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In this paper, we introduce some types of $(\in ,\in \vee q_{\delta }^k)$-fuzzy filters of BL-algebras by applying the $(\delta ,k)$-quasi-coincident relation. By using a level subset of a fuzzy set in a BL-algebra, we study some characterizations of these generalized fuzzy filters and investigate several properties of $(\in ,\in \vee q_{\delta }^k)$-fuzzy filters of BL-algebras. Further, we explore the relationships among $(\in ,\in \vee q_{\delta }^k)$-fuzzy filters and other types of $(\in ,\in \vee q_{\delta }^k)$-fuzzy filters and it is proved that every $(\in ,\in \vee q_{\delta }^k)$-fuzzy Boolean (implicative) filter is a $(\in ,\in \vee q_{\delta }^k)$-fuzzy positive implicative filter and $(\in ,\in \vee q_{\delta }^k)$-fuzzy fantastic filter, but the converse may not be true. Furthermore, we establish the conditions under which an $(\in ,\in \vee q_{\delta }^k)$-fuzzy positive implicative filter is an $(\in ,\in \vee q_{\delta }^k)$-fuzzy Boolean (implicative) filter.

Impulse noise is an image noise that degrades the quality of the image drastically. In this paper, k-means clustering has been incorporated with fuzzy-support vector machine (FSVM) classifier for classification of noisy and non-noisy pixels in removal of impulse noise from gray images. Here, local binary pattern (LBP) has been incorporated with previously used feature vector prediction error of the processing pixel, absolute difference between median value and processing pixel, median pixel, pixel under operation and mean value around the processing kernel. In this work, $k$-means clustering has been used for reducing the feature vector set, where features have been extracted from the images corrupted with 10%, 50%, and 90% impulse noise. If the pixel is depicted as noisy in testing phase, histogram adaptive fuzzy filter is processed over the noisy pixel under operation. It is seen that the proposed filter offers improved performance over some of the state-of-the-art filter in terms of different image quality measures likely PSNR, SSIM, MSE, FSIM, etc. It is observed that performance is increased by $\sim$2–5dB than baseline filters likely SVM fuzzy filter, and artificial neural network based adaptive sized mean filter (ANNASMF) especially at high density noise.

In this paper, the lattice operations and the adjoint pair on the fuzzy filters set on residuated lattices are defined, the conclusion that the fuzzy filters lattice defined as such is a distributive residuated lattice is obtained. An order-reversing involution on the fuzzy strong-prime filters sublattice is introduced. It is proved that the fuzzy strong-prime filters sublattice is a quasi-Boolean algebra.

A general and a comprehensive theory of fuzzy topological spaces on the basis of a fixed quadruple M = (L, ≤, ⊗, *), where (L, ≤), ⊗ and *, respectively, denote a complete lattice and binary operations on L satisfying some further axioms, was introduced by Höhle and Šostak. L-topological spaces, convergence structure of L-topological spaces and L-continuous functions form an important part of their work. The present paper continues the study in this area, and provides new results on the convergence structure of L-topological spaces and the continuity in L-topological spaces.

Based on the theory of falling shadows and fuzzy sets, the notion of falling fuzzy filters of MTL-algebras is introduced. The relations between fuzzy filters and falling fuzzy filters are provided.

The theory of filters and fuzzy filters in logical algebras play a vital role in reasoning mechanism in information sciences, computer sciences, theory of control, artificial intelligence and many other important fields. We introduce the concept of fuzzy sub positive implicative filters of residuated lattice and investigate the properties of it, and further characterize the fuzzy sub positive implicative filters by proposing the equivalent conditions that a fuzzy filters to be a fuzzy sub positive implicative filters.