Behaviour distances to measure the resemblance of two states in a (nondeterministic) fuzzy transition system have been proposed recently in the literature. Such a distance, defined as a pseudo-ultrametric over the state space of the model, provides a quantitative analogue of bisimilarity. In this paper, we focus on the problem of computing these distances. We first extend the definition of the ...

In this paper, the minimum spanning tree problem is investigated on the graph with fuzzy edge weights. The notion of fuzzy α-minimum spanning tree is presented based on the credibility measure, and then the solutions of the fuzzy α-minimum spanning tree problem are discussed under different assumptions. First, we respectively assume that all the edge weights are triangular fuzzy numbers and tra...

The aim of this paper is to present algebraic method which is called Wu's method to solving fuzzy complex systems of linear equations. Wu's method is used as a solution procedure for solving the crisp polynomial equations system. This algorithm leads to solving characteristic sets that are amenable to easy solution. To illustrate the easy application of the proposed method, numerical examples a...

The problem of static output feedback control design for continuous-time TakagiSugeno (T–S) fuzzy systems is addressed in this paper. The membership functions are modeled in a space defined by the Cartesian product of simplexes, called multi-simplex, and are allowed to vary arbitrarily (i.e. no bounds on the time-derivative of the membership functions are assumed). The static output feedback fu...

In this paper, a new architecture of fuzzy neural network (FNN) model is proposed in order to find a fuzzy solution of a fully fuzzy polynomial (FFP) with degree one. The proposed FNN is a two layer feed-forward neural network, that corresponds connection weight to output layer. The proposed architecture of artificial neural network can get a fuzzy input signal and calculates its corresponding ...

Since fuzzy logic was introduced by Lotfi Zadeh in 1965 (41), it has had many successful applications in all fields that one can imagine. The reason is that many real-world applications problems are involved the systems in which at least some parameters are represented by fuzzy numbers rather than crisp numbers and linguistic labels such as small and large are also associated with the fuzzy set...

In the last decades, more than a hundred families of fuzzy implication functions have been proposed. These are generated by adequately combining other logical connectives or univariate functions. However, no attention has given to final expression function, crucial feature for any application. this paper, polynomial implications introduced as those whose is two variables. Polynomials present ad...