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Mathematics
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Uncertain System Optimization and Games
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Uncertain System Optimization and Games

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (15 December 2023) | Viewed by 7265

Special Issue Editors

Prof. Dr. Jinwu Gao

E-Mail Website
Guest Editor
School of Economics, Ocean University of China, Qingdao 266100, China
Interests: uncertainty theory; uncertain system optimization; uncertain game
Dr. Jin Liu

E-Mail Website
Guest Editor
College of System Engineering, National University of Defense Technology, Changsha 410073, China
Interests: game theory; credibilistic game; uncertain differential equation
Dr. Yuefen Chen

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
Interests: uncertain optimal control; uncertain programming
Dr. Guoqing Yang

E-Mail Website
Guest Editor
School of Management, Hebei University, Baoding 071002, China
Interests: uncertain programming; game theory; robust optimization

Special Issue Information

Dear Colleagues,

Nowadays, uncertainty theory has become a new branch of mathematics for modeling indeterminate phenomena, based on normality, duality, subadditivity, and product axioms. It has been applied to analyze uncertain optimization, uncertain games, uncertain differential games, and uncertain finance, etc.

The aim of this Special Issue is to attract leading researchers in these areas, in order to collate the recent advances in uncertain optimization and games, from both a theoretical and an applied point of view. All articles related to uncertain optimization and games are invited for submission for inclusion in this Special Issue.

Prof. Dr. Jinwu Gao
Dr. Jin Liu
Dr. Yuefen Chen
Dr. Guoqing Yang
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • uncertain optimization
  • uncertain statistics
  • uncertain optimal control
  • uncertain differential games
  • uncertain finance
  • uncertain supply chain
  • uncertain optimization applications
  • optimization under uncertainty
  • decision-making under uncertainty
  • uncertain games
  • stochastic programming
  • stochastic optimization problems
  • game theory

Published Papers (5 papers)

