{"title":"A Study on Hutchinson-Barnsley Theory in Product Intuitionistic Fuzzy Fractal Space","authors":"Mathavan Priya, Ramasamy Uthayakumar","doi":"10.26599/fie.2023.9270018","DOIUrl":null,"url":null,"abstract":"This work constitutes classical Hutchinson-Barnsley theory on the product intuitionistic fuzzy fractal space with the aid of iterated function system, in which a finite number of intuitionistic fuzzy <i>B</i>-contractions and intuitionistic fuzzy Edelstein contractions are enclosed. A fixed point theorem is exhibited by proving that the Hutchinson-Barnsley operator is an intuitionistic fuzzy <i>B</i>-contraction and intuitionistic fuzzy Edelstein contraction. To show the primary goal of the article, the Hausdorff product intuitionistic fuzzy metric space is constructed, then the notion of product intuitionistic fuzzy metric space on complete and compact spaces in the sense of intuitionistic fuzzy <i>B</i>-contraction and the intuitionistic fuzzy Edelstein contraction are defined.","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.2023.9270018","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: 0
Abstract
This work constitutes classical Hutchinson-Barnsley theory on the product intuitionistic fuzzy fractal space with the aid of iterated function system, in which a finite number of intuitionistic fuzzy B-contractions and intuitionistic fuzzy Edelstein contractions are enclosed. A fixed point theorem is exhibited by proving that the Hutchinson-Barnsley operator is an intuitionistic fuzzy B-contraction and intuitionistic fuzzy Edelstein contraction. To show the primary goal of the article, the Hausdorff product intuitionistic fuzzy metric space is constructed, then the notion of product intuitionistic fuzzy metric space on complete and compact spaces in the sense of intuitionistic fuzzy B-contraction and the intuitionistic fuzzy Edelstein contraction are defined.
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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