TOPSIS approach for multi-attribute decision making problems based on n-intuitionistic polygonal fuzzy sets description

The polygonal fuzzy set describes a type of fuzzy information with the aid of the orderly representation of real numbers. It can approximate general fuzzy sets and overcome the complexity of arithmetic operations of fuzzy sets based on the Zadeh's extension principle. This research proposes the concept of an n-intuitionistic polygonal fuzzy set based on intuitionistic fuzzy and polygonal fuzzy sets. It then presents its arithmetic operation and Hamming distance formula. In addition, it adopts the standardized and weighting method to obtain the attribute matrix of the positive (negative) ideal solution, and calculates the Hamming distance between each scheme and the positive (negative) ideal solution to provide the TOPSIS (technique for order preference by similarity to an ideal solution) approach for the multi-attribute decision-making problem that describes the multi-attribute index information by n-intuitionistic polygonal fuzzy set. Finally, this research implements optimized ordering on the alternative solutions according to the degree of relative similarity and verifies its effectiveness and practicability through examples.