An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to interval-valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method

Multicriteria Methodology for the NEEDS Project

This report begins with an overview of multicriteria analysis methods, and the basic principles of developing mathematical models for such analysis. An overview of various representation of user preferences is then presented, including methods based on pairwise comparisons of criteria and those based on scalarizing functions. This is followed by a summary of structures of criteria and alternatives. Next, basic properties of multi-criteria analysis are discussed, followed by a more detailed presentation of the similarities of and differences between the main methods based on scalarizing functions. This report concludes that existing methods do not best meet the needs of the NEEDS project, presents the reasons, and proposes a new methodology for development. Depending upon the development and testing of this new methodology, an existing method will also be chosen as a backup for comparative or alternate use

A new dominance intensity method to deal with ordinal information about a DM's preferences within MAVT

Dominance measuring methods are a new approach to deal with complex decision-making problems with imprecise information. These methods are based on the computation of pairwise dominance values and exploit the information in the dominance matrix in dirent ways to derive measures of dominance intensity and rank the alternatives under consideration. In this paper we propose a new dominance measuring method to deal with ordinal information about decision-maker preferences in both weights and component utilities. It takes advantage of the centroid of the polytope delimited by ordinal information and builds triangular fuzzy numbers whose distances to the crisp value 0 constitute the basis for the de?nition of a dominance intensity measure. Monte Carlo simulation techniques have been used to compare the performance of this method with other existing approaches

REPRESENTING AND LEARNING PREFERENCES OVER COMBINATORIAL DOMAINS

Agents make decisions based on their preferences. Thus, to predict their decisions one has to learn the agent\u27s preferences. A key step in the learning process is selecting a model to represent those preferences. We studied this problem by borrowing techniques from the algorithm selection problem to analyze preference example sets and select the most appropriate preference representation for learning. We approached this problem in multiple steps. First, we determined which representations to consider. For this problem we developed the notion of preference representation language subsumption, which compares representations based on their expressive power. Subsumption creates a hierarchy of preference representations based solely on which preference orders they can express. By applying this analysis to preference representation languages over combinatorial domains we found that some languages are better for learning preference orders than others. Subsumption, however, does not tell the whole story. In the case of languages which approximate each other (another piece of useful information for learning) the subsumption relation cannot tell us which languages might serve as good approximations of others. How well one language approximates another often requires customized techniques. We developed such techniques for two important preference representation languages, conditional lexicographic preference models (CLPMs) and conditional preference networks (CP-nets). Second, we developed learning algorithms for highly expressive preference representations. To this end, we investigated using simulated annealing techniques to learn both ranking preference formulas (RPFs) and preference theories (PTs) preference programs. We demonstrated that simulated annealing is an effective approach to learn preferences under many different conditions. This suggested that more general learning strategies might lead to equally good or even better results. We studied this possibility by considering artificial neural networks (ANNs). Our research showed that ANNs can outperform classical models at deciding dominance, but have several significant drawbacks as preference reasoning models. Third, we developed a method for determining which representations match which example sets. For this classification task we considered two methods. In the first method we selected a series of features and used those features as input to a linear feed-forward ANN. The second method converts the example set into a graph and uses a graph convolutional neural network (GCNN). Between these two methods we found that the feature set approach works better. By completing these steps we have built the foundations of a portfolio based approach for learning preferences. We assembled a simple version of such a system as a proof of concept and tested its usefulness