Abstract
The n-intuitionistic polygonal fuzzy set (n-IPFS), combined by the intuitionistic fuzzy and polygonal fuzzy sets, is an extended form of the triangular intuitionistic fuzzy set (TIFS) and the trapezoidal intuitionistic fuzzy set (TrIFS). The aim of this paper is to develop some new aggregation operators for n-IPFSs and apply them to multi-attribute group decision making (MAGDM) problems. First, the operational properties and the score function of n-IPFSs are defined. Then, three kinds of n-intuitionistic polygonal fuzzy aggregation operators are investigated including n-intuitionistic polygonal fuzzy weighted averaging (n-IPFWA) operator, n-intuitionistic polygonal fuzzy ordered weighted averaging (n-IPFOWA) operator and n-intuitionistic polygonal fuzzy hybrid aggregation (n-IPFHA) operator. Finally, we propose an improved technique for order preference by similarity to an ideal solution (TOPSIS) approach with n-IPFSs and unknown attributes weights. The attributes weights are obtained by combining the entropy weights and the subjective weights, and the entropy weights are calculated based on the score function of n-IPFS. The spatial closeness reflected by the Hamming distance and the grey relationship with the positive/negative solution are both considered in getting the relative closeness degree to rank the alternatives. The example analysis of a location selection is given to verify the practicality and the effectiveness of the proposed approach in this paper.
Highlights
Multi-attribute group decision making (MAGDM) problems exist widely in the fields of economy, management, and social science
PRELIMLINARIES we briefly introduce the definition of n-intuitionistic polygonal fuzzy set (n-intuitionistic polygonal fuzzy set (IPFS)), Hamming distance between n-IPFSs and operational laws of n-IPFSs
The proposed MAGDM procedure based on n-IPFA operators is shown as follows: Step 1: Construct the standard decision matrix Ht of n- intuitionistic polygonal fuzzy sets
Summary
Multi-attribute group decision making (MAGDM) problems exist widely in the fields of economy, management, and social science. The intuitionistic fuzzy sets (IFSs) introduced by Atanassov [2] are the generalization of the FSs, which consider membership and non-membership of objects. Liu [4] first proposed the concept of the polygonal fuzzy numbers to overcome the obstacle that the arithmetic operations of FSs based on Zadeh’s extension principle do not satisfy the closeness. The n-IPFHA operator can consider weighting both the given n-intuitionistic polygonal fuzzy values and their ordered positions. An improved TOPSIS is proposed based on the integrated information by the aggregation operators for n-IPFSs. The Hamming distance reflecting the spatial distance combines with the grey relation degree to calculate the relative closeness degree. A balancing factor is introduced to coordinate the given n-intuitionistic polygonal fuzzy values and their ordered positions in the n-IPFHA operator.
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