{"title":"Hesitant Fuzzy Graphs and Their Products","authors":"M. Javaid, Agha Kashif, T. Rashid","doi":"10.1080/16168658.2020.1817658","DOIUrl":null,"url":null,"abstract":"In this article, the notion of hesitant fuzzy graph is introduced. It an extended structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with the system that is designed using fuzzy graphs. Several operations on hesitant fuzzy graphs are defined, namely Cartesian product, composition, tensor product and normal product. Furthermore, the relationship between the degree of vertices of the hesitant fuzzy graphs and the hesitant fuzzy graph obtained by their different products is developed. These operations are highly used in computer science, geometry, algebra, operations research, etc.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"33 1","pages":"238 - 252"},"PeriodicalIF":1.3000,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Information and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/16168658.2020.1817658","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 7
Abstract
In this article, the notion of hesitant fuzzy graph is introduced. It an extended structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with the system that is designed using fuzzy graphs. Several operations on hesitant fuzzy graphs are defined, namely Cartesian product, composition, tensor product and normal product. Furthermore, the relationship between the degree of vertices of the hesitant fuzzy graphs and the hesitant fuzzy graph obtained by their different products is developed. These operations are highly used in computer science, geometry, algebra, operations research, etc.
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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