Fuzzy multilevel programming with a hybrid intelligent algorithm

Gao, Jinwu; Liu, Baoding

doi:10.1016/j.camwa.2004.07.027

Cited by 63 publications

(28 citation statements)

References 29 publications

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“…After that, Gao and Liu (2005) investigated fuzzy multilevel programming, and designed a series of hybrid intelligent algorithms for finding the Stackelberg-Nash equilibrium. Xu, Zhao, and Shu (2005a) discussed equilibrium strategies for two-person zero-sum game with fuzzy payoffs.…”

Section: Applicationsmentioning

confidence: 99%

A survey of credibility theory

Liu

2006

Fuzzy Optim Decis Making

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383

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This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented.

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Section: Applicationsmentioning

confidence: 99%

A survey of credibility theory

Liu

2006

Fuzzy Optim Decis Making

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383

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“…For scientists of fuzzy theory, the quantities like "about 100 tons" are regarded as fuzzy variables. Within the framework of credibility theory, Gao and his coworkers proposed a spectrum of credibilistic game including credibilistic strategic game (Gao and Liu 2005;Gao 2007;Gao et al 2007Gao et al , 2009Liang et al 2010;Gao and Yang 2013), credibilistic coalitional game Gao et al 2011;Zhang and Gao 2012) and credibilistic extensive game (Gao and Yu 2013).…”

Section: Introductionmentioning

confidence: 99%

Bayesian equilibria for uncertain bimatrix game with asymmetric information

Yang

Gao

2014

J Intell Manuf

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In an uncertain bimatrix game, there are two solution concepts of (α, β)-optimistic equilibrium strategy and (u, v)-maximum chance equilibrium strategy. This paper goes further by assuming that the confidence levels α, β and payoff levels u, v are private information. Then, the so-called uncertain bimatrix game with asymmetric information is investigated. Two solution concepts of Bayesian optimistic equilibrium strategy and Bayesian maximum chance equilibrium strategy as well as their existence theorems are presented. Moreover, sufficient and necessary conditions are given for finding the Bayesian equilibrium strategies. Finally, a two-firm advertising problem is analyzed for illustrating our modelling idea.

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“…Credibility theory (Liu 2004) is a branch of mathematical tools for dealing with the behavior of fuzzy phenomena. Based on credibility theory, a spectrum of credibilistic strategic game has been developed by Gao and his coworkers (Gao et al 2004;Gao and Liu 2005;Gao 2007Gao , 2009Liang et al 2010). Moreover, credibilistic extensive game with fuzzy payoffs was proposed by Yu and Gao (2008), and the solution of the game was defined as credibilistic equilibrium and credibilistic subgame perfect equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Coalitional game with fuzzy payoffs and credibilistic core

Shen

Gao

2010

Soft Comput

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As an important branch of game theory, coalitional game deals with situations that involve cooperation among the players. This paper deals with this topic further by incorporating the fuzzy payoff information. Based on the credibility theory, we introduce two decision criteria to define the preferences of players, which leads to two definitions of credibilistic cores-the solution of coalitional game with fuzzy transferable payoffs. Meanwhile, we give a sufficient and necessary condition to ensure non-emptiness of the credibilistic cores. Finally, an example is provided for illustrating the usefulness of the theory developed in this paper.

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Fuzzy multilevel programming with a hybrid intelligent algorithm

Cited by 63 publications

References 29 publications

A survey of credibility theory

A survey of credibility theory

Bayesian equilibria for uncertain bimatrix game with asymmetric information

Coalitional game with fuzzy payoffs and credibilistic core

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