**Lectures 2006:**

Preliminaries:The notion of fuzzy set. System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation. Fuzzy inclusion. Cutworthy and cut-consistent properties. Fuzzy negations. Fuzzy complements. Fuzzy conjunctions (t-norms), fuzzy disjunctions (t-conorms). Fuzzy intersections and unions. Residuated fuzzy implications and biimplications. Laws of fuzzy algebras. Fuzzy relations, their composition, fuzzy equivalence (similarity). Projection of a fuzzy relation. Cylindric extension (cartesian product) of fuzzy sets. Extension principle for unary operations (functions). Convex fuzzy sets. Fuzzy numbers and intervals. Extension principle for binary operations. Arithmetic of fuzzy numbers. Properties of operations with fuzzy numbers.

Fuzzy control:Principles of fuzzy control. Which tasks are suitable for fuzzy control. Mamdani-Assilian and residuum-based controllers. Requirements on a fuzzy rule base. Fuzzy inference and fuzzy relational equations. Methods of defuzzification and their properties. Comparison of fuzzy control to other approaches. Takagi-Sugeno controllers.

Cluster analysis:Algorithms k-means, fuzzy c-means, EM algorithm as a tool for handling incomplete information.

Case studies:

May 16, 2006

Wei Li: Fuzzy logic based robot navigation in uncertain environments by multisensor integration. Proceedings of the 1994 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI'94), Las Vegas, NV, Oct. 2-5, 1994, 259-265.

Indranil Gupta, Denis Riordan: Distance transform path planning for mobile robots using fuzzy logic. In: Yingming Liu, Guoqing Chen, Mingsheng Ying (eds.), Fuzzy Logic, Soft Computing & Computational Intelligence, Eleventh International Fuzzy Systems Association World Congress (IFSA 05), Tsinghua University Press/Springer, Beijing, China, 2005, 1126-1140.

May 23, 2006

P. Brox, I. Baturone, S. Sánchez-Solano: Interlaced to progressive scan conversion using a fuzzy edge-based line average algorithm. Proc. IEEE International Symposium on Intelligent Signal Processing (WISP 2005), Faro, September 1-3, 2005. PDF

May 30, 2006

Steven G. Goodridge, Ren C. Luo and Michael G. Kay: Multi-Layered Fuzzy Behavior Fusion for Real-Time Control of Systems with Many Sensors. Proceedings of the 1994 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI'94), Las Vegas, NY, Oct. 2-5, 1994.

Ajay Mahajan, Kaihong Wang, and Probir Kumar Ray: Multisensor Integration and Fusion Model that Uses a Fuzzy Inference System. IEEE/ASME Transactions on Mechatronics, Vol. 6, No. 2, June 2001, 188-196.