{"title":"A Study of (T, N)– and (N ′, T, N)– Implications","authors":"Dimitrios S. Grammatikopoulos, B. Papadopoulos","doi":"10.1080/16168658.2021.1937903","DOIUrl":null,"url":null,"abstract":"In this paper, we revisit and study the basic properties of two families of fuzzy implications, the so-called and implications. More specific, we study when these fuzzy implications satisfy, or not, the neutrality property , the exchange principle , the identity principle and the ordering property . Moreover, a study is presented for the law of importation with respect to a t- norm. Also, we study the relation of conjugation in implications.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"59 1","pages":"277 - 295"},"PeriodicalIF":1.3000,"publicationDate":"2021-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Information and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/16168658.2021.1937903","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: 5
Abstract
In this paper, we revisit and study the basic properties of two families of fuzzy implications, the so-called and implications. More specific, we study when these fuzzy implications satisfy, or not, the neutrality property , the exchange principle , the identity principle and the ordering property . Moreover, a study is presented for the law of importation with respect to a t- norm. Also, we study the relation of conjugation in implications.
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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