Abstract
The primary aim of this article is to extend the bipolar fuzzy N -soft sets with the concern of pursuing the periodicity involved real-world problems and introduce a new multiskilled hybrid model, namely, complex bipolar fuzzy N -soft sets. The novel model possesses the parametric characteristics of the versatile N -soft set and enjoys the distinguished attributes of a complex bipolar fuzzy set to handle the double-sided periodic vague data. We illustrate that the innovative model assists as a proficient mechanism for grading-based parameterized two-dimensional bipolar fuzzy information. We present some elementary operations and results for a complex bipolar fuzzy N -soft environment. Further, we establish the three dexterous algorithms to find the optimal solution to multiattribute decision-making problems. Moreover, the algorithms are supported with the robust assessment of a real-world application. Lastly, a comparison with existent decision-making techniques, such as choice values, weighted choice values, and D -choice of values of bipolar fuzzy N -soft sets, is also conducted to manifest the phenomenal accountability and authenticity of the presented decision-making approaches.
Highlights
E primary aim of this article is to extend the bipolar fuzzy N-soft sets with the concern of pursuing the periodicity involved realworld problems and introduce a new multiskilled hybrid model, namely, complex bipolar fuzzy N-soft sets. e novel model possesses the parametric characteristics of the versatile N-soft set and enjoys the distinguished attributes of a complex bipolar fuzzy set to handle the double-sided periodic vague data
Among many other extensions of CFS, our focus is on complex bipolar fuzzy sets (CBFS), which was initiated by Akram et al [5]. e rationale of CBFS is to represent the bipolar information having vagueness and periodicity in complex geometry, as shown in Figures 1 and 2
It is superior to the existing bipolar fuzzy NSfS (BFNSfS) as it deals with periodic information
Summary
We will present some fundamental definitions that are essential for further developments. Definition 2.2 (see [3]) Let V be a nonempty set. Let V be a universe of discourse and A be the set of all attributes, L⊆A. Let V be a universe of discourse under consideration and A be the set of all attributes, L⊆A. A pair (℘, L) is called BFSfS over V if ℘: L ⟶ BFV, where BFV is the collection of all bipolar fuzzy subsets of V. Αpl ∈ [0, 1] and βnl ∈ [− 1, 0] for all v ∈ V
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