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Discrete fuzzy optimization. (English) Zbl 0931.90066
Słowiński, Roman (ed.), Fuzzy sets in decision analysis, operations research and statistics. Boston: Kluwer Academic Publishers. Handb. Fuzzy Sets Ser. 1, 249-280 (1998).
The paper presents a survey of selected fuzzy discrete optimization problems and algorithms for their solution. Generally a fuzzy discrete optimization problem is formulated as follows: Maximize (or minimize) \(f(x;C)\) subject to \(x\in X\), where \(C\) is a vector of fuzzy parameters, whose components are fuzzy numbers and \(X\) is a fuzzy set in a countable or finite universe of feasible solutions. The following fuzzy equivalents of the well-known crisp problems are considered in the paper: fuzzy optimization problems in graphs and networks (max-flow, min-cost and shortest route problem), fuzzy transportation and assignment problem, network planning problems (fuzzy CPM and PERT), fuzzy scheduling on machines (fuzzy a-job \(m\)-machine flow shop problem, fuzzy open shop problem with fuzzy due dates, some general job shop problems), some other selected fuzzy discrete optimization problems (fuzzy set covering, fuzzy knapsack and general fuzzy 0-1 linear optimization problems).
For the entire collection see [Zbl 0905.00031].

MSC:
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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