Ifpifs-Matrices

In this paper, limiting behaviour of intuitionistic fuzzy parameterized soft set (intuitionistic FP-soft set) based decision making method is shown by a counter example. Then we define picture fuzzy parameterized soft set (picture FP-soft set). This notion can be used to express fuzzy information in more general and effective way. In particular, some basic operations such as union, intersection, complement and subset of picture FP-soft sets are developed. We also propose a conversion method to construct picture fuzzy set from intuitionistic fuzzy set. Furthermore, reduced PF-soft set and reduced intuitionistic fuzzy set are proposed. Based on these definition decision making method based on picture FP-soft set is developed. Finally, using proposed construction method we convert intuitionistic fuzzy information of counter example in picture fuzzy information and then apply picture FP-soft set based decision making method leading a more clear decision of problem which shows efficiency of proposed set and decision making method.

In this paper, the definition of intuitionistic fuzzy parameterised fuzzy soft set (ifpfs-sets) is introduced with their properties. Two operations on ifpfs-set, namely union and intersection are introduced. Also, some examples for these operations are given. The definition of ifpfsaggregation operator which forms ifpfs-decision making method is introduced.

Image restoration is an important and interesting problem in the field of image processing because it improves the quality of input images, which facilitates postprocessing tasks. The salt-and-pepper noise has a simpler structure than other noises, such as Gaussian and Poisson noises, but is a very common type of noise caused by many electronic devices. In this article, we propose a two-stage filter to remove high-density salt-and-pepper noise on images. The range of application of the proposed denoising method goes from low-density to high-density corrupted images. In the experiments, we assessed the image quality after denoising using the peak signal-to-noise ratio and structural similarity metric. We also compared our method against other similar state-of-the-art denoising methods to prove its effectiveness for salt and pepper noise removal. From the findings, one can conclude that the proposed method can successfully remove super-high-density noise with noise level above 90%.

Soft multi-criteria decision-making, a developing area, is among the most prevalent problems handled by researchers. This study aims to introduce a soft decision-making method and apply it to rank the side effects of COVID-19 vaccines. Based on the literature, the present study features the advantages and disadvantages of previously observed multi-criteria decision-making (MCDM) methods are summarized. This paper achieves to utilize multisets simultaneously with the known soft decision-making methods. The primary concern hereof is to offer an insightful everyday-life example. Finally, the authors discuss the need for further research.

The main focus of this paper is the application of aggregation operators (AOs) in the environment of Fermatean fuzzy soft sets (FFSS). The unique feature of the work is its application in the symptomatic treatment of the COVID-19 disease. For this purpose, the idea of FFSS is introduced which is based on the Senapati and Yagar's Fermatean fuzzy set. Next we have defined Fermatean fuzzy soft aggregation operators (FFSAOs) like, Fermatean fuzzy soft weighted averaging (FFSWA) operator, Fermatean fuzzy soft ordered weighted averaging (FFSOWA) operator, Fermatean fuzzy soft weighted geometric (FFSWG) operator and Fermatean fuzzy soft ordered weighted geometric (FFSOWG). The prominent properties of these operators are given in details. We have also developed some approaches to solve multi-criteria decision making (MCDM) problems in Fermatean fuzzy soft (FFS) information. An introduction to the novel pandemic, safety measures, and then its possible symptomatic treatment is also provided. The developed operators are utilized in the symptomatic treatment of COVID-19 disease in order to show the practical applications and importance of these AOs as well as Fermatean fuzzy soft information. The stability of the proposed work is also proved by the comparative analysis.

This paper redefines picture fuzzy soft matrices (pfs-matrices) because of some of their inconsistencies resulting from Cuong’s definition of picture fuzzy sets. Then, it introduces several distance measures of pfs-matrices. Afterward, this paper proposes a new kNN-based classifier, namely the Picture Fuzzy Soft k-Nearest Neighbor (PFS-kNN) classifier. The proposed classifier utilizes the Minkowski’s metric of pfs-matrices to find the k-nearest neighbor. Thereafter, it performs an experimental study utilizing four UCI medical datasets and compares to the suggested approach using the state-of-the-art kNN-based classifiers. To evaluate the performance of the classification, it conducts ten iterations of five-fold cross-validation on all the classifiers. The findings indicate that PFS-kNN surpasses the state-of-the-art kNN-based algorithms in 72 out of 128 performance results based on accuracy, precision, recall, and F1-score. More specifically, the proposed method achieves higher accu...

