# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Fuzzy linear programming based on statistical confidence interval and interval-valued fuzzy set. (English) Zbl 0994.90143
A standard linear programming problem applied to a production process, with uncertain coefficients ${a}_{ij}$ and right-hand sides ${b}_{i}$ in the constraints, is considered. It is assumed that statistical confidence intervals of the uncertain ${a}_{ij}$ and ${b}_{i}$ for all $i$, $j$ can be calculated. Each ${a}_{ij}$, ${b}_{i}$ is substituted by a $\left(1-\alpha \right)$-level fuzzy number, which is derived by making use of a statistical confidence interval. In this way, a fuzzy linear programming problem is obtained. Similarly two statistical confidence intervals are used to derive $\left(1-\alpha ,1-\beta \right)$-interval-valued fuzzy numbers, which are used as coefficients and right-hand sides in the constraints of an alternative fuzzy linear programming problem. The defuzzification of both fuzzy problems resulting in crisp linear programming problems is carried out using the theory presented at the beginning of the article and some known results from the literature. An illustrative numerical example is solved.
##### MSC:
 90C70 Fuzzy programming 90C05 Linear programming 62F25 Parametric tolerance and confidence regions