Near Rings in the View of Double-Framed Soft Fuzzy Sets

KHAN, Mohammed Bilal; ÇETKİN, Vildan; MAHMOOD, Tahir; JAN, Naeem; ULLAH, Kifayat; AYGÜN, Halis

Near Rings in the View of Double-Framed Soft Fuzzy Sets

Mohammed Bilal KHAN ¹

, Vildan ÇETKİN ²

, Tahir MAHMOOD ¹

, Naeem JAN ¹

, Kifayat ULLAH ¹

, Halis AYGÜN ²

¹Department of Mathematics and Statistics International Islamic University, Islamabad, PAKISTAN
²Department of Mathematics, Kocaeli University, KOCAELI

Sigma J Eng Nat Sci 2019; 37(1): 175-186

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Abstract

In this study, we aim to consider a new kind of a set called by a double framed soft fuzzy set, which is convenient to handle the real world applications and to investigate the near rings in the view of this new set. We define some of the elementary set operations of double framed soft fuzzy sets. We propose the notion of double framed soft fuzzy near rings (ideals) with several properties and characteristics. Further, we illustrate the given notions with some examples.

Keywords: Fuzzy set, soft set, double framed soft fuzzy set, near ring, ideal, homomorphism.