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A fuzzy observer based scheme for synchronizing two hyperchaoticoscillators via a scalar transmitted signal for cryptographic application isproposed. The Takagi-Sugeno fuzzy model exactly represents chaotic systems.Based on the general fuzzy model, the fuzzy observer of a chaotic system isdesigned on the basis of the n-shift multiple state based key encryption algorithm.The scalar transmitted signal is designed in such a way that the hyperchaoticcarrier masks the encrypted signal, which in turn hides the message signal.Simulation results show that the proposed scheme gives a better performanceeven when a small additive stochastic noise is present in the channel.

An asymptotically stable direct adaptive fuzzy PI sliding modecontroller is proposed for a class of nonlinear uncertain systems. In contrast toother existing approaches of handling disturbances, the proposed approachdoes not require this bound to be known, only requiring that it exists.Moreover, a PI control structure is used to attenuate chattering. The approachis applied to stabilize an open-loop unstable nonlinear system as well asthe Duffing forced-oscillation chaotic nonlinear system amid significantdisturbances. Analysis of simulations reveals the effectiveness of the proposedmethod in terms of a significant reduction in chattering while maintainingasymptotic convergence.

The purpose of this paper is to construct the concept of semi$theta$-compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$-compactness and locally semi -compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.

In this note the notion of interval-valued fuzzy B-algebras (briefly,i-v fuzzy B-algebras), the level and strong level B-subalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and B-subalgebras. The images and inverse images ofi-v fuzzy B-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy B-subalgebra becomes i-v fuzzy B-algebras arestudied.

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a group homomorphism.

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