Recently, a precise and stable machine learning algorithm, i.e. eigenvalue classification method (EigenClass), has been developed by using the concept of generalised eigenvalues in contrast to common approaches, such as k-nearest neighbours, support vector machines, and decision trees. In this paper, we offer a new classification algorithm called fuzzy parameterized fuzzy soft aggregation classifier (FPFS-AC) to combine the modelling ability of soft decision-making (SDM) and classification success of generalised eigenvalues. FPFS-AC constructs a decision matrix by employing the similarity measures of fuzzy parameterized fuzzy soft matrices (fpfs-matrices) and a generalised eigenvalue-based similarity measure. Then, it applies an SDM method based on the aggregation operator of fpfs-matrices to a decision matrix and classifies the given test sample. Afterwards, we perform an experimental study using 15 UCI datasets to manifest the success of our approach and compare FPFS-AC with the well-known and state-of-the-art classifiers (kNN, SVM, fuzzy kNN, EigenClass, and BM-fuzzy kNN) in terms of accuracy, precision, recall, macro F-score, micro F-score, and running time. Moreover, we statistically analyse the experimentally obtained data. Experimental and statistical results show that FPFS-AC outperforms the state-of-the-art classifiers in all the datasets concerning the five performance metrics.

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.

In this work, we present definition of intuitionistic fuzzy parameterized (IF P) intuitionistic fuzzy soft set and its operations. Then we define IF P-aggregation operator to form IF P-intuitionistic fuzzy soft-decision-making method which allows constructing more efficient decision processes.

In this work, we first define intuitionistic fuzzy parametrized soft sets (intuitionistic FP-soft sets) and study some of their properties. We then introduce an adjustable approaches to intuitionistic FP-soft sets based decision making. We also give an example which shows that they can be successfully applied to problems that contain uncertainties.

In this work, we first define intuitionistic fuzzy parametrized soft sets (intuitionistic FP-soft sets) and study some of their properties. We then introduce an adjustable approaches to intuitionistic FP-soft sets based decision making. We also give an example which shows that they can be successfully applied to problems that contain uncertainties.

In this work, we define a fuzzy soft set theory and its related properties. We then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.

In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. We then define products of $fs$-matrices andstudy their properties. We finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

In this work, we define soft matrices and their operations which are more functional to make theoretical studies in the soft set theory. We then define products of soft matrices and their properties. We finally construct a soft max-min decision making method which can be successfully applied to the problems that contain uncertainties.

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 ...

Background Li and Chen (Cognit Comput. 2018; 10:496-505) proposed the concept of the D-intuitionistic hesitant fuzzy set as well as proposed a method for comparing two D-intuitionistic fuzzy sets. Method Li and Chen have proposed the concept of the D-intuitionistic hesitant fuzzy set by introducing the degree of belief of the decision maker regarding the opinion of an expert in the existing definition of an intuitionistic hesitant fuzzy set. Results In future, other researchers may use Li and Chen's comparing method in their research work. However, after a deep study, it is observed that Li and Chen's comparing method fails to differentiate two distinct D-intuitionistic fuzzy sets. Conclusion It is inappropriate to use Li and Chen's comparing method.

