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

Year 2021, Issue: 36, 88 - 116, 30.09.2021

Burak Arslan , Tuğçe Aydın , Samet Memiş , Serdar Enginoğlu

https://doi.org/10.53570/jnt.989335

Cited By: 4

Abstract

Recently, the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) has allowed to mathematically model some problems in which the parameters and alternatives exhibit intuitionistic fuzzy uncertainties. To this end, the present study aims to generalise 24 soft decision-making (SDM) methods operating in the fuzzy parameterized fuzzy soft matrices space with a single fpfs-matrix to the ifpifs-matrices spaces. Afterwards, we propose five test scenarios to analyse whether the SDM methods constructed by ifpifs-matrices consistently work. Moreover, we make performance comparisons of the generalised SDM methods successful in the five test scenarios by applying them to the performance-based value assignment (PVA) problem of the well-known noise-removal filters. Finally, we discuss the need for further research.

Keywords

Fuzzy sets, intuitionistic fuzzy sets, soft sets, ifpifs-matrices, soft decision making

Supporting Institution

Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University

Project Number

FHD-2020-3466

Thanks

This work was supported by the Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University, Grant Number: FHD-2020-3466.

References

• K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20(1) (1986) 87–96.
• L. A. Zadeh, Fuzzy Sets, Information and Control 8(3) (1965) 338–353.
• D. Molodtsov, Soft Set Theory-First Results, Computers Mathematics with Applications 37(4-5) (1999) 19–31.
• P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic Fuzzy Soft Sets, The Journal of Fuzzy Mathematics 9(3) (2001) 677–692.
• İ. Deli, N. Çaǧman, Intuitionistic Fuzzy Parameterized Soft Set Theory and Its Decision Making, Applied Soft Computing 28 (2015) 109–113.
• E. El-Yagubi, A. R. Salleh, Intuitionistic Fuzzy Parameterised Fuzzy Soft Set, Journal of Quality Measurement and Analysis 9(2) (2013) 73–81.
• E. Sulukan, N. Çağman, T. Aydın, Fuzzy Parameterized Intuitionistic Fuzzy Soft Sets and Their Application to a Performance-Based Value Assignment Problem, Journal of New Theory (29) (2019) 79–88.
• F. Karaaslan, Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Sets with Applications in Decision Making, Annals of Fuzzy Mathematics and Informatics 11(4) (2016) 607–619.
• S. Enginoğlu, B. Arslan, Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Matrices and Their Application in Decision-Making, Computational and Applied Mathematics 39 (2020) Article No. 325.
• S. Enginoğlu, N. Çağman, Fuzzy Parameterized Fuzzy Soft Matrices and Their a Application in Decision-Making, TWMS Journal of Applied and Engineering Mathematics 10(4) (2020) 1105–1115.
• T. Aydın, S. Enginoğlu, A Configuration of Five of the Soft Decision-Making Methods via Fuzzy Parameterized Fuzzy Soft Matrices and Their Application to a Performance-Based Value Assignment Problem, M. Kılıç, K. Özkan, M. Karaboyacı, K. Taşdelen, H. Kandemir, A. Beram, (Ed.), International Conferences on Science and Technology, Natural Science and Technology (2019) 56–67 Prizren, Kosovo.
• T. Aydın, S. Enginoğlu, Configurations of SDM methods Proposed between 1999 and 2012: A Follow-Up Study, K. Yıldırım, (Ed.) International Conference on Mathematics: “An Istanbul Meeting for World Mathematicians”, (2020) 192–211 Istanbul.
• S. Enginoğlu, T. Aydın, S. Memiş, B. Arslan, Operability-Oriented Configurations of the Soft Decision-Making Methods Proposed between 2013 and 2016 and Their Comparisons, Journal of New Theory (34) (2021) 82–114.
