Knowledge structure, knowledge granulation and knowledge distance in a knowledge base

AbstractOne of the strengths of rough set theory is the fact that an unknown target concept can be approximately characterized by existing knowledge structures in a knowledge base. Knowledge structures in knowledge bases have two categories: complete and incomplete. In this paper, through uniformly expressing these two kinds of knowledge structures, we first address four operators on a knowledge base, which are adequate for generating new knowledge structures through using known knowledge structures. Then, an axiom definition of knowledge granulation in knowledge bases is presented, under which some existing knowledge granulations become its special forms. Finally, we introduce the concept of a knowledge distance for calculating the difference between two knowledge structures in the same knowledge base. Noting that the knowledge distance satisfies the three properties of a distance space on all knowledge structures induced by a given universe. These results will be very helpful for knowledge discovery from knowledge bases and significant for establishing a framework of granular computing in knowledge bases

Computing Perfect Stationary Equilibria in Stochastic Games

The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games and formulate the notion of perfect stationary equilibrium (PeSE). To further promote its applications, we develop a differentiable homotopy method to compute such an equilibrium. We incorporate vanishing logarithmic barrier terms into the payoff functions, thereby constituting a logarithmic-barrier stochastic game. As a result of this barrier game, we attain a continuously differentiable homotopy system. To reduce the number of variables in the homotopy system, we eliminate the Bellman equations through a replacement of variables and derive an equivalent system. We use the equivalent system to establish the existence of a smooth path, which starts from an arbitrary total mixed strategy profile and ends at a PeSE. Extensive numerical experiments further affirm the effectiveness and efficiency of the method

An Interior-Point Path-Following Method to Compute Stationary Equilibria in Stochastic Games

Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following method (IPM), which remedies a number of issues with the existing method called stochastic linear tracing procedure (SLTP). The homotopy system of IPM is derived from the optimality conditions of an artificial barrier game, whose objective function is a combination of the original payoff function and a logarithmic term. Unlike SLTP, the starting stationary strategy profile can be arbitrarily chosen and IPM does not need switching between different systems of equations. The use of a perturbation term makes IPM applicable to all stochastic games, whereas SLTP only works for a generic stochastic game. A transformation of variables reduces the number of equations and variables of by roughly one half. Numerical results show that our method is more than three times as efficient as SLTP

Nonmonotone second-order Wolfe’s line search method for unconstrained optimization problems

AbstractIn this paper, we present a new algorithm using the nonmonotone second-order Wolfe’s line search. By using the negative curvature information from the Hessian, we prove that the generated sequence converges to the stationary points that satisfy the second-order optimality conditions. We also report numerical results which show the efficiency and robustness of the proposed method

Stabilization computation for a kind of uncertain switched systems using non-fragile sliding mode observer method

A non-fragile sliding mode control problem will be investigated in this article. The problem focuses on a kind of uncertain switched singular time-delay systems in which the state is not available. First, according to the designed non-fragile observer, we will construct an integral-type sliding surface, in which the estimated unmeasured state is used. Second, we synthesize a sliding mode controller. The reachability of the specified sliding surface could be proved by this sliding mode controller in a finite time. Moreover, linear matrix inequality conditions will be developed to check the exponential admissibility of the sliding mode dynamics. After that, the gain matrices designed will be given along with it. Finally, some numerical result will be provided, and the result can be used to prove the effectiveness of the method