Garg and Arora (2018) pointed out that it is not appropriate to use the existing intuitionistic fuzzy soft (IFS) aggregations operators (Arora and Garg, 2018a,b), proposed by themselves, as these aggregation operators gives undesirable results under some circumstances. To resolve the flaws of these aggregation operators, Garg and Arora (2018) proposed the improved operational laws of IFS numbers and hence, proposed a new IFS aggregation operator (named as Scaled prioritized intuitionistic fuzzy soft interaction (SPIFSI) aggregation operator). Garg and Arora (2018) also proposed a SPIFSI aggregation operator based intuitionistic fuzzy soft multi criteria decision making (IFSMCDM) approach for solving IFSMCDM problems (Multi criteria decision making problems in which the rating value of each alternative over each criterion is represented by an IFS set). Although, Garg and Arora (2018) have claimed that their proposed SPIFSI aggregation operator is valid as it satisfies the idempotency, boundedness and monotonicity properties. But, in actual case, for the SPIFSI aggregation operator, proposed by Garg and Kumar (2018), the monotonicity property is not satisfying. Therefore, the SPIFSI aggregation operator, proposed by Garg and Arora (2018), and hence, the SPIFSI aggregation operator based IFSMCDM approach, are not valid. Since, in future, other researchers may use the SPIFSI aggregation operator in their research work. Also, the researchers may use the SPIFSI aggregation operator based IFSMCDM approach for solving real life IFSMCDM problems. Therefore, the aim of this note is to make the researchers aware about the discrepancies of the SPIFSI aggregation operator as well as the SPIFSI aggregation operator based IFMCDM approach. Furthermore, to make the researchers aware that improved operational laws of IFS numbers, proposed by Garg and Arora (2018), are also not valid.

In this Paper Multi-objective Intuitionistic Fuzzy Non-linear Programming Problem has been solved through goal programming approach. Solving non-linear programming problem straightaway is quite difficult. So, the Multi-objective Intuitionistic Fuzzy Non-linear Programming Problem is transformed into Multi-objective Intuitionistic Fuzzy Linear Programming Problem by the use of Taylor Polynomial Series. Intuitionistic fuzzy goal programming approach is discussed by forming suitable membership and nonmembership function in which the aspiration level and the tolerance levels are fixed by the decision maker or by finding the best and worst solution of each objective function. Using the membership and non-membership function of each objective, the given problem was formulated and the solutions are found by various approaches and the obtained solutions are identical. Numerical example will illustrate the efficiency of the proposed approach.

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.

− 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 wellknown noise-removal filters. Finally, we discuss the need for further research.

In this paper, the definition of intuitionistic fuzzy parameterised fuzzy soft set (ifpfs-sets) is introduced with their properties. Two operations on ifpfs-set, namely union and intersection are introduced. Also, some examples for these operations are given. The definition of ifpfsaggregation operator which forms ifpfs-decision making method is introduced.

The distance and similarity measures are two interrelated depictions of the patterns which signify the categorization between the Atanassov intuitionistic fuzzy sets (AIFSs) by evaluating the degree of belongingness. In this work, we propose a new similarity measure, termed as hybrid similarity measure, by the combination of intuitionistic fuzzy bounded variation (IFBV) and intuitionistic fuzzy metric based measures. The concept of IFBV which is a technique to approximate arclength of an intuitionistic fuzzy-valued function (IFVF) is also introduced here. The IFVF over an AIFS is geometrically evolved through the generalization of the p-summable IFBV, that is, connecting all the elements of AIFS lie on the structure of IFBV corresponding to power p. The proposed measure overcomes the shortcomings of intuitionistic fuzzy metric based similarity measures by incorporating more flexibility into it. The hybrid similarity measure has been successfully implemented and applied on the several real-world applications in the field of pattern recognition as well as clustering. Further, a detailed comparison of results has been shown against the other existing similarity measures to demonstrate the superiority and validity of the proposed hybrid similarity measure.

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 m...

This paper aims to extend the hesitant fuzzy soft sets to hesitant intuitionistic fuzzy soft sets by merging the concept of hesitant intuitionistic fuzzy sets and soft sets. The authors define some operations on hesitant intuitionistic fuzzy sets, such as complement, union and intersection, and obtain related properties. The similar operations are defined on hesitant intuitionistic fuzzy soft sets, and also some properties such as assosiative and De Morgan's laws are obtained.

