Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior

Yu-Hsien Liao

doi:10.3934/naco.2021047

Article Contents

2022, Volume 12, Issue 1: 1-14. Doi: 10.3934/naco.2021047

This issue Previous Article Preface Next Article Variable fixing method by weighted average for the continuous quadratic knapsack problem

Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior

Yu-Hsien Liao^,

Department of Applied Mathematics, National Pingtung University, Pingtung 900, Taiwan

Received: March 2020

Revised: December 2020

Early access: November 2021

Published: March 2022

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Abstract

By considering the supreme-utilities and the weights simultaneously under fuzzy behavior, we propose two indexes on fuzzy transferable-utility games. In order to present the rationality for these two indexes, we define extended reductions to offer several axiomatic results and dynamics processes. Based on different consideration, we also adopt excess functions to propose alternative formulations and related dynamic processes for these two indexes respectively.

Keywords:

Fuzzy transferable-utility games, reduction,
excess function, axiomatic result, dynamic process.

Mathematics Subject Classification: Primary: 91A; Secondary: 91B.

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