Symmetric and Asymmetric Allocating Concepts Under Multiple-Goals

To analyze utility estimating and allocating under real-world interactive modes, various interrelationships formed by members and its operational extents are always investigated by means of multifaceted approaches. To address this, this study first proposes a symmetric allocating concept under multiple-goals. In order to evaluate relative effects result from varying members and its operational extents under different situations, this study introduces several asymmetric generalizations by applying weights related to the members and its operational extents. Several axiomatic outcomes are also adopted to express the mathematical correctness and practicality for these allocating concepts. Moreover, some more explanations for related axiomatic outcomes and applications are also offered throughout this study.