Ranking Alternatives on the Basis of a Dominance Intensity Measure

The additive multi-attribute utility model is widely used within MultiAttribute Utility Theory (MAUT), demanding all the information describing the decision-making situation. However, these information requirements can obviously be far too strict in many practical situations. Consequently, incomplete information about input parameters has been incorporated into the decisionmaking process. We propose an approach based on a dominance intensity measure to deal with such situations. The approach is based on the dominance values between pairs of alternatives that can be computed by linear programming. These dominance values are transformed into dominance intensities from which a dominance intensity measure is derived. It is used to analyze the robustness of a ranking of technologies for the disposition of surplus weapons-grade plutonium by the Department of Energy in the USA, and compared with other dominance measuring methods

Multi-attribute choice with ordinal information: a comparison of different decision rules

In the context of additive multiattribute aggregation, we address problems with ordinal information, i.e., considering a ranking of the weights (the scaling coefficients). Several rules for ranking alternatives in these situations have been proposed and compared, such as the rank-order-centroid weight, minimum value, central value, and maximum regret rules. This paper compares these rules, together with two rules that had never been studied (quasi-dominance and quasi-optimality) that use a tolerance parameter to extend the concepts of dominance and optimality. Another contribution of this paper is the study of the behavior of these rules in the context of selecting a subset of the most promising alternatives. This study intends to provide guidelines about which rules to choose and how to use them (e.g., how many alternatives to retain and what tolerance to use), considering the contradictory goals of keeping a low number of alternatives yet not excluding the best one. The comparisons are grounded on Monte Carlo simulations

Dominance intensity measure within fuzzy weight oriented MAUT: an application

We introduce a dominance intensity measuring method to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision-making problems on the basis of multi-attribute utility theory (MAUT) and fuzzy sets theory. We consider the situation where there is imprecision concerning decision-makers’ preferences, and imprecise weights are represented by trapezoidal fuzzy weights.The proposed method is based on the dominance values between pairs of alternatives. These values can be computed by linear programming, as an additive multi-attribute utility model is used to rate the alternatives. Dominance values are then transformed into dominance intensity measures, used to rank the alternatives under consideration. Distances between fuzzy numbers based on the generalization of the left and right fuzzy numbers are utilized to account for fuzzy weights. An example concerning the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides illustrates the approach. Monte Carlo simulation techniques have been used to show that the proposed method performs well for different imprecision levels in terms of a hit ratio and a rank-order correlation measure

Dominance measuring methods for the selection of cleaning services in a European underground transportation company

Dominance measuring methods are a recent approach for dealing with complex decisionmaking problems with imprecise, incomplete or partial information within multi-attribute value/utility theory. These methods compute pairwise dominance values and exploit the information included in the dominance matrix in different ways to derive measures of dominance intensity to rank the alternatives under consideration. We review dominance measuring methods proposed in the literature, describing how their possible drawbacks have been progressively overcome, and comparing their performance with other existing approaches, like surrogate weighting methods, the adaptation of classical decision rules to encompass an imprecise decision context, SMAA or Sarabando and Dias’ method. An example of the selection of cleaning services in a European underground transportation company is used to illustrate dominance measuring methods in a real complex decision-making problem

Simulation-based evaluation of defuzzification-based approaches to fuzzy multi-attribute decision making

This paper presents a simulation-based study to evaluate the performance of 12 defuzzification-based approaches for solving the general fuzzy multiattribute decision-making (MADM) problem requiring cardinal ranking of decision alternatives. These approaches are generated based on six defuzzification methods in conjunction with the simple additive weighting (SAW) method and the technique for order preference by similarity to the ideal solution method. The consistency and effectiveness of these approaches are examined in terms of four new objective performance measures, which are based on five evaluation indexes. The Simulation result shows that the approaches, which are capable of using all the available information on fuzzy numbers, effectively in the defuzzification process, produce more consistent ranking outcomes. In particular, the SAW method with the degree of dominance defuzzification is proved to be the overall best performed approach, which is, followed by the SAW method with the area center defuzzification. These findings are of practical significance in real-world settings where the selection of the defuzzification-based approaches is required in solving the general fuzzy MADM problems under specific decision contexts

Ordenación de las alternativas basándose en la intesidad de dominancia y la lógica difusa

Se introduce un nuevo método de ordenación de las alternativas en un problema de decisión multicriterio con imprecisión en la información proporcionada por el decisor, representada por una función de utilidad multiatributo aditiva. Donde las consecuencias de las alternativas se representan mediante distribuciones uniformes, las funciones de utilidad de cada atributo son clases de funciones de utilidad y los pesos asociados a los atributos son números difusos triangulares (trapezoidales)

An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights

This article proposes an approach to multiattribute decision making with incomplete attribute weight information where individual assessments are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). By employing a series of optimization models, the proposed approach derives a linear program for determining attribute weights. The weights are subsequently used to synthesize individual IVIFN assessments into an aggregated IVIFN value for each alternative. In order to rank alternatives based on their aggregated IVIFN values, a novel method is developed for comparing two IVIFNs by introducing two new functions: the membership uncertainty index and the hesitation uncertainty index. An illustrative investment decision problem is employed to demonstrate how to apply the proposed procedure and comparative studies are conducted to show its overall consistency with existing approaches