Multi-Criteria Decsion Making

Fuzzy multi-criteria decision-making (MCDM) methods and problems have increasingly been considered in the past years. Type-1 fuzzy sets are usually used by decision-makers (DMs) to express their evaluations in the process of decision-making. Interval type-2 fuzzy sets (IT2FSs), which are extensions of type-1 fuzzy sets, have more degrees of flexibility in modeling of uncertainty. In this research, a new ranking method to calculate the ranking values of interval type-2 fuzzy sets is proposed. A comparison is performed to show the efficiency of this ranking method. Using the proposed ranking method and the arithmetic operations of IT2FSs, a new method of Assessment based on Fuzzy Ranking and Aggregated Weights (AFRAW) is developed for multi-criteria group decision-making. To obtain more realistic and practical weights for the criteria, the subjective weights expressed by DMs and objective weights calculated based on a deviation-based method are combined, and the aggregated weights are used in the proposed method. A numerical example related to assessment of suppliers in a supply chain and selecting the best one is used to illustrate the procedure of the proposed method. Moreover, a comparison and a sensitivity analysis are performed in this study. The results of these analyses show the validity and stability of the proposed method.

The allocation of groundwater resources has been a challenge for many years due to its unforeseen side effect and lag time issues, which are often overlooked. The full impact of groundwater utilization/abstraction takes time to realize its effect at its full. In this paper, long‐term effects and groundwater dynamics were assessed using a water balance model and a time series analysis, respectively. Undeveloped groundwater systems are commonly found in a state of equilibrium, where, on average, equal amounts of water are recharged and discharged. A water budget is a static accounting of the state of the system at a given time, often before the system is developed. Water balance analysis was carried out together with the groundwater through flow, hydrograph, and surface‐groundwater interaction analysis (base flow index) to develop a conceptual water balance model, which is a very basic representation of a complex natural aquifer system and is instrumental to constrain and build a robust numerical model that can be readily justified and updated. A noble approach was employed to assess and constrain the discharge coming out of the model area to sustain the lake level, located to the north of the study area, using the whole lake catchment and lake water balance analysis. Based on the lake water balance, there is a deficit between input and output computation, and hence there should be a groundwater input to sustain the historical lake area. The analysis showed that the model area contributes 40% of the lake catchment, and hence the portion of the groundwater inflow feeding the lake was computed. This is one of the means to constrain the discharge, which adds more confidence to the recharge estimation. This is very important because the size of a sustainable groundwater development usually depends on how much of the discharge from the system can be captured by the development. Capture is independent of the recharge. Instead, it depends on the dynamic response of the aquifer system to the development. The idea that knowing the recharge is important in determining the size of a sustainable groundwater development is a myth and has no basis. The important entity in determining how a groundwater system reaches a new equilibrium is capture. How capture occurs in an aquifer system is a dynamic process. Following this study, lake water balance assessment was indirectly considered as prior information for the numerical model calibration of the discharge from the model area using a conductance parameter. Conductance is a key parameter to estimate the discharge volume together with the change in the simulated hydraulic head between time steps. The water balance error highlights which one is more sensitive, and this could help to assist in planning for future data collection/field work and where to invest the money. The water balance computation helps to figure out the degree of surface‐groundwater interaction, uncertainty, sensitive parameter, helps in the decision to invest time and money, and operates as a cross check with other analytical or numerical modelling.

Groups often face difficulty reaching consensus. For complex decisions with multiple latent criteria, discourse alone may impede groups from pinpointing fundamental disagreements. To help support a consensus building process, we introduce ConsensUs, a novel visualization tool that highlights disagreements in comparative decisions. The tool facilitates groups to specify comparison criteria and to quantify their subjective opinions across these criteria. ConsensUs then highlights salient differences between members. An evaluation with 87 participants shows that ConsensUs helps individuals identify points of disagreement within groups and leads people to align their scores more with the group opinion. We discuss the larger design space for supporting the group consensus process, and our future directions to extend this approach to large-scale decision making platforms.

Considering a group of users, each specifying individual preferences over categorical attributes, the problem of determining a set of objects that are objectively preferable by all users is challenging on two levels. First, we need to determine the preferable objects based on the categorical preferences for each user, and second we need to reconcile possible conflicts among users' preferences. A naıve solution would first assign degrees of match between each user and each object, by taking into account all categorical attributes, and then for each object combine these matching degrees across users to compute the total score of an object. Such an approach, however, performs two series of aggregation, among categorical attributes and then across users, which completely obscure and blur individual preferences. Our solution, instead of combining individual matching degrees, is to directly operate on categorical attributes, and define an objective Pareto-based aggregation for group preferences. Building on our interpretation, we tackle two distinct but relevant problems: finding the Pareto-optimal objects, and objectively ranking objects with respect to the group preferences. To increase the efficiency when dealing with categorical attributes, we introduce an elegant transformation of categorical attribute values into numerical values, which exhibits certain nice properties and allows us to use well-known index structures to accelerate the solutions to the two problems. In fact, experiments on real and synthetic data show that our index-based techniques are an order of magnitude faster than baseline approaches, scaling up to millions of objects and thousands of users.