Iranian journal of fuzzy systems
Volume:2 Issue: 1, 2005

In previous studies we first concentrated on utilizing crisp simulation to produce discrete event fuzzy systems simulations. Then we extended this research to the simulation of continuous fuzzy systems models. In this paper we continue our study of continuous fuzzy systems using crisp continuous simulation. Consider a crisp continuous system whose evolution depends on differential equations. Such a system contains a number of parameters that must be estimated. Usually point estimates are computed and used in the model. However these point estimates typically have uncertainty associated with them. We propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters. Fuzzy parameters convert the crisp system into a fuzzy system. Trajectories describing the behavior of the system become fuzzy curves. We will employ crisp continuous simulation to estimate these fuzzy trajectories. Three examples are discussed.

The concept of free modules, projective modules, injective modules and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper we give an alternate definition for projective L-modules. We prove that every free L-module is a projective L-module. Also we prove that if $\mu\in L(P)$ is a projective L-module, and if $0\rightarrow\eta\rightarrow\vartheta\rightarrow\mu\rightarrow 0$ is a short exact sequence of L-modules then $\nu\otimes\mu>\vartheta$. Further it is proved that if $\mu\in L(P)$ is a projective L-module then $\mu$ is a fuzzy direct summand of a free L-module.

In this paper, a certain new connectedness of L-fuzzy subsets in L-topological spaces is introduced and studied by means of preclosed sets. It preserves some fundamental properties of connected set in general topology. Especially the famous K. Fan’s theorem holds.

In this note first we shall redefine the notion of a fuzzy hypervector space (see [1]) and then we introduce some further concepts of fuzzy hypervector spaces, such as convex fuzzy sets and balance fuzzy sets in fuzzy hypervector spaces over valued fields. Finally, we briefly discuss on convex (balanced) hull of a given fuzzy set of a hypervector space.

In this note by considering a complete lattice L, we define the notion of an L-Fuzzy hyperrelation on a given non-empty set X. Then we define the concepts of (POM)_L-Fuzzy graph, hypergraph and subhypergroup and then obtain some related results. In particular we construct the categories of the above mentioned notions, and then give a (full and faithful) functor form the category of (POM)_L-Fuzzy subhypergroups ((POM)_L-Fuzzy graphs) into the category of (POM)_L-Fuzzy hypergraphs. Also we show that for each finite objects in the category of (POM)_L-Fuzzy graphs, the coproduct exists, and under a suitable condition the product exists too.

This paper presents the basic concepts of stability in the fuzzy linguistic models. The authors has proposed some criterion for BIBO stability analysis of fuzzy linguistic models associated to linear time invariant systems [1]-[4]. This paper presents the basic concepts of stability in the general nonlinear and linear systems. This stability analysis method is verified using a benchmark system analysis.