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Binary Knapsack Problem (BKP) is to select a subset of an element (item) setwith the highest value while keeping the total weight within the capacity ofthe knapsack. This paper presents an integer programming model for a variationof BKP where the value of each element may depend on selecting or ignoringother elements. Strengths of such Value-Related Dependencies are assumed to beimprecise and hard to specify. To capture this imprecision, we have proposedmodeling value-related dependencies using fuzzy graphs and their algebraicstructure.

An Integer Programming Model for Binary Knapsack Problem with Value-Related Dependencies among Elements