In this study, we propose a new method, i.e. Adaptive Riesz Mean Filter (ARmF), by operationalizing pixel similarity for salt-and-pepper noise (SPN) removal.

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.

Latterly, the fuzzy soft max-min decision-making method denoted by FSMmDM and provided in [Çağman, N., Enginoǧlu, 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 decisionmaking, 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.

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 Machine (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.

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