The Experts below are selected from a list of 238521 Experts worldwide ranked by ideXlab platform
James J Buckley - One of the best experts on this subject based on the ideXlab platform.
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joint Solution to fuzzy programming problems
Fuzzy Sets and Systems, 1995Co-Authors: James J BuckleyAbstract:We propose a new Solution Concept for fuzzy programming problems. It is based on our new method of solving fuzzy equations [ 101. For simplicity we discuss in detail only fuzzy linear programming in this paper. We define, and obtain the basic properties of the joint Solution (a fuzzy vector in Rn and the optimal value of the objective function (a fuzzy number). Three examples are presented illustrating these Concepts.
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solving fuzzy equations a new Solution Concept
Fuzzy Sets and Systems, 1991Co-Authors: James J BuckleyAbstract:Abstract We have previously shown [2] that many fuzzy equations do not have Solutions when the Solution Concept is based on the extension principle. We therefore introduce two new Solution procedures, one based on the unified extension [6] and the other based on possibility theory, after we solve the non-fuzzy equation for the unknown variable. We show, for many types of equations, that: (1) the two new Solutions are identical; (2) the Solution is either a real, or generalized complex, fuzzy number (all uncertain parameters are modeled as real fuzzy numbers); and (3) the previous Solution based on the extension principle (when it exists) is a subset of the new Solution. In particular, we show that the fuzzy quadratic equation, with real fuzzy number coefficients, always has a (new) Solution.
Roland Steinbauer - One of the best experts on this subject based on the ideXlab platform.
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a rigorous Solution Concept for geodesic and geodesic deviation equations in impulsive gravitational waves
Journal of Mathematical Physics, 1999Co-Authors: Michael Kunzinger, Roland SteinbauerAbstract:The geodesic as well as the geodesic deviation equation for impulsive gravitational waves involve highly singular products of distributions (θδ,θ2δ,δ2). A Solution Concept for these equations based on embedding the distributional metric into the Colombeau algebra of generalized functions is presented. Using a universal regularization procedure we prove existence and uniqueness results and calculate the distributional limits of these Solutions explicitly. The obtained limits are regularization independent and display the physically expected behavior.
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a rigorous Solution Concept for geodesic and geodesic deviation equations in impulsive gravitational waves
arXiv: General Relativity and Quantum Cosmology, 1998Co-Authors: Michael Kunzinger, Roland SteinbauerAbstract:The geodesic as well as the geodesic deviation equation for impulsive gravitational waves involve highly singular products of distributions $(\theta\de$, $\theta^2\de$, $\de^2$). A Solution Concept for these equations based on embedding the distributional metric into the Colombeau algebra of generalized functions is presented. Using a universal regularization procedure we prove existence and uniqueness results and calculate the distributional limits of these Solutions explicitly. The obtained limits are regularization independent and display the physically expected behavior.
Jurgen Jost - One of the best experts on this subject based on the ideXlab platform.
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periodic strategies a new Solution Concept and an algorithm for nontrivial strategic form games
Advances in Complex Systems, 2017Co-Authors: V K Oikonomou, Jurgen JostAbstract:We introduce a new Solution Concept for selecting optimal strategies in strategic form games which we call periodic strategies and the Solution Concept periodicity. As we will explicitly demonstrate, the periodicity Solution Concept has implications for non-trivial realistic games, which renders this Solution Concept very valuable. The most striking application of periodicity is that in mixed strategy strategic form games, we were able to find Solutions that result to values for the utility function of each player, that are equal to the Nash equilibrium ones, with the difference that in the Nash strategies playing, the payoffs strongly depend on what the opponent plays, while in the periodic strategies case, the payoffs of each player are completely robust against what the opponent plays. We formally define and study periodic strategies in two player perfect information strategic form games, with pure strategies and generalize the results to include multiplayer games with perfect information. We prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning a game with non-degenerate payoffs. In principle the algorithm we provide, holds true for every non-trivial game, because in degenerate games, inconsistencies can occur. In addition, we also address the incomplete information games in the context of Bayesian games, in which case generalizations of Bernheim’s rationalizability offers us the possibility to embed the periodicity Concept in the Bayesian games framework. Applying the algorithm of periodic strategies in the case where mixed strategies are used, we find some very interesting outcomes with useful quantitative features for some classes of games. Particularly interesting are the implications of the algorithm to collective action games, for which we were able to establish the result that the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue for the case the players have a continuum set of strategies available. We also discuss whether periodic strategies can imply any sort of cooperativity and as we shall exemplify in detail, the periodicity Solution Concept is a purely non-cooperative thinking Concept. Finally, we try to make a simple
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periodic strategies a new Solution Concept and an algorithm for nontrivial strategic form games
Advances in Complex Systems, 2017Co-Authors: V K Oikonomou, Jurgen JostAbstract:We introduce a new Solution Concept, called periodicity, for selecting optimal strategies in strategic form games. This periodicity Solution Concept yields new insight into nontrivial games. In mixed strategy strategic form games, periodic Solutions yield values for the utility function of each player that are equal to the Nash equilibrium ones. In contrast to the Nash strategies, here the payoffs of each player are robust against what the opponent plays. Sometimes, periodicity strategies yield higher utilities, and sometimes the Nash strategies do, but often the utilities of these two strategies coincide. We formally define and study periodic strategies in two player perfect information strategic form games with pure strategies and we prove that every nontrivial finite game has at least one periodic strategy, with nontrivial meaning nondegenerate payoffs. In some classes of games where mixed strategies are used, we identify quantitative features. Particularly interesting are the implications for collective action games, since there the collective action strategy can be incorporated in a purely noncooperative context. Moreover, we address the periodicity issue when the players have a continuum set of strategies available.
