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Complex 𝑚-Polar Fuzzy 𝑁-Soft Model
Muhammad Akram and Maheen Sultan

This research article lays down the foundations of a novel model, namely, the complex 𝑚-polar fuzzy 𝑁-soft set. Both the vagueness of fuzzy sets and the multi-polarity of 𝑚-polar fuzzy 𝑁-soft sets are improved with the incorporation of two-dimensional complex membership degrees. This hybrid model is a response to the inefficiency of 𝑚-polar fuzzy 𝑁-soft sets and complex fuzzy 𝑁-soft sets to properly handle two-dimensional complex data and multi-polarity, respectively. We illustrate the main features of our model with two star ranking examples concerning the appointment of a professor among different candidates equipped with disparate qualities, and the selection of the best game from a catalogue. Furthermore, its elementary operations and their implications (like ring sum, product sum, scalar multiplication, different sorts of complements, union, intersection and threshold), are discussed in detail. These assets enable us to propose a multi-criteria group decision making technique for the new model.

Keywords: 𝑁-soft sets, 𝑚-polar fuzzy sets, complex 𝑚-polar fuzzy 𝑁-soft sets, decision making

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