Picture fuzzy sets in UP-algebras by means of a special type

Volume 25, Issue 1, pp 37--72 http://dx.doi.org/10.22436/jmcs.025.01.05
Publication Date: May 04, 2021 Submission Date: March 14, 2021 Revision Date: April 02, 2021 Accteptance Date: April 07, 2021

Authors

Sunisa Yuphaphin - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Pimwaree Kankaew - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Nattacha Lapo - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Ronnason Chinram - Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. Aiyared Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand.


Abstract

The concept of picture fuzzy sets was first introduced by Cuong and Kreinovich [B. C. Cuong, V. Kreinovich, Proceedings of the Third World Congress on Information and Communication Technologies WIICT, (2013), 1--6] in 2013, which is direct extensions of the fuzzy sets and the intuitionistic fuzzy sets. In this paper, we applied the concept of picture fuzzy sets in UP-algebras to introduce the eight new concepts of picture fuzzy sets by means of a special type: special picture fuzzy UP-subalgebras, special picture fuzzy near UP-filters, special picture fuzzy UP-filters, special picture fuzzy implicative UP-filters, special picture fuzzy comparative UP-filters, special picture fuzzy shift UP-filters, special picture fuzzy UP-ideals, and special picture fuzzy strong UP-ideals. Also, we discuss the relationship between the eight new concepts of picture fuzzy sets in UP-algebras. This idea is extended to the lower and upper level subsets of picture fuzzy sets in UP-algebras. Moreover, we define a picture fuzzy set in the same way as a characteristic function and study its characterizations from the related subset.


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ISRP Style

Sunisa Yuphaphin, Pimwaree Kankaew, Nattacha Lapo, Ronnason Chinram, Aiyared Iampan, Picture fuzzy sets in UP-algebras by means of a special type, Journal of Mathematics and Computer Science, 25 (2022), no. 1, 37--72

AMA Style

Yuphaphin Sunisa, Kankaew Pimwaree, Lapo Nattacha, Chinram Ronnason, Iampan Aiyared, Picture fuzzy sets in UP-algebras by means of a special type. J Math Comput SCI-JM. (2022); 25(1):37--72

Chicago/Turabian Style

Yuphaphin, Sunisa, Kankaew, Pimwaree, Lapo, Nattacha, Chinram, Ronnason, Iampan, Aiyared. "Picture fuzzy sets in UP-algebras by means of a special type." Journal of Mathematics and Computer Science, 25, no. 1 (2022): 37--72


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