Johannes Lankeit - One of the best experts on this subject based on the ideXlab platform.
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on the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms
Nonlinearity, 2019Co-Authors: Elisa Lankeit, Johannes LankeitAbstract:Introducing a suitable Solution Concept, we show that in bounded smooth domains , , the initial boundary value problem for the chemotaxis system with homogeneous Neumann boundary conditions and widely arbitrary initial data has a generalized global Solution for any .
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on the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms
arXiv: Analysis of PDEs, 2018Co-Authors: Elisa Lankeit, Johannes LankeitAbstract:Introducing a suitable Solution Concept, we show that in bounded smooth domains $\Omega\subset \mathbb{R}^n$, $n\ge 1$, the initial boundary value problem for the chemotaxis system \begin{align*} u_t&=\Delta u -\chi\nabla\cdot\left(\frac{u}{v}\nabla v\right)+\kappa u -\mu u^2,\\ v_t&=\Delta v -uv, \end{align*} with homogeneous Neumann boundary conditions and widely arbitrary initial data has a generalized global Solution for any $\mu, \kappa, \chi >0$.
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a generalized Solution Concept for the keller segel system with logarithmic sensitivity global solvability for large nonradial data
Nodea-nonlinear Differential Equations and Applications, 2017Co-Authors: Johannes Lankeit, Michael WinklerAbstract:The chemotaxis system $$\begin{aligned} \left\{ \begin{array}{l} u_t = \Delta u - \chi \nabla \cdot \left( \frac{u}{v}\nabla v\right) , \\ v_t=\Delta v - v+u, \end{array} \right. \end{aligned}$$ is considered in a bounded domain $$\Omega \subset \mathbb {R}^n$$ with smooth boundary, where $$\chi >0$$ . An apparently novel type of generalized Solution framework is introduced within which an extension of previously known ranges for the key parameter $$\chi $$ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that $$\begin{aligned} \chi <\left\{ \begin{array}{ll} \infty \qquad &{} \text{ if } n=2, \\ \sqrt{8} \qquad &{} \text{ if } n=3, \\ \frac{n}{n-2} \qquad &{} \text{ if } n\ge 4, \end{array} \right. \end{aligned}$$ for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized Solution. This Solution inter alia has the property that $$\begin{aligned} u\in L^1_{loc}(\overline{\Omega }\times [0,\infty )). \end{aligned}$$
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a generalized Solution Concept for the keller segel system with logarithmic sensitivity global solvability for large nonradial data
arXiv: Analysis of PDEs, 2017Co-Authors: Johannes Lankeit, Michael WinklerAbstract:The chemotaxis system \[ \left\{ \begin{array}{l} u_t = \Delta u - \chi\nabla \cdot (\frac{u}{v}\nabla v), v_t=\Delta v - v+u, \end{array} \right. \] is considered in a bounded domain $\Omega\subset \mathbb{R}^n$ with smooth boundary, where $\chi>0$. An apparently novel type of generalized Solution framework is introduced within which an extension of previously known ranges for the key parameter $\chi$ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that\[ \chi < \left\{ \begin{array}{ll} \infty \qquad & \mbox{if } n=2, \sqrt{8} \qquad & \mbox{if } n=3, \frac{n}{n-2} \qquad & \mbox{if } n\ge 4, \end{array} \right. \] for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized Solution. This Solution inter alia has the property that \[ u\in L^1_{loc}(\bar\Omega\times [0,\infty)). \]
Haoxun Chen - One of the best experts on this subject based on the ideXlab platform.
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proportional egalitarian core Solution for profit allocation games with an application to collaborative transportation planning
European Journal of Industrial Engineering, 2015Co-Authors: Bo Dai, Haoxun ChenAbstract:For a profit allocation game, one key issue is to find a fair allocation of profit among its players. In this paper, a proportional egalitarian core Solution is proposed, which defines in the core of a game an allocation that takes account of each player’s contribution to the grand coalition. This Solution Concept generalises the egalitarian core Solution for cooperative games. To efficiently compute the new Solution, a row generation method is developed. The applicability of this new Solution Concept and the row generation method is demonstrated by an application to a carrier collaboration problem with numerical experiment results.
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proportional egalitarian core Solution for profit allocation games with an application to collaborative transportation planning
European Journal of Industrial Engineering, 2015Co-Authors: Bo Dai, Haoxun ChenAbstract:For a profit allocation game, one key issue is to find a fair allocation of profit among its players. In this paper, a proportional egalitarian core Solution is proposed, which defines in the core of a game an allocation that takes account of each player's contribution to the grand coalition. This Solution Concept generalises the egalitarian core Solution for cooperative games. To efficiently compute the new Solution, a row generation method is developed. The applicability of this new Solution Concept and the row generation method is demonstrated by an application to a carrier collaboration problem with numerical experiment results. [Received 12 November 2012; Revised 30 July 2013; Accepted 08 September 2013]
