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A classification method in machine learning based on soft decision-making via fuzzy parameterized fuzzy soft matrices
(Springer Science and Business Media Deutschland GmbH, 2022) Memiş, Samet; Enginoğlu, Serdar; Erkan, Uğur
Fuzzy parameterized fuzzy soft matrices (fpfs-matrices) which can model problems involving fuzzy objects and parameters are one of the mathematical tools used to deal with decision-making problems. To utilize soft decision-making methods via fpfs-matrices in machine learning is likely to draw much scholarly attention. In this paper, we propose Comparison Matrix-Based Fuzzy Parameterized Fuzzy Soft Classifier (FPFS-CMC) in order to transfer modeling success of fpfs-matrices to machine learning. We then compare FPFS-CMC with Fuzzy Soft Set Classifier (FSSC), FussCyier, Fuzzy Soft Set Classification Using Hamming Distance (HDFSSC), and Fuzzy k-Nearest Neighbor (Fuzzy kNN) in consideration of accuracy, precision, recall, macro-F-score, and micro-F-score performance metrics, and 15 datasets in UCI Machine Learning Repository. Besides, we compare the proposed classifier with the state-of-the-art Support Vector Machine (SVM), Decision Tree (DT), and Adaptive Boosting (AdaBoost) in terms of five performance metrics herein. Afterward, the results from the experiments are analyzed by employing the Friedman and Nemenyi tests to assess the statistical significance of the differences in performances. Both experimental and statistical results show that FPFS-CMC outperforms the others. Finally, we provide the conclusive remarks and some suggestions for further research.
A Configuration of Some Soft Decision-Making Algorithms via fpfs-matrices
(2018) Enginoğlu, Serdar; Memiş, Samet
Since many problems have a large amount of data or uncertainty, the computer mathematics has become compulsory. To deal with such kinds of these problems, the concept of fuzzy parameterized fuzzy soft matrices (fpfs-matrices) has been defined by Enginoğlu. In this paper, we first give some of its basic definitions. We then configure some decision-making algorithms constructed by soft sets, fuzzy soft sets, fuzzy parameterized soft sets, fpfs-sets, and their matrix representations. We finally discuss later works.
A Generalisation of Fuzzy Soft Max-Min Decision-Making Method and Its Application to a Performance-Based Value Assignment in Image Denoising
(TUBITAK, 2019) Enginoğlu, Serdar; Memiş, Samet; Çağman, Naim
Latterly, the fuzzy soft max-min decision-making method denoted by FSMmDM and provided in [Çağman, N., Engino?lu, S., Fuzzy soft matrix theory and its application in decision making, Iranian Journal of Fuzzy Systems, 2012, 9(1), 109-119] has been configured via fuzzy parameterized fuzzy soft matrices (-matrices) by Enginoğlu and Memiş [A configuration of some soft decision-making algorithms via-matrices, Cumhuriyet Science Journal, 2018, 39(4), 871-881], faithfully to the original. Although this configured method denoted by CE12 and constructed by and-product/or-product (CE12a/CE12o) is useful in decision-making, the method should be made more attractive in terms of time and complexity in the event that a large amount of data is processed. In this paper, we propose two algorithms denoted by EMC19a and EMC19o and being new generalisations of FSMmDM. Moreover, we prove that EMC19a accept CE12a as a special case in the event that the first rows of the-matrices are binary. Afterwards, we compare the running times of these algorithms. The results show that EMC19a and EMC19o outperform CE12a and CE12o, respectively, in any number of data. We then apply EMC19o to a decision-making problem in image denoising. Finally, we discuss the need for further research. © 2019, TUBITAK. All rights reserved.
