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 and 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. 

[2]

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

[3]

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

[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.

[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.

[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.

[7]

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

[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.

[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.

[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.

[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.

[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. 

[13]

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

[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.

[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.

[16]

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

[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.

[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.

[19]

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

[20]

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

[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.

[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.

[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. 

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. 

[2]

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

[3]

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

[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.

[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.

[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.

[7]

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

[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.

[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.

[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.

[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.

[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. 

[13]

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

[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.

[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.

[16]

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

[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.

[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.

[19]

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

[20]

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

[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.

[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.

[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. 

[1]

Zeyang Wang, Ovanes Petrosian. On class of non-transferable utility cooperative differential games with continuous updating. Journal of Dynamics and Games, 2020, 7 (4) : 291-302. doi: 10.3934/jdg.2020020

[2]

Wenjuan Jia, Yingjie Deng, Chenyang Xin, Xiaodong Liu, Witold Pedrycz. A classification algorithm with Linear Discriminant Analysis and Axiomatic Fuzzy Sets. Mathematical Foundations of Computing, 2019, 2 (1) : 73-81. doi: 10.3934/mfc.2019006

[3]

İsmail Özcan, Sirma Zeynep Alparslan Gök. On cooperative fuzzy bubbly games. Journal of Dynamics and Games, 2021, 8 (3) : 267-275. doi: 10.3934/jdg.2021010

[4]

Maria Colombo, Alessio Figalli. An excess-decay result for a class of degenerate elliptic equations. Discrete and Continuous Dynamical Systems - S, 2014, 7 (4) : 631-652. doi: 10.3934/dcdss.2014.7.631

[5]

Jiaquan Zhan, Fanyong Meng. Cores and optimal fuzzy communication structures of fuzzy games. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1187-1198. doi: 10.3934/dcdss.2019082

[6]

Lv Chen, Hailiang Yang. Optimal reinsurance and investment strategy with two piece utility function. Journal of Industrial and Management Optimization, 2017, 13 (2) : 737-755. doi: 10.3934/jimo.2016044

[7]

Alexander J. Zaslavski. Good programs in the RSS model without concavity of a utility function. Journal of Industrial and Management Optimization, 2006, 2 (4) : 399-423. doi: 10.3934/jimo.2006.2.399

[8]

Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial and Management Optimization, 2007, 3 (2) : 381-398. doi: 10.3934/jimo.2007.3.381

[9]

Dmitrii Rachinskii. On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3361-3386. doi: 10.3934/dcdsb.2018246

[10]

Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics and Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013

[11]

Daniel Lear, David N. Reynolds, Roman Shvydkoy. Grassmannian reduction of cucker-smale systems and dynamical opinion games. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5765-5787. doi: 10.3934/dcds.2021095

[12]

Yunsai Chen, Zhao Yang, Liang Ma, Peng Li, Yongjie Pang, Xin Zhao, Wenyi Yang. Efficient extraction algorithm for local fuzzy features of dynamic images. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1311-1325. doi: 10.3934/dcdss.2019090

[13]

Ekaterina Gromova, Ekaterina Marova, Dmitry Gromov. A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games. Journal of Dynamics and Games, 2020, 7 (2) : 105-122. doi: 10.3934/jdg.2020007

[14]

Francesco Sanna Passino, Nicholas A. Heard. Modelling dynamic network evolution as a Pitman-Yor process. Foundations of Data Science, 2019, 1 (3) : 293-306. doi: 10.3934/fods.2019013

[15]

Genlong Guo, Shoude Li. A dynamic analysis of a monopolist's quality improvement, process innovation and goodwill. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022014

[16]

Yan-An Hwang, Yu-Hsien Liao. Reduction and dynamic approach for the multi-choice Shapley value. Journal of Industrial and Management Optimization, 2013, 9 (4) : 885-892. doi: 10.3934/jimo.2013.9.885

[17]

Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417

[18]

Dariush Mohamadi Zanjirani, Majid Esmaelian. An integrated approach based on Fuzzy Inference System for scheduling and process planning through multiple objectives. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1235-1259. doi: 10.3934/jimo.2018202

[19]

Junjie Peng, Ning Chen, Jiayang Dai, Weihua Gui. A goethite process modeling method by Asynchronous Fuzzy Cognitive Network based on an improved constrained chicken swarm optimization algorithm. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1269-1287. doi: 10.3934/jimo.2020021

[20]

Feyza Gürbüz, Panos M. Pardalos. A decision making process application for the slurry production in ceramics via fuzzy cluster and data mining. Journal of Industrial and Management Optimization, 2012, 8 (2) : 285-297. doi: 10.3934/jimo.2012.8.285

 Impact Factor: 

Metrics

  • PDF downloads (121)
  • HTML views (124)
  • Cited by (0)

Other articles
by authors

[Back to Top]