# $(3, 4)$-fuzzy sets and their topological spaces

Volume 28, Issue 2, pp 158--170
Publication Date: May 14, 2022 Submission Date: March 03, 2022 Revision Date: April 07, 2022 Accteptance Date: April 16, 2022
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### Authors

Kh. Kh. Murad - Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Kurdistan Region, Iraq. H. Z. Ibrahim - Department of Mathematics, Faculty of Education, University of Zakho, Zakho, Kurdistan Region, Iraq.

### Abstract

The aim of this paper is to introduce the concept of $(3, 4)$-fuzzy sets. We compare $(3, 4)$-fuzzy sets with intuitionistic fuzzy sets, Pythagorean fuzzy sets, and Fermatean fuzzy sets. We focus on the complement of $(3, 4)$-fuzzy sets. We construct some of the fundamental set of operations of the $(3, 4)$-fuzzy sets. Due to their larger range of describing membership grades, $(3, 4)$-fuzzy sets can deal with more uncertain situations than other types of fuzzy sets. For ranking $(3, 4)$-fuzzy sets, we define a score function and an accuracy function. In addition, we introduce the concept of $(3, 4)$-fuzzy topological space. Ultimately, we define $(3, 4)$-fuzzy continuity of a map defined between $(3, 4)$-fuzzy topological spaces and we characterize this concept.

### Share and Cite

##### ISRP Style

Kh. Kh. Murad, H. Z. Ibrahim, $(3, 4)$-fuzzy sets and their topological spaces, Journal of Mathematics and Computer Science, 28 (2023), no. 2, 158--170

##### AMA Style

Murad Kh. Kh., Ibrahim H. Z., $(3, 4)$-fuzzy sets and their topological spaces. J Math Comput SCI-JM. (2023); 28(2):158--170

##### Chicago/Turabian Style

Murad, Kh. Kh., Ibrahim, H. Z.. "$(3, 4)$-fuzzy sets and their topological spaces." Journal of Mathematics and Computer Science, 28, no. 2 (2023): 158--170

### Keywords

• $(3, 4)$-fuzzy sets
• operations
• $(3, 4)$-fuzzy topology
• $(3, 4)$-fuzzy continuous

•  94D05
•  03E72

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