Network consensus analysis of probabilistic linguistic preference relations for group decision making and its application in urban household waste classification

Abstract

The selection of the urban household waste classification rules is important to both city sustainability and clean production of enterprises using the renewable urban household waste, but few studies focused on it. Probabilistic linguistic preference relations have been proposed to express both quantitative and qualitative preference information, which attracted many researchers’ attention. For the consensus studies of probabilistic linguistic preference relations, current methods have two challenges regarding the information change in normalization and the information loss in integration. To overcome these challenges, from the perspective of experts’ networks under criteria, this study aims to propose a network consensus analysis of probabilistic linguistic preference relations based on a novel probabilistic linguistic Kolmogorov-Smirnov distance measure. To achieve this goal, the cumulative probability distributions of probabilistic linguistic term sets are introduced to define the probabilistic linguistic Kolmogorov-Smirnov distance measure. Based on this novel distance measure, an argument measurement and a programming with analytic solutions are proposed to group experts’ networks into three categories: the harmonious network, adjustable divergent network, and non-adjustable divergent network. The consensus degrees of these three kinds of networks are also given to get the consensus degrees of criteria. A fuzzy Cronbach’s alpha is presented to calculate the weights of criteria and the final consensus degree of a group. Given that the urban household waste classification rule selection is actually an multi-criteria group decision making problem, we then provide an illustration of selecting a suitable urban household waste classification rules to validate the applicability of the proposed method. Comparative analyses are provided to demonstrate the advantages and reliability of the network consensus analysis in selecting urban household waste classification rules.