Neutrosophic AHP-Delphi Group decision making model based on trapezoidal neutrosophic numbers

The main objective of this research is to study the integration of Analytic Hierarchy Process (AHP) into Delphi framework in neutrosophic environment and present a new technique for checking consistency and calculating consensus degree of expert’s opinions. In some pragmatism bearings, the experts might be not able to assign deterministic evaluation values to the comparison judgments due to his/her confined knowledge or the differences of individual judgments in group decision making. To overcome these challenges, we have used neutrosophic set theory to handle the integration of AHP into Delphi framework, where each pairwise comparison judgment is symbolized as a trapezoidal neutrosophic number. The power of AHP is enhanced by adding Delphi technique, since it can reduce noise which result from focusing on group and/or individual interests rather than concentriciting on problem disband and it also increase consensus degree about ideas. Obtaining a consistent trapezoidal neutrosophic preference relation is very difficult in decision making process because in creating a consistent trapezoidal preference relation; each expert should make n×n-12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{n \times \left( {n - 1} \right)}}{2}$$\end{document} consistent judgments for n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} alternatives. When the number of alternatives is increasing, the workload of giving judgments for the experts is heavy and it makes them tired and leads to inconsistent judgments. In the proposed model,experts will focus only on n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {n - 1} \right)$$\end{document} restricted judgments and this also enhances the performance of AHP over the traditional version that is proposed by Saaty. A real life example is developed based on expert opinions about evaluation process of many international search engines. The problem is solved to show the validation of the suggested method in neutrosophic path.