The aim of this paper is to introduce a new framework for studying bi-capacities and its integrals, which is alternative framework from defined by Grabisch and Labreuche ([7], [8]). First, we define bi-capacities through introducing a notion of ternary-element sets. Secondly, we propose model of bipolar Choquet integral with respect to bi-capacity based on ternary-element sets, and we study basic properties of new model.
Keywords: Capacities, Bi-cpacities, Choquet integral, Bipolar Choquet integral, Ternary-element sets.
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