In original Data Envelopment Analysis (DEA) models for measuring the relative efficiencies of a set of Decision Making Units (DMUs) using various inputs to produce various outputs are limited to crisp data. To deal with imprecise data, the notion of fuzziness has been introduced. this paper develops a procedure to measure the efficiencies of DMUs with fuzzy observations. The basic idea is to tr...

In this paper, we deal with fuzzy random variables for inputs andoutputs in Data Envelopment Analysis (DEA). These variables are considered as fuzzyrandom flat LR numbers with known distribution. The problem is to find a method forconverting the imprecise chance-constrained DEA model into a crisp one. This can bedone by first, defuzzification of imprecise probability by constructing a suitablem...

Conceptual neighborhood graphs capture the similarity among qualitative relations. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degrees increases, from the crisp to the broad-boundar...

Cysteine-rich secretory protein-1 (CRISP-1) is a glycoprotein secreted by the epididymal epithelium. It is a member of a large family of proteins characterized by two conserved domains and a set of 16 conserved cysteine residues. In mammals, CRISP-1 inhibits sperm-egg fusion and can suppress sperm capacitation. The molecular mechanism of action of the mammalian CRISP proteins remains unknown, b...

BACKGROUND Whole grain rye products have been shown to increase satiety and elicit lower postprandial insulin response without a corresponding change in glucose response compared with soft refined wheat bread. The underlying mechanisms for these effects have not been fully determined The primary aim of the study was to investigate if whole grain rye crisp bread compared to refined wheat crisp b...

: fried products derived from potato, particularly potato crisp have been widely included in food basket of the households in the recent years in iran. potato crisp, among other products, is of great importance and is considered as competitive products. this product is in the list of the food products with high acrylamide content. therefore, due to the nutritional importance of this product and...

in this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. also necessary and sufficient conditions for existenceof solution are given. some numerical examples illustrate the efficiencyof the method.