k-minitive capacities and k-minitive aggregation functions

Article type: Research Article

Authors: Wu, Jian-Zhang^{a; b; *} | Beliakov, Gleb^b

Affiliations: [a] School of Business, Ningbo University, Ningbo, China | [b] School of Information Technology, Deakin University, Victoria, Australia

Correspondence: [*] Corresponding author. Jian-Zhang Wu, School of Business, Ningbo University, Ningbo 315211, China. E-mail: [email protected]; Gleb Beliakov, [email protected].

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

DOI: 10.3233/JIFS-190008

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 2, pp. 2797-2808, 2019