A new classification method using soft decision-making based on an aggregation operator of fuzzy parameterized fuzzy soft matrices
(2022) Memış, Samet; Enginoğlu, Serdar; Erkan, Uğur
Recently, a precise and stable machine learning algorithm, i.e. eigenvalue classification method (EigenClass),\rhas been developed by using the concept of generalised eigenvalues in contrast to common approaches, such as k-nearest\rneighbours, support vector machines, and decision trees. In this paper, we offer a new classification algorithm called fuzzy\rparameterized fuzzy soft aggregation classifier (FPFS-AC) to combine the modelling ability of soft decision-making (SDM)\rand classification success of generalised eigenvalues. FPFS-AC constructs a decision matrix by employing the similarity\rmeasures of fuzzy parameterized fuzzy soft matrices (fpfs-matrices) and a generalised eigenvalue-based similarity measure.\rThen, it applies an SDM method based on the aggregation operator of fpfs-matrices to a decision matrix and classifies\rthe given test sample. Afterwards, we perform an experimental study using 15 UCI datasets to manifest the success\rof our approach and compare FPFS-AC with the well-known and state-of-the-art classifiers (kNN, SVM, fuzzy kNN,\rEigenClass, and BM-fuzzy kNN) in terms of accuracy, precision, recall, macro F-score, micro F-score, and running time.\rMoreover, we statistically analyse the experimentally obtained data. Experimental and statistical results show that\rFPFS-AC outperforms the state-of-the-art classifiers in all the datasets concerning the five performance metrics.
Adaptive cesáro mean filter for salt-and-pepper noise removal
(TUBITAK, 2020) Enginoğlu, Serdar; Erkan, Uğur; Memiş, Samet
In this study, we propound a salt-and-pepper noise (SPN) removal method, i.e. Adaptive Cesáro Mean Filter (ACmF), and provide some of its basic notions. We then apply ACmF to several test images whose noise densities range from 10% to 90%: 15 traditional test images (Baboon, Boat, Bridge, Cameraman, Elaine, Flintstones, Hill, House, Lake, Lena, Living Room, Parrot, Peppers, Pirate, and Plane) and 40 test images, provided in the TESTIMAGES Database. Afterwards, we compare ACmF with the state-of-art methods, such as Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), and Noise Adaptive Fuzzy Switching Median Filter (NAFSMF). The results by The Peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM) show that ACmF performs better than the methods mentioned above. Moreover, we also compare the running time data of these algorithms. These results show that ACmF outperforms the methods except for DAMF. We finally discuss the need for further research. © 2020, TUBITAK. All rights reserved.
Adaptive Right Median Filter for Salt-and-Pepper Noise Removal
(2019) Erkan, Uğur; Gökrem, Levent; Enginoğlu, Serdar
In image processing, nonlinear filters are commonly used as a pre-process for noise removal before applying any advanced processing such as classification and clustering to an image. The adaptive filters being a kind of the nonlinear filters mainly perform better than the others in salt-and-pepper noise. In this paper, we first define a new median method, i.e. right median (rm). We then define a new adaptive nonlinear filter developed via rm, namely Adaptive Right Median Filter (ARMF), for saltand-pepper noise removal. Afterwards, we compare the results of ARMF with some of the known filters by using 12 test images and two image quality metrics: Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM). The results show that ARMF outperforms the other methods at all the noise density except 80% and 90% in the mean percentages. Finally, we discuss the need for further research.
CONFIGURATIONS OF SEVERAL SOFT DECISION-MAKING METHODS TO OPERATE IN FUZZY PARAMETERIZED FUZZY SOFT MATRICES SPACE
(2020) Enginoğlu, Serdar; Öngel, Tutku
The concept of fuzzy parameterized fuzzy soft matrices (fpfs-matrices), which allows for processing fuzzy parameters andfuzzy subsets of the alternatives by using computers, is a novel and efficient mathematical tool to cope with uncertainties.Contrary to the methods constructed by fpfs-matrices, the known soft decision-making (SDM) methods based on soft sets andfuzzy sets cannot model problems whose parameters and alternatives are fuzzy. Therefore, such methods have been configuredto operate in the fpfs-matrices space. In this paper, we configure two SDM methods constructed by soft sets, six SDM methodsconstructed by fuzzy soft sets, two SDM methods constructed by soft matrices, and four SDM methods constructed by fuzzysoft matrices. We then apply the configured methods using one fpfs-matrix as input data to a performance-based valueassignment problem. Finally, we discuss the need for further research.
