### Chair: Vassil Alexandrov

 62 Modification Of Interval Arithmetic For Modelling And Solving Uncertainly Defined Problems By Interval Parametric Integral Equations System [abstract]Abstract: In this paper we present the concept of modeling and solving uncertainly defined boundary value problems described by 2D Laplace's equation. We define uncertainty of input data (shape of boundary and boundary conditions) using interval numbers. Uncertainty can be considered separately for selected or simultaneously for all input data. We propose interval parametric integral equations system (IPIES) to solve so-define problems. We obtain IPIES in result of PIES modification, which was previously proposed for precisely (exactly) defined problems. For this purpose we have to include uncertainly defined input data into mathematical formalism of PIES. We use pseudo-spectral method for numerical solving of IPIES and propose modification of directed interval arithmetic to obtain interval solutions. We present the strategy on examples of potential problems. To verify correctness of the method, we compare obtained interval solutions with analytical ones. For this purpose, we obtain interval analytical solutions using classical and directed interval arithmetic. Eugeniusz Zieniuk, Marta Kapturczak and Andrzej Kużelewski 276 A Hybrid Heuristic for the Probabilistic Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints [abstract]Abstract: The Probabilistic Capacitated Vehicle Routing Problem (PCVRP) is a generalization of the classical Capacitated Vehicle Rout- ing Problem (CVRP). The main difference is the stochastic presence of the customers, that is, the number of them to be visited each time is a random variable, where each customer associates with a given probability of presence. We consider a special case of the PCVRP, in which a eet of identical vehicles must serve customers, each with a given demand consisting in a set of rectangular items. The vehicles have a two-dimensional loading surface and a maximum capacity. The resolution of problem consists in finding an a priori route visiting all customers which minimizes the expected length over all possibilities. We propose a hybrid heuristic, based on a branch-and-bound algorithm, for the resolution of the problem. The effectiveness of the approach is shown by means of computational results. Soumaya Sassi Mahfoudh and Monia Bellalouna 37 A human-inspired model to represent uncertain knowledge in the Semantic Web [abstract]Abstract: One of the most evident and well-known limitations of the Semantic Web technology is its lack of capability to deal with uncertain knowledge. As uncertainty is often part of the knowledge itself or can be inducted by external factors, such a limitation may be a serious barrier for some practical applications. A number of approaches have been proposed to extend the capabilities in terms of uncertainty representation; some of them are just theoretical or not compatible with the current semantic technology; others focus exclusively on data spaces in which uncertainty is or can be quantified. Human-inspired models have been adopted in the context of different disciplines and domains (e.g. robotics and human-machine interaction) and could be a novel, still largely unexplored, pathway to represent uncertain knowledge in the Semantic Web. Human-inspired models are expected to address uncertainties in a way similar to the human one. Within this paper, we (i) briefly point out the limitations of the Semantic Web technology in terms of uncertainty representation, (ii) discuss the potentialities of human-inspired solutions to represent uncertain knowledge in the Semantic Web, (iii) present a human-inspired model and (iv) a reference architecture for implementations in the context of the legacy technology. Salvatore Flavio Pileggi 392 Novel Monte Carlo Algorithm for Solving Singular Linear Systems [abstract]Abstract: A new Monte Carlo algorithm for solving singular linear sys- tems of equations is introduced. In fact, we consider the convergence of resolvent operator R and we construct an algorithm based on the map- ping of the spectral parameter . The approach is applied to systems with singular matrices. For such matrices we show that fairly high accuracy can be obtained. Behrouz Fathi Vajargah, Vassil Alexandrov, Samaneh Javadi and Ali Hadian