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Ranking fuzzy numbers with maximizing set and minimizing set. (English) Zbl 0618.90047
Several methods of ranking fuzzy numbers have some disadvantages explained on examples. A new method proposed here is a modification of Jain’s approach [see R. Jain, Internat. J. Systems. Sci. 8, 1-7 (1977; Zbl 0347.90001)]. Fuzzy alternatives are ordered according to the utility numbers \[ (*)\quad u_ i=(\sup_{x}\min (M(x),A_ i(x))+1- \sup_{x}\min (N(x),A_ i(x))) \] for \(i=1,...,n\), where \(A_ 1,...,A_ n\) are given fuzzy numbers in the interval [a,b], and \[ M(x)=(\frac{x-a}{b-a})^ k,\quad N(x)=(\frac{x-b}{a-b})^ k\quad for\quad x\in [a,b] \] with a constant \(k>0\). For fuzzy numbers with triangular or trapezoidal membership, formula (*) has the simpliest form depending on suitable intervals determined by the given fuzzy numbers.
Reviewer: J.Drewniak

MSC:
90B50 Management decision making, including multiple objectives
03E72 Theory of fuzzy sets, etc.
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