Diagnosing COVID-19, Prioritizing Treatment, and Planning Vaccination Priority via Fuzzy Parameterized Fuzzy Soft Matrices
(2022) Parmaksız, Zeynep Parla; Arslan, Burak; Memış, Samet; Enginoğlu, Serdar
In the fight against the COVID-19 pandemic, it is vital to rapidly diagnose possible contagions, treat patients, plan follow-up procedures with correct and effective use of resources and ensure the formation of herd immunity. The use of machine learning and statistical methods provides great convenience in dealing with too many data produced during research. Since access to the PCR test used for the diagnosis of COVID-19 may be limited, the test is relatively too slow to yield results, the cost is high, and its reliability is controversial; thus, making a symptomatic classification before the PCR is timesaving and far less costly. In this study, by modifying a state-of-the-art classification method, namely Comparison Matrix-Based Fuzzy Parameterized Fuzzy Soft Classifier (FPFS-CMC), an effective method is developed for a rapid diagnosis of COVID-19. The paper then presents the accuracy, sensitivity, specificity, and F1-score values that represent the diagnostic performances of the modified method. The results show that the modified method can be adopted as a competent and accurate diagnosis procedure. Afterwards, a tirage study is performed by calculating the patients’ risk scores to manage inpatient overcrowding in healthcare institutions. In the subsequent section, a vaccine priority algorithm is proposed to be used in the case of a possible crisis until the supply shortage of a newly developed vaccine is over if a possible variant of COVID-19 that is highly contagious is insensitive to the vaccine. The accuracy of the algorithm is tested with real-life data. Finally, the need for further research is discussed.
Distance and Similarity Measures of Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Matrices and Their Applications to Data Classification in Supervised Learning
(MDPI, 2023) Memiş, Samet; Arslan, Burak; Aydın, Tuğce; Enginoğlu, Serdar; Camcı, Çetin
Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices), proposed by Enginoğlu and Arslan in 2020, are worth utilizing in data classification in supervised learning due to coming into prominence with their ability to model decision-making problems. This study aims to define the concepts metrics, quasi-, semi-, and pseudo-metrics and similarities, quasi-, semi-, and pseudo-similarities over ifpifs-matrices; develop a new classifier by using them; and apply it to data classification. To this end, it develops a new classifier, i.e., Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Classifier (IFPIFSC), based on six pseudo-similarities proposed herein. Moreover, this study performs IFPIFSC’s simulations using 20 datasets provided in the UCI Machine Learning Repository and obtains its performance results via five performance metrics, accuracy (Acc), precision (Pre), recall (Rec), macro F-score (MacF), and micro F-score (MicF). It also compares the aforementioned results with those of 10 well-known fuzzy-based classifiers and 5 non-fuzzy-based classifiers. As a result, the mean Acc, Pre, Rec, MacF, and MicF results of IFPIFSC, in comparison with fuzzy-based classifiers, are 94.45%, 88.21%, 86.11%, 87.98%, and 89.62%, the best scores, respectively, and with non-fuzzy-based classifiers, are 94.34%, 88.02%, 85.86%, 87.65%, and 89.44%, the best scores, respectively. Later, this study conducts the statistical evaluations of the performance results using a non-parametric test (Friedman) and a post hoc test (Nemenyi). The critical diagrams of the Nemenyi test manifest the performance differences between the average rankings of IFPIFSC and 10 of the 15 are greater than the critical distance (4.0798). Consequently, IFPIFSC is a convenient method for data classification. Finally, to present opportunities for further research, this study discusses the applications of ifpifs-matrices for machine learning and how to improve IFPIFSC.
Exponentially Weighted Mean Filter for Salt-and-Pepper Noise Removal
(Springer Science and Business Media Deutschland GmbH, 2022) Enginoğlu, Serdar; Erkan, Uğur; Memiş, Samet
This paper defines an exponentially weighted mean using an exponentially decreasing sequence of simple fractions based on distance. It then proposes a cutting-edge salt-and-pepper noise (SPN) removal filter—i.e., Exponentially Weighted Mean Filter (EWmF). The proposed method incorporates a pre-processing step that detects noisy pixels and calculates threshold values based on the possible noise density. Moreover, to denoise the images operationalizing the calculated threshold values, EWmF employs the exponentially weighted mean (ewmean) in 1-approximate Von Neumann neighbourhoods for low noise densities and k-approximate Moore neighbourhoods for middle or high noise densities. Furthermore, it ultimately removes the residual SPN in the processed images by relying on their SPN densities. The numerical and visual results obtained with MATLAB R2021a manifest that EWmF outperforms nine state-of-the-art SPN filters. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Fuzzy parameterized fuzzy soft matrices and their application in decision-making
(Isik University, 2020) Enginoğlu, Serdar; Çağman, Naim
In this study, we define the concept of fuzzy parameterized fuzzy soft matrices (fpfs-matrices) and present some of their basic properties. By using fpfs-matrices, we then suggest a new algorithm, i.e. Prevalence Effect Method (PEM), and apply this method to a performance-based value assignment, so that we can order noise removal filters regarding performance. The results show that PEM has a potential for several areas, such as machine learning and image processing. Finally, we discuss fpfs-matrices and PEM for further research. © Isik University, Department of Mathematics, 2020.
