Affiliations: [a] School of Business, Ningbo University, Ningbo, China
| [b] School of Information Technology, Deakin University, Victoria, Australia
Correspondence:
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Corresponding author. Jian-Zhang Wu, School of Business, Ningbo University, Ningbo 315211, China. E-mail: sjzwjz@gmail.com; Gleb Beliakov, gleb@deakin.edu.au.
Abstract: The main aim of this paper is to evoke more attentions on the dual concepts of k-maxitive capacity and k-maxitive aggregation, called k-minitive capacity and k-minitive aggregation by convention. We point out that possibility and necessity capacities, and k-tolerant and k-intolerant capacities are special cases of k-maxitive and k-minitive capacities. We also discuss some properties of k-minitive aggregation dual to those of the k-maxitive aggregation functions. For the purport of advocating the application of k-minitive and k-maxitive capacities, we finally present the mixed integer programming based identification method and illustrate its steps and results through an example.
Keywords: Fuzzy measure, k-minitive, k-maxitive, Capacity identification, Aggregation function
