interval valued pythagorean fuzzy set

In this paper, we expose cosine, jaccard and dice similarity measures and rough interval Pythagorean mean operator. Some of the important properties of the defined similarity measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

This paper introduces a new decision support framework for transport projects appraisal, which is based on the multi-criteria decision analysis (MCDA) and the cost-benefit analysis (CBA) to address both monetary and non-monetary characteristics of the problem at the same time. Substantial inaccuracies are present while obtaining non-monetary and monetary inputs to the MCDA and the CBA, respectively. To provide the MCDA part of the framework with uncertainty, an interval-valued Pythagorean fuzzy set (IVPFS) is used as an attractive uncertain modeling tool. Additionally, a new multi-attribute group decision-making (MAGDM) method with partially known attribute weights and unknown expert weights under the IVPFS environment is proposed to find the best sustainable transport project from the non-monetary criteria point of view. Furthermore, a novel uncertainty modeling tool, namely an interval-valued Pythagorean trapezoidal fuzzy set, is introduced to address ill-known quantities and inaccuracies that exist in the estimation of monetary impacts. Finally, this framework is used to handle a real case study of a complex decision process of finding the best transport project to fund several candidate projects. This approach has made it possible to handle the decision process from economic, social, environmental points of view at the same time. The result of this case study shows that the decision-making framework can be used as a valuable decision support tool. Moreover, it is shown that the presented framework can be applied to effectively support appraisals of transport projects.