15538833
An approach to avoiding rank reversal in AHP
Analytic hierarchy process (AHP) has been considerably criticized for possible rank reversal phenomenon caused by the addition or deletion of an alternative. This paper looks into the cause of rank reversal phenomenon and finds that rank reversal is caused by change of local priorities before and after an alternative is added or deleted. An approach is therefore proposed to keep the local priorities unchanged to avoid rank reversal phenomenon. Two well-known numerical examples are re-examined using the proposed approach to demonstrate its validity and practicability in rank preservation.
207640585
On fuzzy multiattribute decision-making models and methods with incomplete preference information
In the paper by Li (Fuzzy Sets and Systems 106 (1999) 113), a minimum average weighted deviation method was investigated to determine the weights of attributes using incomplete preference information. It is shown in this paper that the method is flawed and can only be meaningful if it is revised. Two general ways are presented to revise it and are justified by using Lagrange multiplier method and Hessian matrix. Four specific revised models and approaches are investigated and examined through a numerical example. Different membership functions are suggested and utilized to normalize decision matrix so that a credible ranking order can be achieved.
11256201
On the normalization of interval and fuzzy weights
The normalization of interval and fuzzy weights is often necessary in multiple criteria decision analysis (MCDA) under uncertainty, especially in analytic hierarchy process (AHP) with interval or fuzzy judgements. The existing normalization methods based on interval arithmetic and fuzzy arithmetic are found flawed and need to be revised. This paper presents the correct normalization methods for interval and fuzzy weights and offers relevant theorems in support of them. Numerical examples are examined to show the correctness of the proposed normalization methods and their differences from those existing normalization methods.
19364030
The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees
Abstract Multiple attribute decision analysis (MADA) problems having both quantitative and qualitative attributes under uncertainty can be modeled using the evidential reasoning (ER) approach. Several types of uncertainties such as ignorance and fuzziness can be modeled in the ER framework. In this paper, the ER approach will be extended to model new types of uncertainties including interval belief degrees and interval data that could be incurred in decision situations such as group decision making. The Dempster–Shafer (D–S) theory of evidence is first extended, which is one of the bases of the ER approach. The analytical ER algorithm is used to combine all evidence simultaneously. Two pairs of nonlinear optimization models are constructed to estimate the upper and lower bounds of the combined belief degrees and to compute the maximum and the minimum expected utilities of each alternative, respectively. Interval data are equivalently transformed to interval belief degrees and are incorporated into the nonlinear optimization models. A cargo ship selection problem is examined to show the implementation process of the proposed approach.
18488788
A preference aggregation method through the estimation of utility intervals
In this paper, a preference aggregation method is developed for ranking alternative courses of actions by combining preference rankings of alternatives given on individual criteria or by individual decision makers. In the method, preference rankings are viewed as constraints on alternative utilities, which are normalized, and linear programming models are constructed to estimate utility intervals, which are weighted and averaged to generate an aggregated utility interval. A simple yet pragmatic interval ranking method is used to compare and/or rank alternatives. The final ranking is generated as the most likely ranking with certain degrees of belief. Three numerical examples are examined to illustrate the potential applications of the proposed method.
6142906
Multiple attribute decision making based on fuzzy preference information on alternatives: Ranking and weighting
This paper investigates the multiple attribute decision making (MADM) problem with fuzzy preference information on alternatives and proposes an eigenvector method to rank them. Three optimization models are introduced to assess the relative importance weights of attributes in a MADM problem, which integrate subjective fuzzy preference relations and objective information in different ways. Since the decisions these models lead to are based on both subjective and objective information, they are more balanced and credible than those that consider only one type of information. An example is provided to illustrate the application of the proposed models.
17974516
G-Networks and the Modeling of Adversarial Agents
As a result of the structure and content transformation of an evolving society, many large scale autonomous systems emerged in diverse areas such as biology, ecology or finance. Inspired by the desire to better understand and make the best out of these systems, we propose an approach which builds stochastic mathematical models, in particular G-networks models, that allow the efficient representation of systems of agents and offer the possibility to analyze their behavior using mathematics. This approach is capable of modelling the system at different abstraction levels, both in terms of the number of agents and the size of the geographical location. We demonstrate our approach with some urban military planning scenarios and the results suggest that this approach has tackled the problem in modelling autonomous systems at low computational cost. Apart from offering the numerical estimates of the outcome, the approach helps us identify the characteristics that impact the system most and allows us to compare alternative strategies.
5870530
Mathematical models and properties of games
Games are a decision process under competition where opponent players compete for the maximum gain or a success state in the same environment according to the same rules of the game. Games are conventionally dealt with payoff tables based on random strategies that are found inadequate to describe the dynamic behaviors of games and to rigorously predict the outcomes of games. This paper presents a formal treatment of games by a set of mathematical models for both the layouts and behaviors of games. A formal model of games is introduced, based on which the properties of games in terms of decision strategies and serial matches are described. A wide range of generic zero-sum and nonzero-sum games are formally modeled and analyzed using the mathematical models of games.
12928468
Distributed goal recognition algorithms for modular robots
Modular robots are systems composed of a number of independent units that can be reconfigured to fit the task at hand. When the modules are computationally independent, they form a large distributed system with no central controller. We are concerned with the ability of such modular robots to easily recognize the achievement (or lack thereof) of a given goal configuration. We present algorithms for a class of 2D and 3D modular robots, along with correctness and running time analysis. We have successfully implemented the 2D algorithm on the second-generation Crystalline Atomic robot, a self-reconfigurable modular robot under development in our laboratory and we present implementation details and experimental results.
15514608
Application of Relief-F feature filtering algorithm to selecting informative genes for cancer classification using microarray data
Numerous recent studies have shown that microarray gene expression data is useful for cancer classification. Classification based on microarray data is very different from previous classification problems in that the number of features (genes) greatly exceeds the number of instances (tissue samples). It has been shown that selecting a small set of informative genes can lead to improved classification accuracy. It is thus important to first apply feature selection methods prior to classification. In the machine learning field, one of the most successful feature filtering algorithms is the Relief-F algorithm. In this work, we empirically evaluate its performance on three published cancer classification data sets. We use the linear SVM and the k-NN as classifiers in the experiments, and compare the performance of Relief-F with other feature filtering methods, including Information Gain, Gain Ratio, and /spl chi//sup 2/-statistic. Using the leave-one-out cross validation, experimental results show that the performance of Relief-F is comparable with other methods.
62532074
A decision-theoretic approach to the evaluation of information retrieval systems
Evaluation research on information retrieval (IR) systems has thus far been narrowly focused and disjointed. This research attempts to narrow the gap by providing a comprehensive and integrated multiple criteria decision-theoretic approach for the evaluation of IR systems. The approach, which is based on the Analytic Hierarchy Process (AHP), is illustrated in the context of a domain-specific IR system. The novelty of this approach lies in the focus on the user aspect and the application of decision-making theories in the IR field.