In this paper, we introduce idea of complex fuzzy subfield and discuss its various algebraic aspects. We prove that every complex fuzzy subfield generate two fuzzy fields and shows that intersection of two complex fuzzy subfields is also complex fuzzy subfields. We also present the concept of level subsets of complex fuzzy subfield and shows that level subset of complex fuzzy subfield form subfield. Furthermore, we extend this idea to define the notion of the direct product of two complex fuzzy subfields and also investigate the homomorphic image and inverse image of complex fuzzy subfield.
Unpredictability and fuzziness coexist in decision-making analysis due to the complexity of the decision-making environment. “Pythagorean fuzzy numbers” (PFNs) outperform “intuitionistic fuzzy numbers” (IFNs) when dealing with unclear data. The “Pythagorean fuzzy set” (PFS) is a useful tool because it removes the restriction that the sum of membership degrees be less than or equal to one by substituting the square sum for the sum of membership degrees. This study proposes two aggregating operators (AOs). The recommended operators outperform the already specified PFN operators. The proposed operator is utilised in the multicriteria decision-making process to identify the best candidate for instruction (MCDM).
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