Fuzzy optimization and nuclear production processes

Calculations or management methods, based on fuzzy logic, with its smell of incoherence and fanciness, will only be accepted in the nuclear world if it can be proven that they have better specific operational qualities than crisp methods. It is shown that this is the case when a large population of elements has to be partitioned in smaller subpopulations of similar elements and in such a manner that the different subpopulations are as well separated from each other as possible. Examples of these requirements are encountered in the classification of feed material entering in a process or of semi- or end products leaving a production line. This classical clustering problem, which is highly combinatorial and in most cases can only be solved heuristically, has been shown to be better tractable with a fuzzy than with a crisp approach. A different although related problem is provided by the requirement of homogenization of discrete components. The fact that such a problem is solved by a fuzzy rather than a crisp method is perfectly acceptable even in the nuclear industry as the value of the final solution can objectively be evaluated irrespective of the (fuzziness of the) adapted method. The paper presents a number of examples together with the mathematical tools necessary to tackle this type of problems. The comparisons between the crisp and fuzzy approaches is detailed.