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Research

25 pages, 579 KiB  
Article
Optimization and Coordination of the Fresh Agricultural Product Supply Chain Considering the Freshness-Keeping Effort and Information Sharing
by Jinwu Gao, Zhuolin Cui, Huijie Li and Ruru Jia
Mathematics 2023, 11(8), 1922; https://doi.org/10.3390/math11081922 - 19 Apr 2023
Cited by 5 | Viewed by 1321
Abstract
To solve freshness-keeping problems and analyse a retailer’s information sharing strategies in the fresh agricultural product supply chain (FAPSC), often confronted with challenges in keeping agri-products fresh in an uncertain market, we study an FAPSC via a decentralized mode in which the supplier [...] Read more.
To solve freshness-keeping problems and analyse a retailer’s information sharing strategies in the fresh agricultural product supply chain (FAPSC), often confronted with challenges in keeping agri-products fresh in an uncertain market, we study an FAPSC via a decentralized mode in which the supplier or retailer exerts the freshness-keeping effort while the retailer decides its information sharing strategies regarding private demand forecasting. We consider a contract coordination mode including three incentive contracts, cost-sharing (cs), revenue-sharing (re) and revenue-and-cost-sharing (rc), to facilitate supply chain coordination. The results show that, as opposed to the case where the supplier takes on the freshness-keeping effort, the optimal freshness-keeping effort level, wholesale price and retail price are not only affected by the retailer’s information sharing strategy but also the freshness-keeping efficiency as the retailer exerts the freshness-keeping effort. Regarding the information sharing strategy, when the freshness-keeping effort is undertaken by the retailer, sharing information sometimes benefits the supplier; however, information sharing is never preferable for the retailer. Consequently, it is necessary to explore the supply chain coordination mode via effective incentive contracts which can improve the supplier and retailer’s profit. We also numerically analyze the effects of freshness-keeping efficiency on equilibrium decisions and expected profits in the decentralized mode, and the effects of the three contract parameters on the expected profits in equilibrium in the coordination mode. Full article
(This article belongs to the Special Issue Uncertain System Optimization and Games)
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20 pages, 4208 KiB  
Article
Research on Location Selection for Urban Networks of Less-than-Truckload Express Enterprises Based on Improved Immune Optimization Algorithm
by Kangye Tan, Fang Xu, Xiaozhao Fang and Chunsheng Li
Mathematics 2023, 11(6), 1543; https://doi.org/10.3390/math11061543 - 22 Mar 2023
Cited by 2 | Viewed by 2162
Abstract
With the transformation and upgrading of the world economy entering a new normal, changes in the fields of industry and consumption have brought new business opportunities, and there is a large space for the less-than-truckload (LTL) express market. Considering the urban network resource [...] Read more.
With the transformation and upgrading of the world economy entering a new normal, changes in the fields of industry and consumption have brought new business opportunities, and there is a large space for the less-than-truckload (LTL) express market. Considering the urban network resource operation status, this study aims to solve the optimization problem of urban location selection for LTL express under the common delivery model. To minimize the total cost of logistics and distribution, we established an integer programming model with constraints such as radiation range and service-capacity limitations. A model with a fixed reality-node strategy, an expanded initial antibody group strategy, improved traditional elite individual retention strategy and a node-clustering strategy was introduced. An improved immune optimization algorithm was further designed to obtain globally optimal solutions. With the comparison of existing algorithms, the results verified the practicability of the proposed model to solve the urban location-selection problems for LTL express. We then conducted an empirical analysis of a real-world enterprise’s reasonable urban network location selection in a central-south city of China. The simulation results further verified the effectiveness of our proposed algorithm. This study provides new solutions and methods for resource utilization and urban network optimization of LTL-express enterprises. Full article
(This article belongs to the Special Issue Uncertain System Optimization and Games)
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13 pages, 1358 KiB  
Article
The New Solution Concept to Ill-Posed Bilevel Programming: Non-Antagonistic Pessimistic Solution
by Xiang Li, Tiesong Hu, Xin Wang, Ali Mahmoud and Xiang Zeng
Mathematics 2023, 11(6), 1422; https://doi.org/10.3390/math11061422 - 15 Mar 2023
Viewed by 1110
Abstract
It is hardly realistic to assume that, under all decision circumstances, followers will always choose a solution that leads to the worst upper-level objective functional value. However, this generally accepted concept of the pessimistic solution to the ill-posed bilevel programming problems may lead [...] Read more.
It is hardly realistic to assume that, under all decision circumstances, followers will always choose a solution that leads to the worst upper-level objective functional value. However, this generally accepted concept of the pessimistic solution to the ill-posed bilevel programming problems may lead to the leader’s attitude being more pessimistic vis à vis his anticipation of the follower’s decision being non-antagonistic. It will result in a wrong pessimistic solution and a greater potential of cooperation space between the leader and the followers. This paper presents a new concept of a non-antagonistic pessimistic solution with four numerical examples for bilevel programming problems from a non-antagonistic point of view. We prove that the objective function value of the non-antagonistic pessimistic solution generally dominates or is equal to the objective functional value of the pessimistic solution and the rewarding solution, and the maximum potential space for leader-follower cooperation can be overestimated in a generally applied pessimistic solution. Our research extends the concept of the pessimistic solution. It also sheds light on the insights that the non-antagonistic pessimistic solution can describe the practical potential of cooperation space between the leader and followers in non-antagonistic circumstances. Full article
(This article belongs to the Special Issue Uncertain System Optimization and Games)
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13 pages, 298 KiB  
Article
A Note on Type-Symmetries in Finite Games
by Renato Soeiro and Alberto A. Pinto
Mathematics 2022, 10(24), 4696; https://doi.org/10.3390/math10244696 - 11 Dec 2022
Viewed by 676
Abstract
In two-action generalized polymatrix games, Nash equilibria are support-type-symmetric, i.e., determined by supports for each type of player. We show that such a property does not generalize straightforwardly for games with at least three actions or where interaction weights have different signs (neither [...] Read more.
In two-action generalized polymatrix games, Nash equilibria are support-type-symmetric, i.e., determined by supports for each type of player. We show that such a property does not generalize straightforwardly for games with at least three actions or where interaction weights have different signs (neither all positive nor negative). A non-trivial condition on interaction weights must be satisfied, which may go unnoticed as it is trivially satisfied for: (i) two-action games, (ii) conformity games, and (iii) congestion games. We derive this condition and the corresponding simplified analytic equation for mixed strategies. Full article
(This article belongs to the Special Issue Uncertain System Optimization and Games)
16 pages, 2738 KiB  
Article
Negative Feedback Punishment Approach Helps Sanctioning Institutions Achieve Stable, Time-Saving and Low-Cost Performances
by Jun Qian, Xiao Sun, Ziyang Wang and Yueting Chai
Mathematics 2022, 10(15), 2823; https://doi.org/10.3390/math10152823 - 08 Aug 2022
Viewed by 1203
Abstract
Sanctioning institutions widely exist in human society. Although these institutions play an important role in the management of social affairs, sanctions are often seen to be costly in terms of both time and money. To enable sanctioning institutions to develop effective sanctions, we [...] Read more.
Sanctioning institutions widely exist in human society. Although these institutions play an important role in the management of social affairs, sanctions are often seen to be costly in terms of both time and money. To enable sanctioning institutions to develop effective sanctions, we propose a negative feedback punishment approach for these institutions that combines the feedback control principle and the negative correlation principle. In the negative feedback punishment approach, the punishment intensity imposed on the group is negatively correlated with the current group cooperation proportion. Through evolutionary simulation and theoretical analysis, we found that the negative feedback punishment approach facilitates more stable, time-saving and low-cost performance by sanctioning institutions than other punishment methods. This work offers a feasible solution for sanctioning institutions to solve social dilemmas and provides a possible theoretical starting point for investigating effective pool punishment measures. Full article
(This article belongs to the Special Issue Uncertain System Optimization and Games)
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