March  2022, 12(1): 1-14. doi: 10.3934/naco.2021047

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

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

 

Received  March 2020 Revised  December 2020 Published  March 2022 Early access  November 2021

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.

Citation: Yu-Hsien Liao. Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior. Numerical Algebra, Control & Optimization, 2022, 12 (1) : 1-14. doi: 10.3934/naco.2021047
References:
[1]

J. P. Aubin, Coeur et valeur des jeux flous á paiements latéraux, Comptes Rendus de l'Académie des Sciences, 279 (1974), 891-894.   Google Scholar

[2]

J. P. Aubin, Cooperative fuzzy games, Mathematics of Operations Research, 6 (1981), 1-13.  doi: 10.1287/moor.6.1.1.  Google Scholar

[3]

J. F. Banzhaf, Weighted voting doesn't work: a mathematical analysis, Rutgers Law Rev., 19 (1965), 317-343.   Google Scholar

[4]

S. Borkotokey and R. Neog, Dynamic resource allocation in fuzzy coalitions: a game theoretic model, Fuzzy Optimization and Decision Making, 13 (2014), 211-230.  doi: 10.1007/s10700-013-9172-y.  Google Scholar

[5]

R. BranzeiD. Dimitrov and S. Tijs, Egalitarianism in convex fuzzy games, Mathematical Social Sciences, 47 (2004), 313-325.  doi: 10.1016/j.mathsocsci.2003.09.003.  Google Scholar

[6]

D. Butnariu, Fuzzy games: a description of the concept, Fuzzy Sets and Systems, 1 (1978), 181-192.  doi: 10.1016/0165-0114(78)90003-9.  Google Scholar

[7]

S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica, 57 (1989), 589-614.  doi: 10.2307/1911054.  Google Scholar

[8]

Y. A. Hwang, Fuzzy games: a characterization of the core, Fuzzy Sets and Systems, 158 (2007), 2480-2493.  doi: 10.1016/j.fss.2007.03.009.  Google Scholar

[9]

Y. A. Hwang and Y. H. Liao, Consistency and dynamic approach of indexes, Social Choice and Welfare, 34 (2010), 679-694.  doi: 10.1007/s00355-009-0423-3.  Google Scholar

[10]

S. Li and Q. Zhang, A simplified expression of the Shapley function for fuzzy game, Eur. J. Oper. Res., 196 (2009), 234-245.  doi: 10.1016/j.ejor.2008.02.034.  Google Scholar

[11]

Y. H. Liao, Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches, Fuzzy Optimization and Decision Making, 16 (2017), 257-268.  doi: 10.1007/s10700-016-9248-6.  Google Scholar

[12]

Y. H. Liao and L. Y. Chung, Power allocation rules under fuzzy behavior and multicriteria situations, Iranian Journal of Fuzzy Systems, 17 (2020), 187-198.   Google Scholar

[13]

Y. H. LiaoP. H. Wu and L. Y. Chung, The EANSC: a weighted extension and axiomatization, Economics Bulletin, 35 (2015), 475-480.   Google Scholar

[14]

M. Maschler and G. Owen, The consistent Shapley value for hyperplane games, International Journal of Game Theory, 18 (1989), 389-407.  doi: 10.1007/BF01358800.  Google Scholar

[15]

E. Molina and J. Tejada, The equalizer and the lexicographical solutions for cooperative fuzzy games: characterizations and properties, Fuzzy Sets and Systems, 125 (2002), 369-387.  doi: 10.1016/S0165-0114(01)00023-9.  Google Scholar

[16]

H. Moulin, On additive methods to share joint costs, The Japanese Economic Review, 46 (1995), 303-332.   Google Scholar

[17]

S. MutoS. IshiharaS. FukudaS. Tijs and R. Branzei, Generalized cores and stable sets for fuzzy games, International Game Theory Review, 8 (2006), 95-109.  doi: 10.1142/S0219198906000801.  Google Scholar

[18]

M. Sakawa and I. Nishizaki, A lexicographical concept in an n-person cooperative fuzzy games, Fuzzy Sets and Systems, 61 (1994), 265-275.  doi: 10.1016/0165-0114(94)90169-4.  Google Scholar

[19]

J. S. Ransmeier, The Tennessee Valley Authority, Vanderbilt University Press in Nashville, 1942. Google Scholar

[20]

L. S. Shapley, Discussant's comment, In Moriarity S (ed) Joint Cost Allocation, University of Oklahoma Press in Tulsa, 1982. Google Scholar

[21]

S. TijsR. BranzeiS. Ishihara and S. Muto, On cores and stable sets for fuzzy games, Fuzzy Sets and Systems, 146 (2004), 285-296.  doi: 10.1016/S0165-0114(03)00329-4.  Google Scholar

[22]

M. TsurumiT. Tanino and M. Inuiguchi, A Shapley function on a class of cooperative fuzzy games, Eur. J. Oper. Res., 129 (2001), 596-618.  doi: 10.1016/S0377-2217(99)00471-3.  Google Scholar

[23]

