Soft set theory and uni–int decision making

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

Soft matrix theory and its decision making

The first aim of this study is to define soft topological spaces and to define soft continuity of soft mappings. Second is to introduce soft product topology and study properties of soft projection mappings. Third is to define soft compactness and generalize Alexander subbase theorem and Tychonoff theorem to the soft topological spaces.

Some notes on soft topological spaces

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we prove that certain De Morgan's law hold in soft set theory with respect to different operations on soft sets. Then, we discuss the basic properties of operations on soft sets such as intersection, extended intersection, restricted union and restricted difference. Moreover, we illustrate their interconnections between each other. Also we define the notion of restricted symmetric difference of soft sets and investigate its properties. The main purpose of this paper is to extend the theoretical aspect of operations on soft sets.

On operations of soft sets

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Two Dimensional Signal And Image Processing

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.

https://ijfs.usb.ac.ir/article_292_22928400ec0d727700fd251a4f63fa07.pdf

Fuzzy soft set theory and its applications

Different applied median filter in salt and pepper noise

We propose an Iterative Mean Filter (IMF) to eliminate the salt-and-pepper noise. IMF uses the mean of gray values of noise-free pixels in a fixed-size window. Unlike other nonlinear filters, IMF does not enlarge the window size. A large size reduces the accuracy of noise removal. Therefore, IMF only uses a window with a size of $3\times3$ . This feature is helpful for IMF to be able to more precisely evaluate a new gray value for the center pixel. To process high-density noise effectively, we propose an iterative procedure for IMF. In the experiments, we operationalize Peak Signal-to-Noise Ratio (PSNR), Visual Information Fidelity, Image Enhancement Factor, Structural Similarity (SSIM), and Multiscale Structure Similarity to assess image quality. Furthermore, we compare denoising results of IMF with ones of the other state-of-the-art methods. A comprehensive comparison of execution time is also provided. The qualitative results by PSNR and SSIM showed that IMF outperforms the other methods such as Based-on Pixel Density Filter (BPDF), Decision-Based Algorithm (DBA), Modified Decision-Based Untrimmed Median Filter (MDBUTMF), Noise Adaptive Fuzzy Switching Median Filter (NAFSMF), Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), Adaptive Type-2 Fuzzy Filter (FDS): for the IMAGESTEST dataset - BPDF (25.36/0.756), DBA (28.72/0.8426), MDBUTMF (25.93/0.8426), NAFSMF (29.32/0.8735), AWMF (32.25/0.9177), DAMF (31.65/0.9154), FDS (27.98/0.8338), and IMF (33.67/0.9252); and for the BSDS dataset - BPDF (24.95/0.7469), DBA (26.84/0.8061), MDBUTMF (26.25/0.7732), NAFSMF (27.26/0.8191), AWMF (28.89/0.8672), DAMF (29.11/0.8667), FDS (26.85/0.8095), and IMF (30.04/0.8753).

/pdf/an-iterative-mean-filter-for-image-denoising-31athaae9w.pdf

Serdar Enginoğlu

Papers

Soft set theory and uni–int decision making

Soft matrix theory and its decision making

Fuzzy soft set theory and its applications

Different applied median filter in salt and pepper noise

An Iterative Mean Filter for Image Denoising