http://popups.lib.uliege.be/1373-5411/index.php?id=2196 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=3586 Fuzzy relational equations are without doubt the most important inverse problems arising from fuzzy set theory, and in particular from fuzzy relational calculus. Indeed, the calculus of fuzzy relations is a powerful one, with applications in fuzzy control and fuzzy systems modelling in general, approximate reasoning, relational databases, clustering, etc. In this paper, fuzzy relational equations are approached from an order-theoretical point of view. It is shown how all inverse problems can be reduced to systems of polynomial lattice equations. The exposition is limited to the description of exact solutions of systems of sup-T equations, and analytical ways are presented for obtaining the complete solution set when working in a broad and interesting class of distributive lattices. Thu, 26 Sep 2024 10:05:26 +0200 Thu, 26 Sep 2024 10:05:54 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3586 http://popups.lib.uliege.be/1373-5411/index.php?id=2195 Optimization theory is a key technology for inverse problems of reconstruction with applications in science, technology and economy. Discrete tomography is a modern research field which deals with finite objects from VLSI chip design or medical imaging. This paper focuses on the utilization of modern optimization methods to approximately resolve the NP-hard reconstruction problem of discrete tomography. Our new approaches and introductions are based on modeling and algorithms from coding theory and optimal experimental design. Here, we combine continuous and discrete optimization with exploiting geometrical symmetries, or more generally, equivariances, in a framework of statistical learning. Tue, 30 Jul 2024 13:22:50 +0200 Tue, 30 Jul 2024 13:23:02 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2195