Abstract
Interval-valued Pythagorean fuzzy set (IVPFS) as a generalization of Pythagorean fuzzy set (PFS) increases its elasticity drastically. However, the expressions and calculations of IVPFS are slightly complicated. To overcome this drawback, in this research study, we greatly simplify the expressions of IVPFS by introducing a new concept of simplified interval-valued Pythagorean fuzzy set (SIVPFS), constituted by two Pythagorean fuzzy numbers (PFNs) with the relationships of intersection and union simultaneously. We develop systematic aggregation operators to aggregate simplified interval-valued Pythagorean fuzzy information. Meanwhile, we propose a new generalization of fuzzy graph, called simplified interval-valued Pythagorean fuzzy graph (SIVPFG), to describe uncertain information in graph theory. We develop a series of operations on two SIVPFGs and investigate their desirable properties. Finally, we develop a SIVPFG-based multi-agent decision-making approach to solve a common kind of situation where the graphic structure of agents is obscure. A numerical example is provided to illustrate the proposed approach as well as the applicability of SIVPFS and SIVPFG in decision making.
Highlights
As an effective framework, multi-criteria decision making (MCDM) has consistently been used to choose the optimal alternative(s) from a given finite set of alternatives with respect to a collection of criteria
In this research study, we have introduced the new concepts of simplified interval-valued Pythagorean fuzzy set (SIVPFS) and corresponding simplified interval-valued Pythagorean fuzzy number (SIVPFN), which is characterized by two Pythagorean fuzzy numbers (PFNs)
We have investigated some aggregation techniques for SIVPFNs
Summary
Multi-criteria decision making (MCDM) has consistently been used to choose the optimal alternative(s) from a given finite set of alternatives with respect to a collection of criteria. Case II: If the weights of agents are not provided, a method can be developed to calculate the weights of all agents according to some known information, like simplified interval-valued Pythagorean fuzzy graphic structure and the degrees of vertices in a SIVPFG. In the SIVPFG-based MCDM problems, if there exist the prioritization relations among the agents, we shall solve this kind of problems by utilizing the prioritized aggregation operators [31] together with the necessary simplified interval-valued Pythagorean fuzzy graphic structure.
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