Robust optimization analysis for multiple attribute decision making problems with imprecise information

This paper considers ranking decision alternatives under multiple attributes with imprecise information on both attribute weights and alternative ratings. It is demonstrated that regret results from the decision maker??s inadequate knowledge about the true scenario to occur. Potential optimality analysis is a traditional method to evaluate alternatives with imprecise information. The essence of this approach is to identify any alternative that outperforms the others in its best-case scenario. Our analysis shows that potential optimality analysis is optimistic in nature and may lead to a significant loss if an unfavorable scenario occurs. We suggest a robust optimization analysis approach that ranks alternatives in terms of their worst-case absolute or relative regret. A robust optimal alternative performs reasonably well in all scenarios and is shown to be desirable for a risk-concerned decision maker. Linear programming models are developed to check robust optimality.     

A lexicographical compromise method for multiple criteria group decision problems with imprecise information

This paper addresses multiple criteria group decision making problems where each group member offers imprecise information on his/her preferences about the criteria. In particular we study the inclusion of this partial information in the decision problem when the individuals’ preferences do not provide a vector of common criteria weights and a compromise preference vector of weights has to be determined as part of the decision process in order to evaluate a finite set of alternatives. We present a method where the compromise is defined by the lexicographical minimization of the maximum disagreement between the value assigned to the alternatives by the group members and the evaluation induced by the compromise weights.     

An action learning evaluation procedure for multiple criteria decision making problems

In this paper we focus on an extension of the Analytic Hierarchy Process (AHP) that accommodates ambiguity on the part of the decision maker (DM), and facilitates the exploration of the decision domain. We propose a systematic action learning process that builds confidence as it converges from numeric interval estimates to numeric point estimates. Our Multiple Criteria Decision Making (MCDM) problem procedure structures the problem as a hierarchy, evaluates all objects using pairwise comparisons that accommodate vagueness and ambiguity, uses interval prioritization techniques, and does synthesis using the linear additive value function. This action learning process facilitates the understanding of key stakeholders, which is imperative for the successful implementation of the subsequent decision.     

Sequential incorporation of imprecise information in multiple criteria decision processes

In this paper we deal with multicriteria decision processes and develop tools that permit to ease the task of analysing such models. We provide a methodology to sequentially incorporate imprecise preference information which is given by means of general linear relations in the weighting coefficients. The results presented allow us to evaluate the quality of the information supplied and can be used to reduce the number of irrelevant alternatives to be presented to the decision maker (DM). Several examples based on multiple criteria linear programming illustrate the results of the paper.     

Dominance and potential optimality in multiple criteria decision analysis with imprecise information

This paper discusses multiple criteria models of decision analysis with finite sets of alternatives. A weighted sum of criteria is used to evaluate the performance of alternatives. Information about the weights is assumed to be in the form of arbitrary linear constraints. Conditions for checking dominance and potential optimality of decision alternatives are presented. In the case of testing potential optimality, the proposed appoach leads to the consideration of a couple of mutually dual linear programming problems. The analysis of these problems gives valuable information for the decision maker. In particular, if a decision alternative is not potentially optimal, then a mixed alternative dominating it is defined by a solution to one of the LP problems. This statement generalizes similar results known for some special cases. The interpretation of the mixed alternative is discussed and compared to its analogue in a data envelopment analysis context.     

Modeling action-interdependence in multiple criteria decision making

A problem of subset selection when actions are interdependent is formulated within a multiple criteria framework. More specifically, a novel definition and characterization of interdependence of actions applicable to Multiple Criteria Decision Making (MCDM) are presented. The effects of interdependence of actions on the modeling and resolution of a subset choice problem are shown, and the importance of taking interdependence of actions into account is discussed. Most of the discussion is generalized to independence and interdependence of sets of actions, which are then compared to the case of individual actions. A general approach to evaluate a combination of interdependent actions is proposed and the use of the multiple criteria structure to eliminate some difficulties in evaluating a set of interdependent actions is explained.     

Dynamic parametric bounds on efficient outcomes in interactive multiple criteria decision making problems

Bounds on efficient outcomes in interactive multiple criteria decision making problems are derived. Bounds are dynamic, i.e., they become stronger with the growing number of explicitly identified outcomes. They are also parametric with respect to weighting coefficients. Computational cost to calculate bounds is negligible.Bounds of the sort offer a breakthrough for prohibitive size and/or solution time bottlenecks by allowing a decision maker to interact with an approximation of the underlying mathematical model rather the model itself.Possible applications of bounds to existing interactive decision making algorithms are discussed. Illustrative numerical examples are given.     

