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On the Banzhaf-like Value for Cooperative Games with Interval Payoffs

1
School of Business, Central South University, Yuelu District, Changsha 410083, China
2
School of Economics and Management, South China Normal University, Guangzhou Higher Education Mega Center, No. 378, Waihuan Xi Road, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 372; https://doi.org/10.3390/math8030372
Received: 7 February 2020 / Revised: 2 March 2020 / Accepted: 3 March 2020 / Published: 7 March 2020
(This article belongs to the Section Fuzzy Set Theory)
By using Moore’s subtraction operator and a total order on the set of closed intervals, we introduce a new variation of the Banzhaf value for cooperative interval games called the interval Banzhaf-like value which may accommodate the shortcomings of the interval Banzhaf value. We first reveal the relation between this introduced value and the interval Banzhaf value. Then, we present two sets of properties that may be used to determine whether an interval value is median-indifferent to the interval Banzhaf-like value. Finally, in order to overcome the disadvantages of the interval Banzhaf-like value, we propose the contracted interval Banzhaf-like value and give an axiomatization of this proposed value. View Full-Text
Keywords: cooperative interval game; interval Banzhaf value; interval Banzhaf-like value; contracted interval Banzhaf-like value cooperative interval game; interval Banzhaf value; interval Banzhaf-like value; contracted interval Banzhaf-like value
MDPI and ACS Style

Tan, C.; Feng, W.; Han, W. On the Banzhaf-like Value for Cooperative Games with Interval Payoffs. Mathematics 2020, 8, 372.

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