{"title":"论模糊环境中参数广义多目标博弈解图的半连续性和连续性","authors":"Nguyen Van Hung","doi":"10.1016/j.cam.2024.116303","DOIUrl":null,"url":null,"abstract":"<div><div>The purpose of this article is to study new results on the continuity of solution maps for parametric generalized multiobjective games in fuzzy environments. Firstly, we revisit parametric fuzzy generalized multiobjective games. Secondly, we establish some sufficient conditions for upper semi-continuity, Hausdorff upper semi-continuity, closedness and compactness of solution maps for such problem under suitable conditions. Thirdly, we introduce the auxiliary problem of parametric fuzzy generalized multiobjective games and the concept of strong <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>-convexity of objective functions for these problems. Finally, results on the lower semi-continuity, Hausdorff lower semi-continuity, continuity and Hausdorff continuity of solution maps to parametric generalized multiobjective games in fuzzy environments are established and studied. Many examples are given to illustrate our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"457 ","pages":"Article 116303"},"PeriodicalIF":2.6000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On semi-continuity and continuity of solution maps of parametric generalized multiobjective games in fuzzy environments\",\"authors\":\"Nguyen Van Hung\",\"doi\":\"10.1016/j.cam.2024.116303\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The purpose of this article is to study new results on the continuity of solution maps for parametric generalized multiobjective games in fuzzy environments. Firstly, we revisit parametric fuzzy generalized multiobjective games. Secondly, we establish some sufficient conditions for upper semi-continuity, Hausdorff upper semi-continuity, closedness and compactness of solution maps for such problem under suitable conditions. Thirdly, we introduce the auxiliary problem of parametric fuzzy generalized multiobjective games and the concept of strong <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>-convexity of objective functions for these problems. Finally, results on the lower semi-continuity, Hausdorff lower semi-continuity, continuity and Hausdorff continuity of solution maps to parametric generalized multiobjective games in fuzzy environments are established and studied. Many examples are given to illustrate our results.</div></div>\",\"PeriodicalId\":50226,\"journal\":{\"name\":\"Journal of Computational and Applied Mathematics\",\"volume\":\"457 \",\"pages\":\"Article 116303\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2025-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S037704272400551X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/10/5 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037704272400551X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/5 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
On semi-continuity and continuity of solution maps of parametric generalized multiobjective games in fuzzy environments
The purpose of this article is to study new results on the continuity of solution maps for parametric generalized multiobjective games in fuzzy environments. Firstly, we revisit parametric fuzzy generalized multiobjective games. Secondly, we establish some sufficient conditions for upper semi-continuity, Hausdorff upper semi-continuity, closedness and compactness of solution maps for such problem under suitable conditions. Thirdly, we introduce the auxiliary problem of parametric fuzzy generalized multiobjective games and the concept of strong -convexity of objective functions for these problems. Finally, results on the lower semi-continuity, Hausdorff lower semi-continuity, continuity and Hausdorff continuity of solution maps to parametric generalized multiobjective games in fuzzy environments are established and studied. Many examples are given to illustrate our results.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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