Paper:

# On Inheritance of Complementarity in Non-Additive Measures Under Bounded Interactions

## Katsushige Fujimoto

College of Symbiotic Systems Science, Fukushima University

1 Kanayagawa, Fukushima 960-1293, Japan

The notions of *k*-monotonicity and superadditivity for non-additive measures (e.g., capacity and cooperative games) are used as indices to measure the complementarity of criteria/coalitions in decision-making involving multiple criteria and/or cooperative game theory. To avoid exponential complexity in capacity-based multicriteria decision-making models, *k*-additive capacities and/or 𝒞-decomposable capacities are often adopted. While, in cooperative game theory, under communication-restricted situations, some coalitions cannot generally be formed. This paper investigates the inheritance of complementary relationships/effects in non-additive measures with restricted domains (or under bounded interactions).

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