalised Hamming pseudo-similarity of fuzzy parameterized fuzzy soft matrices. Bilgesci 3(Special Issue), 1–8 (2019)
Memiş, S., Enginoğlu, S., Erkan, U.: Numerical data classification via distance-based similarity measures of fuzzy parameterized fuzzy soft matrices. IEEE Access 9, 88583–88601 (2021)
Molodtsov, D.: Soft set theory-first results. Comput Math Appl 37(4-5), 19–31 (1999)
Sheikh, H. R., Bovik, A. C.: Image information and visual quality. IEEE Trans Image Process 15(2), 430–444 (2006)
Srinivasan, K. S., Ebenezer, D.: A new fast and efficient decision-based algorithm for removal of high-density impulse noises, IEEE Signal Process. Lett. 14(3), 189–192 (2007).
Tang, Z., Yang, Z., Liu, K., Pei, Z.: A new adaptive weighted mean filter for removing high density impulse noise. In: Falco, C. M., Jiang, X. (eds) 8th International Conference on Digital Image Processing, Series in International Society for Optics and Photonics, Vol. 10033 (SPIE - International Society for Optics and Photonics). China, Chengu, pp 1003353/1–5 (2016)
Toh, K. K. V., Isa, N. A. M.: Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction. IEEE Signal Process Lett 17(3), 281–284 (2010)
Wang, Z., Bovik, A. C., Sheikh, H. R., Simoncelli, E. P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans Image Process 13(4), 600–612 (2004)
Zadeh, L. A.: Fuzzy sets, Inf Control 8(3), 338–353 (1965)
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Çanakkale Onsekiz Mart Üniversitesi
Grant numbers FHD-2020-3466