H. C. WeiP. T. Liu and Y. H. Liao, Two optimal allocations under management systems: Game-theoretical approaches, International Journal of Information and Management Sciences, 30 (2019), 99-112.   Google Scholar

show all references

References:
[1]

J. P. Aubin, Coeur et valeur des jeux flous á paiements latéraux, Comptes Rendus de l'Académie des Sciences, 279 (1974), 891-894.   Google Scholar

[2]

J. P. Aubin, Cooperative fuzzy games, Mathematics of Operations Research, 6 (1981), 1-13.  doi: 10.1287/moor.6.1.1.  Google Scholar

[3]

J. F. Banzhaf, Weighted voting doesn't work: a mathematical analysis, Rutgers Law Rev., 19 (1965), 317-343.   Google Scholar

[4]

S. Borkotokey and R. Neog, Dynamic resource allocation in fuzzy coalitions: a game theoretic model, Fuzzy Optimization and Decision Making, 13 (2014), 211-230.  doi: 10.1007/s10700-013-9172-y.  Google Scholar

[5]

R. BranzeiD. Dimitrov and S. Tijs, Egalitarianism in convex fuzzy games, Mathematical Social Sciences, 47 (2004), 313-325.  doi: 10.1016/j.mathsocsci.2003.09.003.  Google Scholar

[6]

D. Butnariu, Fuzzy games: a description of the concept, Fuzzy Sets and Systems, 1 (1978), 181-192.  doi: 10.1016/0165-0114(78)90003-9.  Google Scholar

[7]

S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica, 57 (1989), 589-614.  doi: 10.2307/1911054.  Google Scholar

[8]

Y. A. Hwang, Fuzzy games: a characterization of the core, Fuzzy Sets and Systems, 158 (2007), 2480-2493.  doi: 10.1016/j.fss.2007.03.009.  Google Scholar

[9]

Y. A. Hwang and Y. H. Liao, Consistency and dynamic approach of indexes, Social Choice and Welfare, 34 (2010), 679-694.  doi: 10.1007/s00355-009-0423-3.  Google Scholar

[10]

S. Li and Q. Zhang, A simplified expression of the Shapley function for fuzzy game, Eur. J. Oper. Res., 196 (2009), 234-245.  doi: 10.1016/j.ejor.2008.02.034.  Google Scholar

[11]

Y. H. Liao, Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches, Fuzzy Optimization and Decision Making, 16 (2017), 257-268.  doi: 10.1007/s10700-016-9248-6.  Google Scholar

[12]

Y. H. Liao and L. Y. Chung, Power allocation rules under fuzzy behavior and multicriteria situations, Iranian Journal of Fuzzy Systems, 17 (2020), 187-198.   Google Scholar

[13]

Y. H. LiaoP. H. Wu and L. Y. Chung, The EANSC: a weighted extension and axiomatization, Economics Bulletin, 35 (2015), 475-480.   Google Scholar

[14]

M. Maschler and G. Owen, The consistent Shapley value for hyperplane games, International Journal of Game Theory, 18 (1989), 389-407.  doi: 10.1007/BF01358800.  Google Scholar

[15]

E. Molina and J. Tejada, The equalizer and the lexicographical solutions for cooperative fuzzy games: characterizations and properties, Fuzzy Sets and Systems, 125 (2002), 369-387.  doi: 10.1016/S0165-0114(01)00023-9.  Google Scholar

[16]

H. Moulin, On additive methods to share joint costs, The Japanese Economic Review, 46 (1995), 303-332.   Google Scholar

[17]

S. MutoS. IshiharaS. FukudaS. Tijs and R. Branzei, Generalized cores and stable sets for fuzzy games, International Game Theory Review, 8 (2006), 95-109.  doi: 10.1142/S0219198906000801.  Google Scholar

[18]

M. Sakawa and I. Nishizaki, A lexicographical concept in an n-person cooperative fuzzy games, Fuzzy Sets and Systems, 61 (1994), 265-275.  doi: 10.1016/0165-0114(94)90169-4.  Google Scholar

[19]

J. S. Ransmeier, The Tennessee Valley Authority, Vanderbilt University Press in Nashville, 1942. Google Scholar

[20]

L. S. Shapley, Discussant's comment, In Moriarity S (ed) Joint Cost Allocation, University of Oklahoma Press in Tulsa, 1982. Google Scholar

[21]

S. TijsR. BranzeiS. Ishihara and S. Muto, On cores and stable sets for fuzzy games, Fuzzy Sets and Systems, 146 (2004), 285-296.  doi: 10.1016/S0165-0114(03)00329-4.  Google Scholar

[22]

M. TsurumiT. Tanino and M. Inuiguchi, A Shapley function on a class of cooperative fuzzy games, Eur. J. Oper. Res., 129 (2001), 596-618.  doi: 10.1016/S0377-2217(99)00471-3.  Google Scholar

[23]

H. C. WeiP. T. Liu and Y. H. Liao, Two optimal allocations under management systems: Game-theoretical approaches, International Journal of Information and Management Sciences, 30 (2019), 99-112.   Google Scholar

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