Water–Energy–Food nexus evaluation using an inverse approach of the graph model for conflict resolution based on incomplete fuzzy preferences

Abstract

With the continuous development of economic globalization and the increasing strengthening of human exchanges, the Water–Energy–Food (WEF) nexus evaluation has become a new research area. The purpose of this paper is to develop an inverse approach of graph model for conflict resolution (GMCR) to the conflict problems of WEF nexus evaluation in real life. Specifically, due to lack of information, some decision makers’ (DMs’) preferences over states may be incomplete fuzzy preference relations. Therefore, an algorithm is devised to amend the incomplete fuzzy preference relation to the complete fuzzy preference relation. Subsequently, a complete ordinal score vector is proposed to describe the preference ranking over different states based on the complete fuzzy preference relation. Moreover, in the framework of the inverse approach of GMCR, some mathematical models with the least constraint conditions are proposed to obtain all the required preference relations for opponent DM, which are required to make a given state be stable under four basic stability definitions. Finally, WEF nexus evaluation in Shandong province is illustrated to demonstrate the usefulness of the inverse approach of GMCR with the incomplete fuzzy preference relations.