Beliakov, Gleb 2005, Fitting triangular norms to empirical data. In Klement, Erich Peter and Mesiar, Radko (ed), Logical, algebraic, analytic, and probabilistic aspects of triangular norms, Elsevier, Boston, Mass., pp.262-272.
This chapter discusses some specific tools that can be used to build triangular norms based on a finite number of (possibly noisy) observations. Such problem arises in applications, when observed data (e.g., decision patterns of experts) need to be modelled with a special class of functions, such as triangular norms. We show how this problem can be transformed into a constrained regression problem, and then efficiently solved. We also discuss related operators: uninorms, nullnorms and associative copulas.
Field of Research
010107 Mathematical Logic, Set Theory, Lattices and Universal Algebra
Socio Economic Objective
970101 Expanding Knowledge in the Mathematical Sciences
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