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Fuzzy approaches to multicriteria de Novo programs. (English) Zbl 0719.90092

The authors expose in a clear straightforward way the multicriteria de Novo program for which they develop two types of solutions. In a first proposal each of the criteria are satisfied to a same relative extend between the extreme possible values. This solution is generally not an “efficient” one. In a second approach the authors seek to maximize the average degree of satisfaction between the extreme feasible values of all the criteria, which do provide an “efficient” solution. A pair of well- chosen examples illustrates the theoretical developments.
In a second part the model is extended to include fuzziness with respect to all of the “fixed” constants included in the model, such as the unit prices, the total budget, the specific contributions of each asset to the criteria and the unit amount of each asset needed. The same pair of solutions are also developed for this fuzzy model, which is further illustrated by an adequate example.
On the whole, this is a clearly written article, generally easy to follow. However, some readers confronted with a few unexplained idiomatic terms could be disturbed unless they have easy access to some of the references mentioned at the end of the articles. More puzzling is the fact that quite a number of errors have remained in the text. Some are merely typewriting errors without real consequences; others concern the symbols, variables or indices and may render the understanding of the arguments more difficult than they ought to; finally, calculation or typing errors in each of the three examples are probably the most harmful as they reduce to a large extend the demonstrative strength of these pedagogical means. The warned reader however should take great interest in this article.
Reviewer: E.Trauwaert (Mol)

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C29 Multi-objective and goal programming
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