  Binary Knapsack Problem (BKP) is to select a subset of an element (item) set
with the highest value while keeping the total weight within the capacity of
the knapsack. This paper presents an integer programming model for a variation
of BKP where the value of each element may depend on selecting or ignoring
other elements. Strengths of such Value-Related Dependencies are assumed to be
imprecise and hard to specify. To capture this imprecision, we have proposed
modeling value-related dependencies using fuzzy graphs and their algebraic
structure.
