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Öğe A classification method based on Hamming pseudo-similarity of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices(Tokat Gaziosmanpasa University, 2021) Memiş, Samet; Arslan, Burak; Aydın, Tuğçe; Enginoğlu, Serdar; Camcı, ÇetinIn this study, firstly, Hamming pseudo-similarity of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) have been defined. Afterwards, a classifier based on Hamming pseudo-similarity of ifpifs-matrices (IFPIFS-HC) has been developed. The classifier's simulations have been performed using datasets provided in the UCI Machine Learning Database, and its performance results via the performance metrics accuracy, precision, recall, macro F-score, and micro F-score have been obtained. Thereafter, the results have been compared with those of the well-known methods. Then, the statistical evaluations of the performance results have been conducted using Friedman and Nemenyi post-hoc tests, and the critical diagrams of the Nemenyi post-hoc test are presented. The results and the statistical evaluations show that the proposed classifier has performed better than the others in 12 of 21 datasets in terms of the five performance metrics, in 4 of 21 in terms of the four performance metrics, and 17 of 21 in terms of accuracy performance metric. Moreover, the mean accuracy, precision, recall, precision, macro F-score, and micro F-score results of Fuzzy kNN, FSSC, FussCyier, HDFSSC, and FPFS-EC for the 21 datasets are 84.90, 71.96, 67.95, 71.91, and 75.28; 78.12, 68.01, 68.05, 66.53, and 67.68; 80.76, 68.63, 69.07, 68.36, and 70.65; 81.93, 69.43, 69.95, 70.25, and 72.36; and 89.59, 80.27, 78.40, 81.20, and 83.60, while those of IFPIFS-HC are 90.59, 82.88, 80.75, 82.89, and 85.48, respectively. Finally, the applications of ifpifs-matrices to machine learning have been discussed for further research.Öğe Comment (2) on Soft Set Theory and uni-int Decision Making [European Journal of Operational Research](2018) Enginoğlu, Serdar; Memiş, Samet; Arslan, Burak[Abstract Not Available]Öğe Diagnosing COVID-19, Prioritizing Treatment, and Planning Vaccination Priority via Fuzzy Parameterized Fuzzy Soft Matrices(2022) Parmaksız, Zeynep Parla; Arslan, Burak; Memış, Samet; Enginoğlu, SerdarIn 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.Öğe 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, ÇetinIntuitionistic 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.Öğe Esnek Türev(Çanakkale Onsekiz Mart Üniversitesi, 2024) Arslan, Burak; Enginoğlu, SerdarEle alınan bu çalışmada, Molodtsov tarafından 1987, 1999 ve 2004 yıllarında çalışılan ve esnek analizin temel kavramlarından olan esnek türev ve üst (alt) esnek türev tanıtıldı. Ayrıca, bu kavramlara teorik olarak katkı sağlandı. Üstelik, bu çalışmada, sol ve sağ esnek türevler tanımlandı. Ek olarak, temel esnek türev kuralları, esnek türev ve esnek süreklilik arasındaki ilişki, esnek türev ve sınırlılık arasındaki ilişki, bahsi geçen kavramların geometrik yorumları, bir fonksiyonun mutlak ve yerel ?-ekstremumları, Rolle Teoremi ve Ortalama Değer Teoremi gibi bazı temel özellikler araştırıldı. Diğer taraftan, bu çalışmada, yüksek mertebeden hemen hemen esnek türev ve yüksek mertebeden esnek türev kavramları sunuldu. Ek olarak, kısmi esnek türev kavramı ortaya atıldı ve temel kısmi esnek türev kuralları, temel çıkarımlar ve geometrik yorum gibi bazı temel özellikler incelendi. Daha sonra, bu çalışmada, yüksek mertebeden kısmi esnek türev ve esnek diferansiyellenebilme kavramları tanımlandı ve onların bazı temel özellikleri araştırıldı. Ayrıca, yönlü esnek türev ve esnek gradyan kavramları ileri sürüldü ve onların bazı temel özellikleri araştırıldı. Son olarak, bu çalışmada, söz konusu kavramlar üzerine bir tartışmaya yer verildi.Öğe 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, SerdarRecently, 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.Öğe Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making(Springer Heidelberg, 2020) Enginoglu, Serdar; Arslan, BurakThis study aims to propose the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) and to present several of its basic properties. Therefore, it would be possible to improve the problem-modelling capabilities of the available intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets in the occurrence of a large number of data. Moreover, by using ifpifs-matrices, we suggest a new soft decision-making method, denoted by EA20, and apply it to a multi-criteria group decision-making (MCGDM) problem. We then compare the ranking performance of EA20 for five noise-removal filters with those of ten state-of-the-art soft decision-making methods. The results show that EA20 successfully models performance-based value assignment problems. Finally, we discuss ifpifs-matrices and EA20 for further research.Öğe Investigating Concepts in Soft Topological Structures through Subspaces(World Scientific Publ Co Pte Ltd, 2025) Arslan, Burak; Aydin, TugceFollowing the study of Molodtsov on soft topological structures in 2015, this study discusses the concepts in soft topological structures through subspaces, investigates some of their crucial properties, and provides their characterizations. To ensure consistency with Molodtsov's framework, this paper defines the tau-neighborhood in a subspace S subset of X of any x is an element of S as tau(x) boolean AND S, noting that his definition of the tau-neighborhood in X of any x is an element of X is tau(x), which equals tau(x) boolean AND X. Moreover, this study researches some of the relations between concepts in a space and their correspondences in subspaces. Besides, it explores whether being tau-C-, tau-T-, tau-B-, and tau-I-soft discrete and indiscrete topologies is hereditary or not. Finally, this study handles if further research concerning these aspects is needed.