• S. Enginoğlu, T. Aydın, S. Memiş, B. Arslan, SDM Methods’ Configurations (2017-2019) and Their Application to a Performance-Based Value Assignment Problem: A Follow up Study, Annals of Optimization Theory and Practice 4(1) (2021) 41–85.
• S. Enginoğlu, S. Memiş, A Review on Some Soft Decision-Making Methods, Eds: Akgül, M., Yılmaz, İ., İpek, A. International Conference on Mathematical Studies and Applications (2018) 437–442 Karaman, Turkey.
• S. Enginoğlu, S. Memiş, A Configuration of Some Soft Decision-Making Algorithms via fpfs-matrices. Cumhuriyet Science Journal 39(4) (2018) 871–881.
• S. Enginoğlu, S. Memiş, B. Arslan, Comment (2) on Soft Set Theory and uni-int Decision-Making [European Journal of Operational Research, (2010) 207, 848-855]. Journal of New Theory, (25) (2018) 84–102.
• S. Enginoğlu, S. Memiş, F. Karaaslan, A New Approach to Group Decision-Making Method Based on TOPSIS under Fuzzy Soft Environment, Journal of New Results in Science 8(2) (2019) 42–52.
• S. Enginoğlu, S. Memiş, T. Öngel, Comment on Soft Set Theory and Uni-Int Decision Making [European Journal of Operational Research, (2010) 207, 848-855], Journal of New Results in Science 7(3) (2018) 28–43.
• S. Enginoğlu, T. Öngel, Configurations of Several Soft Decision-Making Methods to Operate in Fuzzy Parameterized Fuzzy Soft Matrices Space, Eskişehir Technical University Journal of Science and Technology A-Applied Sciences and Engineering 21(1) (2020) 58–71.
• S. Enginoğlu, S. Memiş, N. Çağman, A Generalisation of Fuzzy Soft Max-Min Decision-Making Method and Its Application to A Performance-Based Value Assignment in Image Denoising, El-Cezerî Journal of Science and Engineering 6(3) (2019) 466–481.
• S. Enginoğlu, S. Memiş, A New Approach to the Criteria-Weighted Fuzzy Soft Max-Min Decision-Making Method and Its Application to a Performance-Based Value Assignment Problem, Journal of New Results in Science 9(1) (2020) 19–36.
• N. Çağman, S. Enginoğlu, Soft Sets Theory and uni-int Decision-Making, European Journal of Operational Research 207(2) (2010) 848–855.
• P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft Sets, The Journal of Fuzzy Mathematics 9(3) (2001) 589–602.
• N. Çağman, S. Enginoğlu, F. Çıtak, Fuzzy Soft Set Theory and Its Applications, Iranian Journal of Fuzzy Systems 8(3) (2011) 137–147.
• N. Çağman, F. Çıtak, S. Enginoğlu, FP-Soft Set Theory and Its Applications, Annals of Fuzzy Mathematics and Informatics 2(2) (2011) 219–226.
• N. Çağman, F. Çıtak, S. Enginoğlu, Fuzzy Parameterized Fuzzy Soft Set Theory and Its Applications, Turkish Journal of Fuzzy Systems 1(1) (2010) 21–35.
• N. Çağman, S. Enginoğlu, Soft Matrix Theory and Its Decision Making, Computers and Mathematics with Applications 59(10) (2010) 3308–3314.
• N. Çağman, S. Enginoğlu, Fuzzy Soft Matrix Theory and Its Application in Decision Making, Iranian Journal of Fuzzy Systems 9(1) (2012) 109–119.
• S. Enginoğlu, S. Memiş, 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], Eds: Akgül, M., Yılmaz, İ., İpek, A. International Conference on Mathematical Studies and Applications, pp. 173–178, October 4-6, Karaman, Turkey.
• S. Enginoğlu, S. Memiş, Comment on “Fuzzy soft sets” [The Journal of Fuzzy Mathematics, 9(3), 2001, 589-602], International Journal of Latest Engineering Research and Applications 3(9) (2018) 1–9.
• S. Enginoğlu, S. Memiş, B. Arslan, A Fast and Simple Soft Decision-Making Algorithm: EMA18an, Eds: Akgül, M., Yılmaz, İ., İpek, A. International Conference on Mathematical Studies and Applications, pp. 428–436, October 4-6, Karaman, Turkey.
• S. Enginoğlu, S. Memiş, T. Öngel, A Fast and Simple Soft Decision-Making Algorithm: EMO18o, Eds: Akgül, M., Yılmaz, İ., İpek, A. International Conference on Mathematical Studies and Applications, pp. 179–187, October 4-6, Karaman, Turkey.
