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Fuzzy and Soft Poly-Optimization in the Digital Environment: Examples
Abstract
TThe standard optimality problem is when the triad is given: <x, F(x), O(x)>, where x is the decision variables vector, F(x) is an overall optimality criterion and O(x) is a set of constraints, defined in a fully mathematical form. But in the real practice in business, logistics, medicine, and even in engineering – where a decision–maker has for his/her disposal comparatively good unique mathematical models – it is very rarely. Another trouble may be, the computations are time consuming and/or algorithms do not converged satisfactory. In this chapter examples of two non-standard techniques of poly-optimization (Multi Attribute Decision Making, Multi Criteria Decision Making) are presented. The first is a dialog procedure of finding satisfactory solution on hierarchical play of constraints, with extensive computer simulations, what is called here as a soft optimization. The other is a standard poly-optimization on fuzzy mathematical definition of criteria and of a model. A few examples are given.
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