A survey of the design, development and implementation of a flexible decision technology called the graph model for conflict resolution (GMCR) is discussed for systematically investigating real world conflicts within a system of systems engineering outlook. This encompassing GMCR methodology has been constructed during the past three decades by the authors, their colleagues and students from many countries for addressing a rich range of conflict situations. GMCR can be used for studying large and small conflicts and includes methods for preference elicitation, preference uncertainty (unknown, fuzzy, grey numbers and probabilistic). Many kinds of definitions exist for possible human behavior under pure competition which can be transformed for utilization in coalition analysis. GMCR can handle emotions, attitudes, and misperceptions. Within inverse GMCR, one can calculate the preferences needed by decision makers (DMs) to reach a desirable equilibrium. Under behavioral GMCR one can ascertain the strategic thinking of DMs when the input and output are known. Decision support systems can be built for implementing the array of GMCR advancements. Future expansions of GMCR can be guided by key characteristics of actual disputes. Artificial intelligence (AI) GMCR is a promising subfield of study within GMCR.

Three methods for modeling allocation of water rights under different types of water rights systems are presented. The priority-based maximal multiperiod network flow (PMMNF) programming method searches for optimal allocations over the whole river basin and multiple periods, strictly preserving priority order by sequential programming. PMMNF is a flexible method that can be applied under prior, riparian and public water regimes with priorities determined by different criteria. The modified riparian water rights allocation (MRWRA) approach for water allocation under a riparian rights system is a special form of PMMNF, which assigns senior priorities to the basic water demands of all riparian landowners and junior priorities to their surplus demands. MRWRA recognizes that, an upstream riparian has the privilege to take water but should constrain its diversions for surplus demands to meet the basic needs of downstream riparian demands. The lexicographic minimax water shortage ratios method is a technique for...

Hesitant fuzzy preference relations (HFPRs) are formally proposed to model the conflict situation in which each decision maker (DM) consists of multiple individuals and each individual has its own fuzzy preferences over the feasible states within the framework of the graph model for conflict resolution (GMCR). Based on HFPRs, new definitions for hesitant fuzzy Nash stability, hesitant fuzzy general metarationality, hesitant fuzzy symmetric metarationality, and hesitant fuzzy sequential stability permit stability analyses to be carried out. Moreover, a new option prioritization technique, called hesitant fuzzy option prioritization, is developed for modeling a DM’s HFPRs based on the DM’s priority sequence of preference statements, the DM’s fuzzy truth values and levels of confidence. The groundwater contamination conflict of Elmira, Ontario, Canada, is utilized as a case study to illustrate the usefulness and applicability of the hesitant fuzzy option prioritization technique and GMCR with HFPRs.