• Z. Xu, R. R. Yager, Some Geometric Aggregation Operators Based on Intuitionistic Fuzzy Sets, International Journal of General Systems 35(4) (2006) 417–433.
• U. Erkan, L. Gökrem, A New Method Based on Pixel Density in Salt and Pepper Noise Removal, Turkish Journal of Electrical Engineering and Computer Sciences 26 (2018) 162–171.
• K. S. Srinivasan, D. Ebenezer, A New Fast and Efficient Decision-Based Algorithm for Removal of High-Density Impulse Noises, IEEE Signal Processing Letters 14(3) (2007) 189–192.
• S. Esakkirajan, T. Veerakumar, A. N. Subramanyam, C. H. PremChand, Removal of High Density Salt and Pepper Noise Through Modified Decision Based Unsymmetric Trimmed Median Filter, IEEE Signal Processing Letters 18(5) (2012) 287–290.
• K. K. V. Toh, N. A. M. Isa, Noise Adaptive Fuzzy Switching Median Filter for Salt-and-Pepper Noise Reduction, IEEE Signal Processing Letters 17(3) (2010) 281–284.
• U. Erkan, L. Gökrem, S. Enginoğlu, Different Applied Median Filter in Salt and Pepper Noise, Computers & Electrical Engineering 70 (2018) 789–798.
• Z Tang, Z Yang, K Liu, Z Pei, A New Adaptive Weighted Mean Filter for Removing High Density Impulse Noise, Proceeding SPIE 10033, Eighth International Conference on Digital Image Processing (ICDIP), Eds: C M Falco, X Jiang, August 2016 1003353 pp. 1–5.
• S Enginoğlu, U Erkan, S Memiş, Pixel Similarity-based Adaptive Riesz Mean Filter for Salt-and-Pepper Noise Removal, Multimedia Tools and Applications 78 (2019) 35401–35418.
• Z Wang, A Bovik, H Sheikh, E Simoncelli, Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE Transactions on Image Processing 13(4) (2004) 600–612.
• S. Enginoğlu, M. Ay, N. Çağman, V. Tolun, Classification of The Monolithic Columns Produced in Troad and Mysia Region Ancient Granite Quarries in Northwestern Anatolia via Soft Decision-Making, Bilge International Journal of Science and Technology Research 3(Special Issue) (2019) 21–34.
• S. Memiş, S. Enginoğlu, U. Erkan, A Data Classification Method in Machine Learning Based on Normalised Hamming Pseudo-Similarity of Fuzzy Parameterized Fuzzy Soft Matrices, Bilge International Journal of Science and Technology Research 3(Special Issue) (2019) 1–8.
• S. Memiş, S. Enginoğlu, An Application of Fuzzy Parameterized Fuzzy Soft Matrices in Data Classification, M. Kılıç, K. Özkan, M. Karaboyacı, K. Taşdelen, H. Kandemir, A. Beram, (Ed.), International Conferences on Science and Technology, Natural Science and Technology (2019) 68–77 Prizren, Kosovo.
• S. Memiş, S. Enginoğlu, U. Erkan, Numerical Data Classification via Distance-Based Similarity Measures of Fuzzy Parameterized Fuzzy Soft Matrices, IEEE Access 9 (2021) 88583–88601.
• S. Memiş, B. Arslan, T. Aydın, S. Enginoğlu, Ç. Camcı, A Classification Method Based on Hamming Pseudo-Similarity of Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Matrices, Journal of New Results in Science 10(2) (2021) 59–76.
• T. Aydın, S. Enginoğlu, Interval-Valued Intuitionistic Fuzzy Parameterized Interval-Valued Intuitionistic Fuzzy Soft Sets and Their Application in Decision-Making, Journal of Ambient Intelligence and Humanized Computing 12 (2021) 1541–1558.
• T. Aydın, Interval-Valued Intuitionistic Fuzzy Parameterized Interval-Valued Intuitionistic Fuzzy Soft Matrices and Their Application to A Performance-Based Value Assignment, Doctoral Dissertation, Çanakkale Onsekiz Mart University, Çanakkale, Turkey (2021) (In Turkish).
• B. C. Cuong, Picture Fuzzy Sets, Journal of Computer Science and Cybernetics 30(4) (2014) 409–420.
• S. Memiş, A Study on Picture Fuzzy Sets, G. Çuvalcıoğlu (Ed.), 7th IFS and Contemporary Mathematics Conference (2021) 125–132 Mersin, Turkey.