Interval-valued Intuitionistic Fuzzy Analytic Network Process And Its Application In Groundwater Vulnerability Assessment

Groundwater vulnerability assessment is a stylish multi-criteria decision problem.In the groundwater vulnerability assessment,there is often dependence and feedback between the evaluation attributes,and the preference information of the evaluation attributes given by decision makers has a tendency to show a strong ambiguity.The analysis network process is a multi-criteria decision-making method that considers the dependency and feedback of decision attributes.Interval-valued intuitionistic fuzzy preference information comes closer to the true expression of decision makers in describing the ambiguity of the preference information.Therefore,researching the analysis network process based on the interval-valued intuitionistic fuzzy preference information will provide a novel research idea for the groundwater vulnerability assessment.According to the characteristics of the groundwater vulnerability assessment,the interval-valued intuitionistic fuzzy preference information is introduced into the analysis network process,and the complete interval-valued intuitionistic fuzzy analysis network process,the incomplete interval-valued intuitionistic fuzzy analysis network process,and the mixed interval-valued intuitionistic fuzzy analysis network process are constructed respectively.The proposed method is applied to the groundwater vulnerability assessment of Handan,which has strong heoretical significance and application value.The main content of this paper is organized as follows:First,the complete interval-valued intuitionistic fuzzy analysis network process is proposed.In the beginning,the definition of complete interval-valued intuitionistic fuzzy preference relationship is given,and consistent definitions of its multiplicative and approximate multiplicative are given based on the Me measure.Then,the corresponding weight vector optimization model is constructed,and the parameter solution method is used to solve the problem.Finally,the calculation steps of the network layer supermatrix are given,and the algorithm flow of the complete interval-valued intuitionistic fuzzy analysis network process is established.Second,the incomplete interval-valued intuitionistic fuzzy analysis network process is proposed.In the beginning,the definition of incomplete interval-valued intuitionistic fuzzy preference relationship is given,and consistent definitions of itsmultiplicative and approximate multiplicative are given based on the Me measure.Then,the corresponding weight vector optimization model is constructed,and the parameter solution method is used to solve the problem.Finally,the calculation steps of the network layer supermatrix are given,and the algorithm flow of the incomplete interval-valued intuitionistic fuzzy analysis network process is established.Third,the mixed interval-valued intuitionistic fuzzy analysis network process is proposed.In the beginning,the definition of preference relationship between the mixed intuitionistic fuzzy and mixed interval-valued intuitionistic fuzzy is given.Then,consistent definitions of multiplicative and approximate multiplicative of the mixed intuitionistic fuzzy preference and the mixed interval-valued intuitionistic fuzzy preference are given.And then,the corresponding weights are constructed.The vector optimization model is solved based on the parameter decomposition method.Finally,the calculation steps of the network layer supermatrix are given,and the algorithm flow of the mixed interval-valued intuitionistic fuzzy analysis network process is established.Fourth,the interval-valued intuitionistic fuzzy analysis network process is used to evaluate groundwater vulnerability in Handan.Based on the interval-valued intuitionistic fuzzy analysis network process,GIS,and DRASTIC evaluation model,the groundwater vulnerability of Handan is evaluated,and the groundwater vulnerability index and the groundwater vulnerability level of Handan are given.The research in this paper will further enrich the theory of uncertain multi-criteria decision-making,broaden the application scope of theory of uncertain multi-criteria decision-making,and provide a theoretical basis and a decision basis for groundwater vulnerability assessment.