This paper aims to extend the hesitant fuzzy soft sets to hesitant intuitionistic fuzzy soft sets by merging the concept of hesitant intuitionistic fuzzy sets and soft sets. The authors define some operations on hesitant intuitionistic fuzzy sets, such as complement, union and intersection, and obtain related properties. The similar operations are defined on hesitant intuitionistic fuzzy soft sets, and also some properties such as assosiative and De Morgan's laws are obtained.

Introduced is a new algorithm for the classification of numerical data using the theory of fuzzy soft set, named Fuzzy Soft Set Classifier (FSSC). The algorithm uses the fuzzy approach in the pre-processing stage to obtain features, and similarity concept in the process of classification. It can be applied not only to binary-valued datasets, but also be able to classify the data that consists of real numbers. Comparison tests on seven datasets from UCI Machine Learning Repository have been carried out. It is shown that the proposed algorithm provides better accuracy and higher accuracy as compared to the baseline algorithm using soft set theory.

Soft matrices was firstly defined by Çağman and Enginoğlu [3]. These are representations of soft sets, introduced by Molodtsov [1], for modelling vagueness and uncertainties inherent in the problems of engineering, physical science, biological science, economics, social science, medical science, etc. Çağman and Enginoğlu [3], presented a decision making method, called soft max-min decision making method, by using the concept of soft matrix. In this study, firstly, we define two new soft matrix operations and obtain some of their properties. Secondly, we construct a new decision making method by using soft matrices. The soft decision making we constructed in this study is more practical among the other decision making methods and can be successfully applied to many problems that contain uncertainties. Finally, two applications of decision making problems in which it is necessary to use these new soft matrix operations, are presented. Since this decision making method constructed on soft matrices, then it can be easily transferred to a computer.

Alcantud and Santos-García [2] revisit the soft set based decision making problem under incomplete information. Their solution relies on a classical Laplacian argument from probability theory. In view of the computational characteristics of such algorithm, we propose two related solutions that efficiently evaluate problems with many more incomplete data. A computational analysis assesses the performance of our algorithms and compares them with earlier solutions in the literature.

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.

In this study, we propose a classification method based on normalised Hamming pseudosimilarity of fuzzy parameterized fuzzy soft matrices (fpfs-matrices). We then compare the proposed method with Fuzzy Soft Set Classifier (FSSC), FussCyier, Fuzzy Soft Set Classification Using Hamming Distance (HDFSSC), and Fuzzy k-Nearest Neighbor (Fuzzy kNN) in terms of the performance criterions (accuracy, precision, recall, and F-measure) and running time by using four medical data sets in the UCI machine learning repository. The results show that the proposed method performs better than FSSC, FussCyier,

− 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 wellknown noise-removal filters. Finally, we discuss the need for further research.

In a general setting, decision makers can face the situation where different criteria apply for the different options among which they have to choose the best one. We call such options scenarios. In this paper we study criteria evaluation in a multi-criteria decision method for the handling of different scenarios. A novel intuitionistic fuzzy evaluation method based on index matrices is proposed. This approach permits to efficiently handle the indifference caused by the inapplicability of criteria in specific scenarios. An illustrative example is provided.

Soft multi-criteria decision-making, a developing area, is among the most prevalent problems handled by researchers. This study aims to introduce a soft decision-making method and apply it to rank the side effects of COVID-19 vaccines. Based on the literature, the present study features the advantages and disadvantages of previously observed multi-criteria decision-making (MCDM) methods are summarized. This paper achieves to utilize multisets simultaneously with the known soft decision-making methods. The primary concern hereof is to offer an insightful everydaylife example. Finally, the authors discuss the need for further research.

Nowadays, it appears essential to design automatic and efficacious classification algorithm for the musical instruments. Automatic classification of musical instruments is made by extracting relevant features from the audio samples, afterward classification algorithm is used (using these extracted features) to identify into which of a set of classes, the sound sample is possible to fit. The aim of this paper is to demonstrate the viability of soft set for audio signal classification. A dataset of 104 (single monophonic notes) pieces of Traditional Pakistani musical instruments were designed. Feature extraction is done using two feature sets namely perception based and mel-frequency cepstral coefficients (MFCCs). In a while, two different classification techniques are applied for classification task, which are soft set (comparison table) and fuzzy soft set (similarity measurement). Experimental results show that both classifiers can perform well on numerical data. However, soft set a...

