{"title":"有向粗糙模糊图中的若干概念及其在公司合并中的应用","authors":"Iqra Nawaz, Uzma Ahmad","doi":"10.26599/fie.2023.9270019","DOIUrl":null,"url":null,"abstract":"A directed rough fuzzy graph (DRFG) is a unique and innovative hybrid model because it deals with more complex problems of uncertainty in the presence of incomplete data information or rough universe. A DRFG can be obtained from two given DRFGs by union, Cartesian product and composition. When we study operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG presents a confusing picture. Therefore, a mechanism for determining the degree of vertices for DRFG operations is needed. The main objective of this study is to analyze and investigate the degree of vertices in DRFGs formed by certain operations, which will provide clear explanations of operations on DRFGs and their effects on vertex degrees with examples. In this paper, we find the degree of a vertex in DRFGs formed by these operations in terms of the degree of vertices in the given DRFGs in some special cases. We explain these operations with some examples. In addition, we provide an application to the corporate merger problem to test our approach and obtain an optimal result. We have developed two algorithms to elaborate the procedure for our application. Finally, we created a comparison table comparing our results for Algorithms 1 and 2 for the same enterprise merger network.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"25 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Certain Concepts in Directed Rough Fuzzy Graphs and Application to Mergers of Companies\",\"authors\":\"Iqra Nawaz, Uzma Ahmad\",\"doi\":\"10.26599/fie.2023.9270019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A directed rough fuzzy graph (DRFG) is a unique and innovative hybrid model because it deals with more complex problems of uncertainty in the presence of incomplete data information or rough universe. A DRFG can be obtained from two given DRFGs by union, Cartesian product and composition. When we study operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG presents a confusing picture. Therefore, a mechanism for determining the degree of vertices for DRFG operations is needed. The main objective of this study is to analyze and investigate the degree of vertices in DRFGs formed by certain operations, which will provide clear explanations of operations on DRFGs and their effects on vertex degrees with examples. In this paper, we find the degree of a vertex in DRFGs formed by these operations in terms of the degree of vertices in the given DRFGs in some special cases. We explain these operations with some examples. In addition, we provide an application to the corporate merger problem to test our approach and obtain an optimal result. We have developed two algorithms to elaborate the procedure for our application. Finally, we created a comparison table comparing our results for Algorithms 1 and 2 for the same enterprise merger network.\",\"PeriodicalId\":37623,\"journal\":{\"name\":\"Fuzzy Information and Engineering\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fuzzy Information and Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26599/fie.2023.9270019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Information and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26599/fie.2023.9270019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Certain Concepts in Directed Rough Fuzzy Graphs and Application to Mergers of Companies
A directed rough fuzzy graph (DRFG) is a unique and innovative hybrid model because it deals with more complex problems of uncertainty in the presence of incomplete data information or rough universe. A DRFG can be obtained from two given DRFGs by union, Cartesian product and composition. When we study operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG presents a confusing picture. Therefore, a mechanism for determining the degree of vertices for DRFG operations is needed. The main objective of this study is to analyze and investigate the degree of vertices in DRFGs formed by certain operations, which will provide clear explanations of operations on DRFGs and their effects on vertex degrees with examples. In this paper, we find the degree of a vertex in DRFGs formed by these operations in terms of the degree of vertices in the given DRFGs in some special cases. We explain these operations with some examples. In addition, we provide an application to the corporate merger problem to test our approach and obtain an optimal result. We have developed two algorithms to elaborate the procedure for our application. Finally, we created a comparison table comparing our results for Algorithms 1 and 2 for the same enterprise merger network.
期刊介绍：
Fuzzy Information and Engineering—An International Journal wants to provide a unified communication platform for researchers in a wide area of topics from pure and applied mathematics, computer science, engineering, and other related fields. While also accepting fundamental work, the journal focuses on applications. Research papers, short communications, and reviews are welcome. Technical topics within the scope include: (1) Fuzzy Information a. Fuzzy information theory and information systems b. Fuzzy clustering and classification c. Fuzzy information processing d. Hardware and software co-design e. Fuzzy computer f. Fuzzy database and data mining g. Fuzzy image processing and pattern recognition h. Fuzzy information granulation i. Knowledge acquisition and representation in fuzzy information (2) Fuzzy Sets and Systems a. Fuzzy sets b. Fuzzy analysis c. Fuzzy topology and fuzzy mapping d. Fuzzy equation e. Fuzzy programming and optimal f. Fuzzy probability and statistic g. Fuzzy logic and algebra h. General systems i. Fuzzy socioeconomic system j. Fuzzy decision support system k. Fuzzy expert system (3) Soft Computing a. Soft computing theory and foundation b. Nerve cell algorithms c. Genetic algorithms d. Fuzzy approximation algorithms e. Computing with words and Quantum computation (4) Fuzzy Engineering a. Fuzzy control b. Fuzzy system engineering c. Fuzzy knowledge engineering d. Fuzzy management engineering e. Fuzzy design f. Fuzzy industrial engineering g. Fuzzy system modeling (5) Fuzzy Operations Research [...] (6) Artificial Intelligence [...] (7) Others [...]
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