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In the case of widely-uncertain non-linear system control design, it was very difficult to design a single controller to overcome control design specifications in all of its dynamical characteristics uncertainties. To resolve these problems, a new design method of robust fuzzy control proposed. The solution offered was by creating multiple soft-switching with Takagi-Sugeno fuzzy model for optimal solution control at all operating points that generate uncertainties. Optimal solution control at each operating point was calculated using genetic algorithm. A case study of engine torque control of spark ignition engine model was used to prove this new method of robust fuzzy control design. From the simulation results, it can be concluded that the controller operates very well for a wide uncertainty.

The paper presents a novel type of fuzzy sets, called time-Varying Fuzzy Sets (VFS). These fuzzy sets are based on the Gaussian membership functions, they are depended on the error and they are characterized by the displacement of the kernels to both right and left side of the universe of discourse, the two extremes kernels of the universe are fixed for all time. In this work we focus only on the midpoint movement of the universe, all points of supports (kernels) are shifted by the same distance and in the same direction excepted the two extremes points of supports are always fixed for all computation time. To show the effectiveness of this approach we used these VFS to develop a PDC (Parallel Distributed Compensation) fuzzy controller for a nonlinear and certain system in continuous time described by the T-S fuzzy model, the parameters of the functions defining the midpoint movements are optimized by a PSO (Particle Swarm Optimization) approach.

Medical Image segmentation is to partition the image into a set of regions that are visually obvious and consistent with respect to some properties such as gray level, texture or color. Brain tumor classification is an imperative and difficult task in cancer radiotherapy. The objective of this research is to examine the use of pattern classification methods for distinguishing different types of brain tumors, such as primary gliomas from metastases, and also for grading of gliomas. Manual classification results look better because it involves human intelligence but the disadvantage is that the results may differ from one person to another person and takes long time. MRI image based automatic diagnosis method is used for early diagnosis and treatment of brain tumors. In this article, fully automatic, multi class brain tumor classification approach using hybrid structure descriptor and Fuzzy logic based Pair of RBF kernel support vector machine is developed. The method was applied to a population of 102 brain tumors histologically diagnosed as Meningioma (115), Metastasis (120), Gliomas grade II (65) and Gliomas grade II (70). Classification accuracy of proposed system in class 1(Meningioma) type tumor is 98.6%, class 2 (Metastasis) is 99.29%, class 3(Gliomas grade II) is 97.87% and class 4(Gliomas grade III) is 98.6%.

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.

We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabilistic and approach uniform convergence spaces as examples. We show that the resulting category $sLMN$-$UCTS$ is topological, well-fibred and Cartesian closed. We furthermore define stratified $LMN$-uniform tower spaces and show that the category of these spaces is isomorphic to the subcategory of stratified $LMN$-principal uniform convergence tower spaces. Finally we study the underlying stratified $LMN$-convergence tower spaces.

Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander {v S}ostak in cite{BS}. In this paper, the authors generalize the structure of diuniformity in ditopological texture spaces defined in cite{OB} to the graded ditopological texture spaces and investigate graded ditopologies generated by graded diuniformities. The autors also compare the properties of diuniformities and graded diuniformities.

In this paper, we define the notion of (dual) multi-fuzzy normedspaces and describe some properties of them. We then investigate Ulam-Hyers stability of Jensen's functional equation for mappings from linear spaces into multi-fuzzy normed spaces. We establish an asymptotic behavior of the Jensen equation in the framework of multi-fuzzy normed spaces.

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is established. In details, we show that the category of strong $L$-topological spaces is concretely isomorphic to that of strong $L$-topological $top$-convergence spaces categorically and bireflectively embedded in that of $top$-convergence spaces.

In this paper, the notion of closure operators of matroids is generalized to fuzzy setting which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroids are given.

In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework.

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known comparable results in the literature. Furthermore, several illustrative examples are given to support the usability of our obtained results.

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