Iranian journal of fuzzy systems
Volume:3 Issue: 2, 2007

In this paper we present, for the first time, complete proofs of the facts that have already been announced in [A. Daneshgar, A. Hashemi, A general model for I/O system theory, Proc. AIMC31, 2000, 292–299]. Our approach here is to focus on the aspects related to fuzzy set theory and we leave other connections to other mathematical disciplines such as quantum groups, categorical logic, homological algebra and measure theory to appear elsewhere. The main contribution is to introduce a general framework based on enriched category theory that covers the theory of translation invariant systems as a special case, as well as the construction of Haar fraction on a locally compact group.

A fuzzy observer based scheme for synchronizing two hyperchaotic oscillators via a scalar transmitted signal for cryptographic application is proposed. The Takagi-Sugeno fuzzy model exactly represents chaotic systems. Based on the general fuzzy model, the fuzzy observer of a chaotic system is designed 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 hyperchaotic carrier masks the encrypted signal, which in turn hides the message signal. Simulation results show that the proposed scheme gives a better performance even when a small additive stochastic noise is present in the channel.

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

The purpose of this paper is to construct the concept of semi \teta-compactness in intuitionistic fuzzy topological spaces. We give some characterizations of semi \teta-compactness and locally semi \teta-compactness. Also, we compare these concepts with some other types of compactness in intuitionistic fuzzy 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 relationship between these notions and B-subalgebras. The images and inverse images of i-v fuzzy B-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy B-subalgebra becomes i-v fuzzy B-algebras are studied.

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