In this paper, we study the computational complexity of solution concepts in the context of coalitional games. Firstly, we distinguish two different kinds of core, the undominated core and excess core, and investigate the difference and relationship between them. Secondly, we thoroughly investigate the computational complexity of undominated core and three farsighted solution concepts—farsighte...

A study is presented on solutions of the Yule-Walker equations for singular AR processes that are stationary outputs of a given AR system. If the Yule-Walker equations admit more than one solution and the order of the AR system is no less than two, the solution set includes solutions which define unstable AR systems. The solution set also includes one solution, the minimal norm solution, which ...

When the coefficients of a linear system are known with interval uncertainty, instead of a single solution, we have the whole set of possible solutions – known as the united set. It is known that in general, computing this united set is NP-hard. There exist several proofs of this NPhardness; all known proofs use examples with intervals of different width – corresponding to different accuracy in...

The paper relates set-valued Lyapunov functions to pointwise asymptotic stability in systems described by a difference inclusion. Pointwise asymptotic stability of a set is a property which requires that each point of the set be Lyapunov stable and that every solution to the inclusion, from a neighborhood of the set, be convergent and have the limit in the set. Weak set-valued Lyapunov function...

This paper presents a study on the performance of the Hopfield neural network algorithm for the graph path search problem. Specifically, performance of the Hopfield network is studied from the dynamic systems stability perspective. Simulations of the time behavior of the neural network is augmented with exhaustive stability analysis of the equilibrium points of the network dynamics. The goal is...

The paper deals with a solution of a fuzzy interval system of linear equations, i.e. a system in which fuzzy intervals (numbers) appear instead of crisp numbers. We obtain general results and then use them for finding the united solution set in the case when all fuzzy interval occurring in the system have the trapezoidal shape.

In this paper, we introduce a concept of a farsighted stable set for a partition function game and interpret the union of all farsighted stable sets as the core of the game, to be called the strongcore, which reduces to the traditional core if the worth of every coalition is independent of the partition to which it belongs and the game is adequately represented by a characteristic function. We ...

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...