When Coca-Cola determines the bottled-water competitors for its Dasani brand by identifying the products or sets of products with which a brand competes and which function as close substitutes, it is determining Dasani's .

Category membership

Explanation:    

 According to the given question, the given situation is basically determining the dasani's category membership as it helps in categorizing the various types of products and the services on the basis of their similar features and the characteristics.

The main purpose of the category membership is that it helps in understanding the various types of offers related to the specific brand and also the high competitive choice.

The customers basically wanted the product at lower price with high quality and they usually prefer the discount offers. Therefore, Category membership is the correct answer.