Combination of t-norms and their conorms

Abstract

Non-negative linear combinations of t min -norms and their conorms are used to formulate some decision making problems using systems of max-separable equations and inequalities and optimization problems under constraints described by such systems. The systems have the left hand sides equal to the maximum of increasing functions of one variable and on the right hand sides are constants. Properties of the systems are studied as well as optimization problems with constraints given by the systems and appropriate solution methods are proposed. Motivation of this research are decision making investment situations both in deterministic and uncertain environment. Possibilities of further research are briefly discussed in the concluding remarks of the paper.