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Zur linearen Optimierung mit unscharfen Daten. (German)
Fachbereich Mathematik der Universität Kaiserslautern 171 S. (1985).
The dissertation contains an extensive discussion of a linear programming problem under the presence of imprecision. Denote by $P=(A,b,c)$ the data attached to a standard as well as a dual problem, $\max \{c\sp Tx\vert x\in X\}$, $X=\{x\in R\sp n\vert$ $Ax=b$, $x\ge 0\}$, and $\min \{b\sp Ty\vert y\in Y\}$, $Y=\{y\in R\sp m\vert$ $A\sp Ty\ge e\}$, $\dim (A)=m\times n$, $\dim (b)=m$, $\dim (x)=n$. Imprecision is modelled via interval analysis. Thus the data set P is constructed by real compact intervals, $P=([A],[b],[c])$ where e.g. $[a]=(\underline a,\bar a)=\{x\in R\sp n\vert$ \b{a}$\le x\le \bar a\}$. The algorithms for solving the programming problem are given in detail and the result from theoretical considerations are presented in the paper.
Reviewer: W.Pedrycz