Decision making is very important to deal with many complex problems in various sectors involving imprecise data and uncertainties. Generalized fuzzy soft matrix theory is a powerful tool for decision making. In this paper we defined some new types of generalized fuzzy soft matrices and gave a decision making method based on generalized fuzzy soft matrices.

This paper deals with a new notion called fuzzy $\alpha$-cut and its properties. A notion called localic frame is also introduced. Algebraic structures arising out of the family of fuzzy $\alpha$-cuts have been investigated. It will be seen that this family forms a localic frame. Some significance and usefulness of fuzzy $\alpha$-cuts are discussed.

In a general setting, decision makers can face the situation where different criteria apply for the different options among which they have to choose the best one. We call such options scenarios. In this paper we study criteria evaluation in a multi-criteria decision method for the handling of different scenarios. A novel intuitionistic fuzzy evaluation method based on index matrices is proposed. This approach permits to efficiently handle the indifference caused by the inapplicability of criteria in specific scenarios. An illustrative example is provided.

In this paper, we first define eight pseudo-metrics and eight pseudo-similarities based on these pseudo-metrics over fpfs-matrices. We then propose a new classification algorithm, i.e. Fuzzy Parameterized Fuzzy Soft Euclidean Classifier (FPFS-EC), based on Euclidean pseudo-similarity. After that, we compare FPFS-EC with Support Vector Machines (SVM), Fuzzy k-Nearest Neighbor (Fuzzy kNN), Fuzzy Soft Set Classifier (FSSC), FussCyier, Fuzzy Soft Set Classification Using Hamming Distance (HDFSSC), and Fuzzy kNN Based on the Bonferroni Mean (BM-Fuzzy kNN) in terms of the performance criteria - namely accuracy, precision, recall, macro F-score, and micro F-score - and running time by using 18 real-world datasets in the UCI machine learning repository. The results show that FPFS-EC performs better in the occurrence of the 13 of 18 datasets in question than SVM, Fuzzy kNN, FSSC, FussCyier, HDFSSC, and BM-Fuzzy kNN.

The uni-int decision-making method constructed by and-product/or-product was defined and applied to a decision-making problem by Cagman and Enginoglu. The method has a potential for applications in several areas such as machine learning and image processing. Recently, this method has been configured by Enginoglu and Memis via fuzzy parameterized fuzzy soft matrices (fpfs-matrices), faithfully to the original, because a more general form is needed for the method in the event that the parameters or objects have uncertainties. However, in the case that a large amount of data is processed, the method has a disadvantage regarding time and complexity. To deal with this problem and to be able to use this configured method denoted by CE10 effectively, we suggest two algorithms in this paper, i.e. EMO18a and EMO18o, and prove that CE10 constructed by and-product (CE10a) and constructed by or-product (CE10o) are special cases of EMO18a and EMO18o, respectively, if first rows of the fpfs-matri...

In the present communication, we introduce Pythagorean fuzzy soft matrix and its various possible types. Some binary operations and various properties over the matrices are also being defined with their proof of validity. Further, the Pythagorean fuzzy soft matrices have been taken into account for proposing a new algorithm for decision making by using choice matrix and weighted choice matrix. In addition to this, an algorithm for medical diagnosis problem by making use of score matrix and utility matrix has also been proposed. Numerical examples for each of the applications have been successfully illustrated. A comparative analysis with other existing methods has also been carried out.

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.

This paper is being carried out to discuss Intuitionistic Fuzzy Soft Matrices and their operations have been described employing decisive issues by using Score Function of Intuitionistic Fuzzy soft matrices resulting in the efficiency of Intuitionistic Matrices over fuzzy matrices. Finally at the end we have presented a case study for the best selection of laptop.

