Abstract
In this paper, we introduce the notions of Pythagorean fuzzy strong bi-ideals and Direct Product Pythagorean fuzzy ideals in near ring. Also, study some of their related properties in detail.
Highlights
The concept of fuzzy set was first proposed by Zadeh [16] in 1965 and fuzzy subgroup was presented by Rosenfeld [13]
The notions of fuzzy sub near ring, fuzzy ideal and fuzzy N-subgroup of a near ring was introduced by Salah Abou-Zaid [1] and it has been studied by several authors (Kim and Jun [9], [8]; Narayanan [11]; Narayanan and Manikandan [12]; Saikia and Barthakur [14]; Kim and Kim [7], respectively)
Pythagorean fuzzy set was introduced by Yager [15] in 2013
Summary
The concept of fuzzy set was first proposed by Zadeh [16] in 1965 and fuzzy subgroup was presented by Rosenfeld [13]. In Liu [10] introduced the notion of fuzzy ideal of a ring. The concept of intuitionistic fuzzy set was introduced by Atanassov [2] as a generalisation of fuzzy set. This concept was further discussed by Dutta and Biswas [5]. Devi et al [4] studied the intuitionistic fuzzy strong bi-ideal of near ring. Pythagorean Fuzzy Strong Bi-ideal and Direct Product. We introduce the concept of a Pythagorean fuzzy strong bi-ideal of a near ring and direct product of Pythagorean fuzzy ideal in near ring. We establish that every Pythagorean fuzzy left N-subgroup or Pythagorean fuzzy left ideal of a near ring is a Pythagorean fuzzy strong bi-ideal of a near ring and direct product of Pythagorean fuzzy ideals in the near ring and we establish that every Pythagorean left permutable fuzzy right N-subgroup or Pythagorean left permutable fuzzy right ideal of the near ring is a Pythagorean fuzzy strong fuzzy bi-ideal of the near ring
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