Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications

We investigate the structure of acyclic binary relations from different points of view. On the one hand, given a nonempty set we study real-valued bivariate maps that satisfy suitable functional equations, in a way that their associated binary relation is acyclic. On the other hand, we consider acyclic directed graphs as well as their representation by means of incidence matrices. Acyclic binary relations can be extended to the asymmetric part of a linear order, so that, in particular, any directed acyclic graph has a topological sorting.

[1]  J. Casillas,et al.  A Multiobjective Genetic Fuzzy System with Imprecise Probability Fitness for Vague Data , 2006, 2006 International Symposium on Evolving Fuzzy Systems.

[2]  Anna Stachowiak,et al.  Improving medical decisions under incomplete data using interval-valued fuzzy aggregation , 2015, IFSA-EUSFLAT.

[3]  Talbi El-Ghazali,et al.  Optimization algorithms for multi-objective problems with fuzzy data , 2014, 2014 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM).

[4]  David Ginsbourger,et al.  Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations , 2015, Eur. J. Oper. Res..

[5]  Giovanni Petrone Optimization under Uncertainty: theory, algorithms and industrial applications , 2011 .

[6]  G. P. Dimuro,et al.  Interval-valued implications and interval-valued strong equality index with admissible orders , 2017, Int. J. Approx. Reason..

[7]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

[8]  El-Ghazali Talbi,et al.  New Pareto Approach for Ranking Triangular Fuzzy Numbers , 2014, IPMU.

[9]  Kalyanmoy Deb,et al.  Searching for Robust Pareto-Optimal Solutions in Multi-objective Optimization , 2005, EMO.

[10]  Arnaud Liefooghe Métaheuristiques pour l'optimisation multiobjectif: Approches coopératives, prise en compte de l'incertitude et application en logistique. (Metaheuristics for multiobjective optimisation: Cooperative approaches, uncertainty handling and application in logistics) , 2009 .

[11]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[12]  Mario Köppen,et al.  Fuzzy-Pareto-Dominance and its Application in Evolutionary Multi-objective Optimization , 2005, EMO.

[13]  Jürgen Teich,et al.  Pareto-Front Exploration with Uncertain Objectives , 2001, EMO.

[14]  Nikolaos V. Sahinidis,et al.  Optimization under uncertainty: state-of-the-art and opportunities , 2004, Comput. Chem. Eng..

[15]  Maciej Wygralak,et al.  Dealing with Uncertainty in Ovarian Tumor Diagnosis , 2013 .

[16]  Gaoping Wang,et al.  Fuzzy-Dominance and Its Application in Evolutionary Many Objective Optimization , 2007, 2007 International Conference on Computational Intelligence and Security Workshops (CISW 2007).

[17]  Arnaud Liefooghe,et al.  Indicator-based approaches for multiobjective optimization in uncertain environments: An application to multiobjective scheduling with stochastic processing times , 2010 .

[18]  Ricardo C. Silva,et al.  Definition of Fuzzy Pareto-Optimality by Using Possibility Theory , 2009, IFSA/EUSFLAT Conf..

[19]  Carlos Henggeler Antunes,et al.  Robustness Analysis in Multi-Objective Optimization Using a Degree of Robustness Concept , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[20]  Jian Xu,et al.  Vehicle routing problem with time windows and fuzzy demands: an approach based on the possibility theory , 2009, Int. J. Adv. Oper. Manag..

[21]  Philipp Limbourg,et al.  An optimization algorithm for imprecise multi-objective problem functions , 2005, 2005 IEEE Congress on Evolutionary Computation.

[22]  Urmila M. Diwekar Optimization Under Uncertainty , 2008 .

[23]  Eckart Zitzler,et al.  Handling Uncertainty in Indicator-Based Multiobjective Optimization , 2006 .

[24]  El-Ghazali Talbi,et al.  Metaheuristics - From Design to Implementation , 2009 .

[25]  Twan Basten,et al.  Pareto Analysis with Uncertainty , 2011, 2011 IFIP 9th International Conference on Embedded and Ubiquitous Computing.

[26]  Christian Haubelt,et al.  Accelerating design space exploration using pareto-front arithmetics , 2003, ASP-DAC '03.

[27]  Eulalia Szmidt,et al.  Atanassov's Intuitionistic Fuzzy Sets in Classification of Imbalanced and Overlapping Classes , 2008, Intelligent Techniques and Tools for Novel System Architectures.

[28]  Anna Stachowiak,et al.  Solving the problem of incomplete data in medical diagnosis via interval modeling , 2016, Appl. Soft Comput..

[29]  M. P. Saka,et al.  Recent Developments in Metaheuristic Algorithms: A Review , 2012 .

[30]  Kay Chen Tan,et al.  Evolutionary Multi-objective Optimization in Uncertain Environments - Issues and Algorithms , 2009, Studies in Computational Intelligence.

[31]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[32]  Jonathan E. Fieldsend,et al.  Multi-objective optimisation in the presence of uncertainty , 2005, 2005 IEEE Congress on Evolutionary Computation.

[33]  Min Jiang,et al.  An Objective Penalty Functions Algorithm for Multiobjective Optimization Problem , 2011 .

[34]  Philipp Limbourg,et al.  Multi-objective Optimization of Problems with Epistemic Uncertainty , 2005, EMO.