representation and modeling of economic uncertainty is addressed by different modeling methods, namely stochastic variables and probabilities, interval analysis, and fuzzy numbers, in particular triple estimates. fo-cusing on discounted cash flow analysis numerical results are presented, comparisons are made between alter-native modeling methods, and characteristics of the methods are discussed.

for the current research the records of 62 farms in isfahan province were available. to estimate genetic and phonotypic trends of reproductive traits such as age at first calving, calving interval, days open and number of insemination to conception rate the records of 63,866 cows including 167793 reproductive records were employed. farms were covered by vahdat industrial agriculturists and dair...

The interval number of a graph G is the minimum k such that one can assign to each vertex union intervals on real line, intersection these sets, i.e., two vertices are adjacent in if and only corresponding sets have non-empty intersection. Scheinerman West (1983) [14] proved any planar at most 3. However original proof has flaw. We give different shorter this result.