Fuzzy Mathematical Programming: Theory, Applications and Extension

Mathematical programming has been successfully used for years in a variety of problems related to hard systems in which the structure, relations and behaviour are well-defined and quantifiable. Unfortunately, attempts to apply similar means to soft systems have not been generally successful. One of the reasons for this mismatching is the key role played by human judgement and preferences which are subjective, imprecise and not easily quantifiable. Although probabilistic theories claim to model decision making under imprecision, there is qualitatively different kind of indeterminacy which are not covered by these tools, that is: inexactness, illdefinedness, vagueness. The aim of this paper is twofold. First, it takes a general look at core ideas aimed at softening mathematical programming models by making it possible to incorporate non-stochastic imprecision into these models. Second, it extends these ideas to situations where both fuzziness and randomness are under one roof in a mathematical programming setting. The paper ends with some concluding remarks along with lines for further developments in the fiel