FUZZY PARAMETERIZED FUZZY SOFT MATRICES AND THEIRAPPLICATION IN DECISION-MAKING
(2020) Enginoğlu, Serdar; Çagman, Naim
Abstract.In this study, we define the concept of fuzzy parameterized fuzzy soft ma-trices (fpfs-matrices) and present some of their basic properties. By usingfpfs-matrices,we then suggest a new algorithm, i.e. Prevalence Effect Method (PEM), and apply thismethod to a performance-based value assignment, so that we can order noise removalfilters regarding performance.The results show that PEM has a potential for severalareas, such as machine learning and image processing. Finally, we discussfpfs-matricesand PEM for further research.
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
(2021) Arslan, Burak; Aydın, Tuğçe; Memış, Samet; Enginoğlu, Serdar
Recently, the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy\rsoft matrices (ifpifs-matrices) has allowed to mathematically model some problems in which\rthe parameters and alternatives exhibit intuitionistic fuzzy uncertainties. To this end, the\rpresent study aims to generalise 24 soft decision-making (SDM) methods operating in the\rfuzzy parameterized fuzzy soft matrices space with a single fpfs-matrix to the ifpifs-matrices\rspaces. Afterwards, we propose five test scenarios to analyse whether the SDM methods\rconstructed by ifpifs-matrices consistently work. Moreover, we make performance\rcomparisons of the generalised SDM methods successful in the five test scenarios by\rapplying them to the performance-based value assignment (PVA) problem of the wellknown\rnoise-removal filters. Finally, we discuss the need for further research.
Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making
(Springer Science and Business Media Deutschland GmbH, 2021) Aydın, Tuğçe; Enginoğlu, Serdar
Although some statistical tools, such as mean and median, used for modelling a problem containing parameters or alternatives with multiple intuitionistic fuzzy values because these values are obtained in a specific period, decrease uncertainty, they lead to data loss. However, interval-valued intuitionistic fuzzy values can overcome such a concern. For this reason, the present study proposes the concept of interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets (d-sets) and presents several of its basic properties. Moreover, by using d-sets, we suggest a new soft decision-making method and apply it to a problem concerning the eligibility of candidates for two vacant positions in an online job advertisement. Since it is the first method proposed in relation to this structure (d-sets), it is impossible to compare this method with another in this sense. To deal with this difficulty, we introduce four new concepts, i.e. mean reduction, mean bireduction, mean bireduction-reduction, and mean reduction-bireduction. By using these concepts, we apply four state-of-the-art soft decision-making methods to the problem. We then compare the ranking performances of the proposed method with those of the four methods. Besides, we apply five methods to a real problem concerning performance-based value assignment to some filters used in image denoising and compare the ranking performances of these methods. Finally, we discuss d-sets and the proposed method for further research.
Operability-Oriented Configurations of the Soft Decision-Making Methods Proposed between 2013 and 2016 and Their Comparisons
(2021) Enginoğlu, Serdar; Aydın, Tuğçe; Memış, Samet; Arslan, Burak
The concept of fuzzy parameterized fuzzy soft matrices (fpfs-matrices) is a mathematical\rtool coming into prominence with its ability to model decision-making problems. Therefore, in the present study, we configure soft decision-making (SDM) methods having been constructed with soft sets, soft matrices, and their fuzzy hybrid versions and introduced between 2013 and 2016 to operate them in fpfs-matrices space faithfully to the original. We then analyse the decision-making performances of the configured methods herein by using five test cases containing totally ordered alternatives. Thus, we determine the methods producing a valid ranking order according to all the test cases and apply the determined methods to a performance-based value assignment (PVA) problem in which the filters are to be ranked in terms of their image denoising performances. Therefore, we compare the performance ranking of the filters by using the methods. Finally, we discuss the need for further research.

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