Consider the homogeneous equation u ′(t) = l(u)(t) for a.e. t ∈ [a, b] where l : C([a, b];R) → L([a, b];R) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvabili...

Recently, the local stability and local stabilization problems have been investigated by several authors for nonlinear systems described by Takagi–Sugeno (T–S) fuzzy systems. In this paper, we study the local stabilization problem for discrete-time T–S fuzzy systems with magnitudeand energy-bounded disturbances. The control design problem is cast as a linear matrix inequality (LMI) optimization...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

In this paper, we study a pair of fuzzy primal–dual linear programming problems and calculate duality results using an aspiration level approach. We use an exponential membership function, which is in contrast to the earlier works that relied on a linear membership function. As the fuzzy environment causes a duality gap, we investigate how choosing the exponential membership function impacts th...

A new method namely, bound and decomposition method is proposed to find an optimal fuzzy solution for fully fuzzy linear programming (FFLP) problems. In the proposed method, the given FFLP problem is decomposed into three crisp linear programming (CLP) problems with bounded variables constraints, the three CLP problems are solved separately and by using its optimal solutions, the fuzzy optimal ...

In this paper a fuzzy tracking control is proposed for non linear dynamic system with bounded external disturbances and admissible uncertainties described as TakagiSugeno (T-S) fuzzy model. Using a tracking reference model, a stability condition scheme based on an augmented system with a guaranteed H∞ performance is proposed to obtain tracking performances. The main result of this paper is to p...

In the cumulative prospect theory (CPT) the preference (utility functional) is represented by the difference of two Choquet integrals. We investigate representations of the corresponding functional by two fuzzy integrals, specially the difference representations of the asymmetric Choquet integral with respect to a signed fuzzy measure with bounded chain variation. We discuss non-monotone, real ...