A Fast Approach to Bimatrix Games with Intuitionistic Fuzzy Payoffs

The aim of this paper is to develop an effective method for solving bimatrix games with payoffs of intuitionistic fuzzy value. Firstly, bimatrix game model with intuitionistic fuzzy payoffs (IFPBiG) was put forward. Secondly, two kinds of nonlinear programming algorithms were discussed with the Nash equilibrium of IFPBiG. Thirdly, Nash equilibrium of the algorithm was proved by the fixed point theory and the algorithm was simplified by linear programming methods. Finally, an example was solved through Matlab; it showed the validity, applicability, and superiority.

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A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers

Journal of Applied Mathematics ◽

10.1155/2013/697261 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Deng-Feng Li ◽

Jie Yang

Keyword(s):

Nash Equilibrium ◽

Equilibrium Solution ◽

Fuzzy Numbers ◽

Order Relation ◽

Bilinear Programming ◽

Bimatrix Games ◽

Bimatrix Game ◽

Intuitionistic Fuzzy Numbers ◽

Intuitionistic Fuzzy ◽

Trapezoidal Intuitionistic Fuzzy Numbers

The aim of this paper is to develop a bilinear programming method for solving bimatrix games in which the payoffs are expressed with trapezoidal intuitionistic fuzzy numbers (TrIFNs), which are called TrIFN bimatrix games for short. In this method, we define the value index and ambiguity index for a TrIFN and propose a new order relation of TrIFNs based on the difference index of value index to ambiguity index, which is proven to be a total order relation. Hereby, we introduce the concepts of solutions of TrIFN bimatrix games and parametric bimatrix games. It is proven that any TrIFN bimatrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bimatrix game. The latter can be obtained through solving the auxiliary parametric bilinear programming model. The method proposed in this paper is demonstrated with a real example of the commerce retailers’ strategy choice problem.

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Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

Georgian Mathematical Journal ◽

10.1515/gmj-2021-2102 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Alberto Cabada ◽

Om Kalthoum Wanassi

Keyword(s):

Existence And Uniqueness ◽

Fixed Point Theory ◽

Mixed Boundary ◽

Point Theory ◽

Uniqueness Of Solutions ◽

Nonlinear Part ◽

Banach Contraction ◽

Fractional Differential ◽

Exhaustive Study ◽

The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

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On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

Open Mathematics ◽

10.1515/math-2021-0069 ◽

2021 ◽

Vol 19 (1) ◽

pp. 760-772

Author(s):

Ahmed Alsaedi ◽

Bashir Ahmad ◽

Badrah Alghamdi ◽

Sotiris K. Ntouyas

Keyword(s):

Nonlinear System ◽

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Fixed Point Theory ◽

Point Theory ◽

Numerical Examples ◽

Multipoint Boundary ◽

Multipoint Boundary Conditions ◽

Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

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Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0126 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Mudasir Younis ◽

Deepak Singh ◽

Ishak Altun ◽

Varsha Chauhan

Keyword(s):

Metric Spaces ◽

Fixed Point Theory ◽

Directed Graphs ◽

Point Theory ◽

Graph Structure ◽

Open Ball ◽

Open Problems ◽

Graphical Structure ◽

State Of Art ◽

Transverse Oscillations

Abstract The purpose of this article is to present the notion of graphical extended b-metric spaces, blending the concepts of graph theory and metric fixed point theory. We discuss the structure of an open ball of the new proposed space and elaborate on the newly introduced ideas in a novel way by portraying suitably directed graphs. We also provide some examples in graph structure to show that our results are sharp as compared to the results in the existing state-of-art. Furthermore, an application to the transverse oscillations of a homogeneous bar is entrusted to affirm the applicability of the established results. Additionally, we evoke some open problems for enthusiastic readers for the future aspects of the study.

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Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2018074 ◽

2019 ◽

Vol 14 (3) ◽

pp. 311 ◽

Cited By ~ 39

Author(s):

Muhammad Altaf Khan ◽

Zakia Hammouch ◽

Dumitru Baleanu

Keyword(s):

Fixed Point ◽

Existence And Uniqueness ◽

Numerical Scheme ◽

Arbitrary Order ◽

Fixed Point Theory ◽

Hepatitis E ◽

Point Theory ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

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Modeling of assembly systems with complex structures for throughput analysis during transients

Assembly Automation ◽

10.1108/aa-12-2017-172 ◽

2019 ◽

Vol 39 (2) ◽

pp. 262-271

Author(s):

Yukan Hou ◽

Yuan Li ◽

Yuntian Ge ◽

Jie Zhang ◽

Shoushan Jiang

Keyword(s):

Steady State ◽

Fixed Point Theory ◽

Point Theory ◽

Assembly Systems ◽

Complex Structures ◽

Throughput Performance ◽

Throughput Analysis ◽

Content Type ◽

Serial Production Lines ◽

Transient And Steady State

Purpose The purpose of this paper is to present an analytical method for throughput analysis of assembly systems with complex structures during transients. Design/methodology/approach Among the existing studies on the performance evaluation of assembly systems, most focus on the system performance in steady state. Inspired by the transient analysis of serial production lines, the state transition matrix is derived considering the characteristics of merging structure in assembly systems. The system behavior during transients is described by an ergodic Markov chain, with the states being the occupancy of all buffers. The dynamic model for the throughput analysis is solved using the fixed-point theory. Findings This method can be used to predict and evaluate the throughput performance of assembly systems in both transient and steady state. By comparing the model calculation results with the simulation results, this method is proved to be accurate. Originality/value This proposed modeling method can depict the throughput performance of assembly systems in both transient and steady state, whereas most exiting methods can be used for only steady-state analysis. In addition, this method shows the potential for the analysis of complex structured assembly systems owing to the low computational complexity.

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