Affiliations: [a] Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan
| [b] School of Science, Xi’an Polytechnic University, Xi’an, China
| [c] School of Mathematics, Northwest University, Xi’an, China
| [d] Govt, Girls Degree College Khwazakhela Swat, Pakistan
| [e] Govt, Girls Degree College Madyan Swat, Pakistan
Correspondence:
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Corresponding author. Xiao Long Xin. E-mail: xlxin@nwu.edu.cn.
Abstract: In multiple criteria decision making (MCDM) problem, the decision maker deal with a situation where the sum of membership and non-membership grade of an attributes does not belongs to [0, 1]. To avoid such a situation, we proposed a new type of fuzzy system known as fermatean fuzzy system. More precisely, we presented the notion of fermatean fuzzy ideal theory and rough fermatean fuzzy sets in semigroups. The idea of lower and upper approximation in fermatean fuzzy sets has been initiated. The study has been further extended to rough fermatean fuzzy left(resp. right, interior) ideals in semigroup. Several results related to this notion are determined.
