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All Journal Indonesian Journal of Electrical Engineering and Computer Science
Muhammad Gulzar
Government College University Faisalabad

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Pythagorean fuzzy N-Soft groups M. Shazib Hameed; Salman Mukhtar; Haq Nawaz Khan; Shahbaz Ali; Muhammad Haris Mateen; Muhammad Gulzar
Indonesian Journal of Electrical Engineering and Computer Science Vol 21, No 2: February 2021
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v21.i2.pp1030-1038

Abstract

We elaborate in this paper a new structure pythagorean fuzzy $N$-soft groups which is the generalization of intuitionistic fuzzy soft group initiated by Karaaslan in 2013. In Pythagorean fuzzy N-soft sets concepts of fuzzy sets, soft sets, N-soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets are generalized. We also talk about some elementary basic concepts and operations on Pythagorean fuzzy N-soft sets with the assistance of illusions. We additionally define three different sorts of complements for Pythagorean fuzzy N-soft sets and examined a few outcomes not hold in Pythagorean fuzzy N-soft sets complements as they hold in crisp set hypothesis with the assistance of counter examples. We further talked about {$(\alpha, \beta, \gamma)$-cut of Pythagorean fuzzy N-soft set and their properties}. We likewise talk about some essential properties of Pythagorean fuzzy N-soft groups like groupoid, normal group, left and right cosets, $(\alpha, \beta,\gamma)$-cut subgroups and some fundamental outcomes identified with these terms. Pythagorean fuzzy N-soft sets is increasingly efficient and adaptable model to manage uncertainties. The proposed models of Pythagorean fuzzy N-soft groups can defeat a few disadvantages of the existing statures.
Certain properties of ω-Q-fuzzy subrings Dilshad Alghazzawi; Wafaa H. Hanoon; Muhammad Gulzar; Ghazanfar Abbas; Nasreen Kausar
Indonesian Journal of Electrical Engineering and Computer Science Vol 21, No 2: February 2021
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v21.i2.pp822-828

Abstract

In this paper, we define the fuzzy subring and discussed various fundamental aspects of fuzzy subrings. We introduce the concept of level subset of this new fuzzy set and prove that level subset of fuzzy subring form a ring. We define fuzzy ideal and show that set of all fuzzy cosets form a ring. Moreover, we investigate the properties of homomorphic image of fuzzy subring.
Co-Authors Dilshad Alghazzawi Ghazanfar Abbas Haq Nawaz Khan M. Shazib Hameed Muhammad Haris Mateen Nasreen Kausar Salman Mukhtar Shahbaz Ali Wafaa H. Hanoon