Öğe 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, BurakThe 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.Öğe Operability-Oriented Configurations of the Soft Decision-Making Methods Proposed between 2013 and 2016 and Their Comparisons(Naim ÇAĞMAN, 2021) Enginoğlu, Serdar; Aydın, Tuğçe; Memiş, Samet; Arslan, BurakThe concept of fuzzy parameterized fuzzy soft matrices (fpfs-matrices) is a mathematical tool 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.Öğe Partial Soft Derivative(Emrah Evren KARA, 2024) Arslan, Burak; Enginoğlu, SerdarThe concept of soft derivative, introduced by Molodtsov in 1999, is one of the fundamental concepts in soft analysis. The handled paper defines partial soft derivative and studies some of its basic properties, such as the relation between partial soft derivative and boundedness, some basic partial soft derivative rules, e.g., sum rule, constant multiple rule, and difference rule, the relation between soft derivative and partial soft derivative, the relation between classical partial derivative and partial soft derivative, and the geometric interpretation of partial soft derivative. Moreover, it exemplifies the theoretical part of the study and provides figures for the geometric interpretation. Finally, this study discusses the need for further research.Öğe Sezgisel bulanık parametreli sezgisel bulanık esnek matrisler(Çanakkale Onsekiz Mart Üniversitesi, 2019) Arslan, Burak; Enginoğlu, SerdarBu çalışmada, sezgisel bulanık parametreli sezgisel bulanık esnek matris (ifpifs-matris) kavramı tanımlandı ve bazı temel özellikleri verildi. Ardından, ifpifs-matrisler kullanılarak, yeni bir esnek karar verme yöntemi önerildi ve bu yöntem bir karar verme problemine uygulandı. Son olarak, ifpifs-matrisler ve önerilen yöntem hakkında bir tartışmaya yer verildi.Öğe Soft Decision-Making Methods Employing Multiple ifpifs-Matrices and Their Application(Soc Paranaense Matematica, 2025) Arslan, Burak; Aydın, Tuğçe; Memiş, Samet; Enginoğlu, SerdarThe present study generalizes 36 soft decision-making (SDM) methods employing multiple fuzzy parameterized fuzzy soft matrices (fpfs-matrices) to operable in the intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) space and obtains 44 SDM methods containing several variants of the aforesaid methods. It then compares all the SDM methods herein using three ifpifs-matrices for each test case proposed by the authors' previous study. The comparison shows that 23 of 44 passed all the test cases. Moreover, this study applies the 23 SDM methods to a performance-based value assignment (PVA) problem in which seven well-known salt-and-pepper noise removal filters used in digital images are considered. The results manifest that 10 of 23 produce the same ranking order at the high noise density, just as 8 of 23 do at the low noise density. Finally, this study discusses SDM methods' applications and the need for further research.Öğe Soft Derivative(Soc Paranaense Matematica, 2025) Arslan, Burak; Enginoglu, SerdarThis study presents a comprehensive investigation of soft and upper (lower) soft derivatives within the framework of Molodtsov's soft set theory, extending it through the introduction of novel and complementary notions: left and right soft derivatives. It rigorously develops the fundamental properties of these concepts, including algebraic and order-theoretic rules, and establishes their relationships with boundedness and soft continuity types. The paper offers insightful geometric interpretations that significantly enhance conceptual understanding. Furthermore, it introduces absolute epsilon-extrema, investigates their fundamental properties, and characterizes the local (tau, epsilon)-extrema defined by Molodtsov. This study presents analogs of Rolle's Theorem for upper and lower soft derivatives and interprets them geometrically with supporting visual illustrations. Moreover, it establishes and geometrically interprets analogs of the Mean Value Theorem for upper and lower soft derivatives. By systematically investigating fundamental concepts in soft analysis and presenting detailed results, the present paper constructs a comprehensive foundation that strengthens the mathematical structure of soft analysis and paves the way for advanced developments, such as soft integrals, soft directional derivatives, and soft gradients.Öğe Soft Limit and Soft Continuity(Mdpi, 2025) Sapan, Kenan; Arslan, Burak; Enginoglu, SerdarThis study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano's theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed.Öğe Statistical Riesz and Nörlund convergence for sequences of fuzzy numbers(Amasya Üniversitesi, 2023) Arslan, Burak; Jalali, Samira; Enginoğlu, SerdarNuray and Savaş proposed statistical convergence of fuzzy number sequences. Afterward, Tripathy and Baruah presented Riesz and Nörlund convergence for sequences of fuzzy numbers. This paper defines statistical Riesz and Nörlund convergence of fuzzy number sequences. It then shows that if a sequence of fuzzy numbers is convergent, then it is statistical Riesz/Nörlund convergent, but the converse is not always true. Finally, this paper discusses the need for further research.
