Abstract
The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-membership functions have been described on a one-to-one scale and a quadratic function scale. There is a symmetry between the values of this membership and non-membership functions. The scales of any power functions are used here in order to increase the scope of the decision-making problems. The theory of n-PFS introduces a conceptual apparatus analogous to the classic theory of Zadeh fuzzy sets, consistently striving to correctly define the n-PFS algebra.
Highlights
Zadeh [1] introduced the fuzzy set idea, which generalizes the theory of classical sets
Since the work of Zadeh, the fuzzy set theory has been used in different disciplines such as management sciences, engineering, mathematics, social sciences, statistics, signal processing, artificial intelligence, automata theory, and medical and life sciences
The decision-making problems in the model of Pythagorean fuzzy sets will significantly increase the application range of solving these problems than in the model of intuitionistic fuzzy sets
Summary
Zadeh [1] introduced the fuzzy set idea, which generalizes the theory of classical sets. In order to create model for imprecise information, the model of Pythagorean fuzzy sets (PFSs) was proposed by Yager [4,5] This model is different than the IFSs model because it uses the condition. The decision-making problems in the model of Pythagorean fuzzy sets will significantly increase the application range of solving these problems than in the model of intuitionistic fuzzy sets. It is because more pairs (μ, v) satisfy the condition 0 ≤ μ2 + v2 ≤ 1 than the condition 0 ≤ μ + v ≤ 1.
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