In 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.

Being a follow-up study, this paper configures soft decision-making (SDM) methods (2017-2019), having been constructed with soft sets, soft matrices, and their fuzzy hybrid versions, to operate them in fuzzy parameterized fuzzy soft (fpfs) matrices space faithfully to the original. It then analyses the decision-making performances of the configured methods herein by using five test cases. Afterwards, it applies the methods, producing valid ranking order according to all the test cases, to the ranking of seven known noise-removal filters. This paper completes the configurations that allow the available methods (1999-2019) to operate in the fpfs-matrices space. Finally, the need for further research studies is discussed.

This paper is being carried out to discuss Intuitionistic Fuzzy Soft Matrices and their operations have been described employing decisive issues by using Score Function of Intuitionistic Fuzzy soft matrices resulting in the efficiency of Intuitionistic Matrices over fuzzy matrices. Finally at the end we have presented a case study for the best selection of laptop.

Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) is a new and useful mathematical tool proposed to model uncertainties. In this study, to improve the modelling capability of ifpifs-matrices, we define algebraic sum and algebraic product operations on this concept and investigate some of their basic properties. Moreover, we propose two soft decision-making methods via these operations. Afterwards, we apply these two soft decision-making methods, i.e. AE20/1 and AE20/2, to a performance-based value assignment (PVA) problem for state-of-the-art filters used in image denoising. The results show that the proposed methods herein efficaciously order the filters in terms of performance. Besides, we compare the proposed methods with EA20, which was the only soft decision-making method in the ifpifs-matrices space. The comparison reveals that AE20/1 and AE20/2 produce more acceptable ranking orders than EA20 does. Finally, we discuss the proposed methods and the need for further research.

Recently, the criteria-weighted fuzzy soft max-min decision-making (WFSMmDM) method provided in [Razak, S. A., Mohamad, D., A decision making method using fuzzy soft sets, Malaysian Journal of Fundamental and Applied Sciences, 2013, 9(2), 99-104] has been configured to operate in the fuzzy parameterized fuzzy soft matrices (fpfs-matrices) space by Enginoğlu and Memiş [A configuration of some soft decision-making algorithms via fpfs-matrices, Cumhuriyet Science Journal, 2018, 39(4), 871-881] faithfully to the original. Even though this configured method, which is denoted by RM13 and constructed by and-product/or-product (RM13a/RM13o), is useful in soft decision-making, it is of great importance to improve the method in terms of running time and complexity when processing a large number of data. In this study, to improve WFSMmDM, we propose two algorithms, denoted by EM20a and EM20o. Furthermore, we prove that EM20a is equivalent to RM13a. Thereafter, we compare the running time of these algorithms. The results show that EM20a and EM20o outperform RM13a and RM13o, respectively, in any number of data. We then apply EM20o to the problem of performance-based value assignment concerning seven filters used in image denoising. Besides, we compare the proposed two methods' performance ranking with that of eight state-of-art soft decision-making methods. Finally, we provide the conclusive remarks and some suggestions for further research.

TOPSIS, developed in 1981 by Hwang and Yoon, is one of the known multi-criteria decision-making (MCDM) methods. In 2015, the group decision-making method based on TOPSIS under fuzzy soft environment was defined and applied to a decision-making problem by Eraslan and Karaaslan. Recently, this method has been configured by Enginoğlu and Memiş via fuzzy parameterized fuzzy soft matrices (fpfs-matrices), faithfully to the original, because a more general form is needed for the method in the event that the parameters have uncertainties. However, the configured method has two drawbacks which affect its running time and the ranking order negatively. We, in this study, improve this method by removing the disadvantages. We then compare the running time of these algorithms. The results show that the new method outperforms it, in particular, a large number of data come into question. For example, the proposed method offers up to 97.7672% of time advantage for ten objects and 9000 parameters. Afterwards, we apply the new method to a performance-based value assignment to seven state-of-art filters used in image denoising, so that we can order them in terms of performance. Finally, we discuss the need for further research.