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Interval-valued n-person Cooperative games with satisfactory degree constraints. (English) Zbl 07100451

Summary: The aim of this study is to develop several nonlinear programming models for interval-valued cooperative games in which taking into account the decision makers’ risk attitudes. First, we investigate several existing used satisfactory degree comparison methods for ranking interval-valued fuzzy numbers, and point out by an example that the method proposed by F. Liu et al. [Soft Comput. 22, No. 8, 2557–2565 (2018; Zbl 1398.91188)] is more efficient than the method proposed by F. X. Hong and D. F. Li [“Nonlinear programming method for interval-valued \(n\)-person cooperative games”, Oper. Res., Int. J. 17, No. 2, 1–19 (2016; doi:10.1007/s12351-016-0233-1)]. Second, by taking into account decision makers’ risk attitudes, several corresponding nonlinear programming models are constructed based on satisfactory degree formulas that were proposed by Liu et al. [loc. cit.]. Third, an illustrative example in conjunction with comparative analyses are employed to demonstrate the validity and applicability of the proposed models. Finally, to further highlight the validity of the proposed method, we discuss the relationship of the satisfactory degree formulas between Hong and Li [loc. cit.]’s method and Z. S. Xu and Q. L. Da [“Possibility degree method for ranking interval numbers andits application.”, J. Syst. Eng. 18, 67–70 (2003)]’s method.

MSC:

90Bxx Operations research and management science

Citations:

Zbl 1398.91188
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References:

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