Journal
OPERATIONAL RESEARCH
Volume 16, Issue 1, Pages 1-24Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s12351-015-0183-z
Keywords
Interval fuzzy game; Shapley function; Multilinear extension; Choquet integral
Categories
Funding
- State Key Program of National Natural Science of China [71431006]
- Funds for Creative Research Groups of China [71221061]
- Projects of Major International Cooperation NSFC [71210003]
- National Natural Science Foundation of China [71201089, 71271217, 71201110, 71271029]
- National Science Foundation for Postdoctoral Scientists of China [2014M560655]
- Program for New Century Excellent Talents in University of China [NCET-12-0541]
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In this paper, a generalized form of fuzzy games with interval characteristic functions is proposed, which can be seen as an extension of games with crisp characteristic functions. Based on the extended Hukuhara difference, the interval Shapley function for interval fuzzy games is studied. Then, the concept of interval population monotonic allocation function (IPMAF) is defined. When interval fuzzy games are convex, we prove that the interval Shapley function is an IPMAF. Furthermore, two special types of interval fuzzy games are researched, and the associated interval Shapley function is studied.
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