Regularized estimation for preference disaggregation in multiple criteria decision making

Disaggregation methods have been extensively used in multiple criteria decision making to infer preferential information from reference examples, using linear programming techniques. This paper proposes simple extensions of existing formulations, based on the concept of regularization which has been introduced within the context of the statistical learning theory. The properties of the resulting new formulations are analyzed for both ranking and classification problems and experimental results are presented demonstrating the improved performance of the proposed formulations over the ones traditionally used in preference disaggregation analysis.     

A visual interactive approach for multiple criteria decision making with monotone utility functions

We consider the problem of choosing the best of a set of alternatives where each alternative is evaluated on multiple criteria. We develop a visual interactive approach assuming that the decision maker (DM) has a general monotone utility function. The approach partitions the criteria space into nonoverlapping cells. The DM uses various graphical aids to move between cells and to further manipulate selected cells with the goal of creating cells that have ideal points less preferred than an alternative. When the DM identifies such cells, all alternatives in those cells are eliminated from further consideration. The DM may also compare pairs of alternatives. The approach terminates with the most preferred alternative of the DM.     

A data model for algorithmic multiple criteria decision analysis

Various software tools implementing multiple criteria decision analysis (MCDA) methods have appeared over the last decades. Although MCDA methods share common features, most of the implementing software have been developed independently from scratch. Majority of the tools have a proprietary storage format and exchanging data among software is cumbersome. Common data exchange standard would be useful for an analyst wanting to apply different methods on the same problem. The Decision Deck project has proposed to build components implementing MCDA methods in a reusable and interchangeable manner. A key element in this scheme is the XMCDA standard, a proposal that aims to standardize an XML encoding of common structures appearing in MCDA models, such as criteria and performance evaluations. Although XMCDA allows to present most data structures for MCDA models, it almost completely lacks data integrity checks. In this paper we present a new comprehensive data model for MCDA problems, implemented as an XML schema. The data model includes types that are sufficient to represent multi-attribute value/utility models, ELECTRE III/TRI models, and their stochastic extensions, and AHP. We also discuss use of the data model in algorithmic MCDA.     

Searching for psychologically stable solutions of multiple criteria decision problems

In interactive decision making, a choice behavior of the decision maker may differ depending on proximity of a current solution to satisfactory values of objectives. An interactive approach proposed in this paper allows the decision maker to use different search principles depending on his/her perception of the achieved values of objectives and trade-offs. While an analysis of the values of objectives may guide the initial search for a final solution, it can be replaced by trade-off evaluations at some later stages. Such an approach allows the decision maker to change search principles, and to identify a psychologically stable solution to the multiple criteria decision problem.     

A Bayesian approach for multiple criteria decision making with applications in Design for Six Sigma

Linking end-customer preferences with variables controlled at a manufacturing plant is a main idea behind popular Design for Six Sigma management techniques. Multiple criteria decision making (MCDM) approaches can be used for such purposes, but in these techniques the decision-maker's (DM) utility function, if modelled explicitly, is considered known with certainty once assessed. Here, a new algorithm is proposed to solve a MCDM problem with applications to Design for Six Sigma based on a Bayesian methodology. At a first stage, it is assumed that there are process responses that are functions of certain controllable factors or regressors. This relation is modelled based on experimental data. At a second stage, the utility function of one or more DMs or customers is described in a statistical model as a function of the process responses, based on surveys. This step considers the uncertainty in the utility function(s) explicitly. The methodology presented then maximizes the probability that the DM's or customer's utility is greater than some given lower bound with respect to the controllable factors of the first stage. Both stages are modelled with Bayesian regression techniques. The advantages of using the Bayesian approach as opposed to traditional methods are highlighted.     

Revising the OWA operator for multi criteria decision making problems under uncertainty

Multi criteria decision making (MCDM) problems are usually under uncertainty. One of these uncertain parameters is the decision maker (DM)’s degree of optimism, which has an important effect on the results. Fuzzy linguistic quantifiers are used to obtain the assessments of this parameter from DM and then, because of its uncertainty it is assumed to have stochastic nature. A new approach, entitled FSROWA, is introduced to combine the Fuzzy and Stochastic features into a Revised OWA operator.     

Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting

Multiple criteria group decision making (MCGDM) problems have become a very active research field over the last decade. Many practical problems are often characterized by MCGDM. The aim of this paper is to develop a new approach for MCGDM problems with incomplete weight information in linguistic setting based on the projection method. Firstly, to reflect the reality accurately, a method to determine the weights of decision makers in linguistic setting is proposed by calculating the degree of similarity between 2-tuple linguistic decision matrix given by each decision maker and the average 2-tuple linguistic decision matrix. By using the weights of decision makers, all individual 2-tuple linguistic decision matrices are aggregated into a collective one. Then, to determine the weight vector of criteria, we establish a non-linear optimization model based on the basic ideal of the projection method, i.e., the optimal alternative should have the largest projection on the 2-tuple linguistic positive ideal solution (TLPIS). Calculate the 2-tuple linguistic projection of each alternative on the TLPIS and rank all the alternatives according to the 2-tuple linguistic projection value. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the validity is verified by comparing the evaluation results of the proposed method with that of the technique for order preference by similarity to ideal solution (TOPSIS) method.     

A new method for multiple criteria group decision making with incomplete weight information under linguistic environment

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method.     

Multiple criteria decision making with interactive over-achievement programming

Whereas in goal programming the under-achievement with respect to (usually) unattainable goals are minimized, we propose the maximization of the over-achievements with respect to feasible goals or required values. An interactive algorithm, in which the over-achievements are maximized via a barrier function, is presented to implement the proposed approach.     

An integrated multiple criteria decision making model applying axiomatic fuzzy set theory

This article presents a hybrid model for the multiple criteria decision making problems. The proposed decision model consists of three parts: (i) DEA (data envelopment analysis) is used to provide the best combination on the performance parameters of original data; (ii) By the application of AFS (axiomatic fuzzy set) theory and AHP (analytic hierarchy process) method, the weight of each attribute is calculated and (iii) TOPSIS (technique for order preference by similarity to ideal solution) is applied to provide the ranking order of that best combination based on the weights of attributes. In addition, we also provide the definitely semantic interpretations for the decision results by AFS theory. Specially, the model not only employs the performance parameters from raw data, but also considers the preferences from decision-makers that can make the decision results more reasonable. The proposed model is used for robot selection to verify the proposed model. Using the selection index, the evaluation of alternative robots and the selection of the most appropriate are eventually feasible. Moreover, a numerical example for supplier selection is included to illustrate the application of the model for the newly developed problems.     

A visual reference direction approach to solving discrete multiple criteria problems

In this paper, we propose a new visual interactive method for solving discrete multiple criteria problems. The method is based on the use of a reference direction, which is determined by the aspiration levels for the criteria specified by the decision maker. The reference direction is projected onto the set of efficient alternatives. A subset found in this way is presented to a decision maker in a visual form using computer graphics. He can choose any efficient alternatives he pleases.We need notmake any assumptions about the properties of the utility function.The method has been implemented on an IBM/PC1 microcomputer. The name of the program is Vimda (a Visual Interactive Method for Discrete Alternatives).     

Decision making with imprecise parameters

We analyze the impact of imprecise parameters on performance of an uncertainty-modeling tool presented in this paper. In particular, we present a reliable and efficient uncertainty-modeling tool, which enables dynamic capturing of interval-valued clusters representations sets and functions using well-known pattern recognition and machine learning algorithms. We mainly deal with imprecise learning parameters in identifying uncertainty intervals of membership value distributions and imprecise functions. In the experiments, we use the proposed system as a decision support tool for a production line process. Simulation results indicate that in comparison to benchmark methods such as well-known type-1 and type-2 system modeling tools, and statistical machine-learning algorithms, proposed interval-valued imprecise system modeling tool is more robust with less error.     

A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations

This paper proposes a method for solving stochastic multiple criteria decision making (MCDM) problems, where evaluations of alternatives on considered criteria are random variables with known probability density functions or probability mass functions. Probabilities on all possible results of pairwise comparisons of alternatives are first calculated using Probability Theory. Then, all possible results of pairwise comparisons are classified into superior, indifferent and inferior ones using a predefined identification rule. Consequently, the probabilities on all possible results of pairwise comparisons are partitioned into superior, indifferent and inferior probabilities. Furthermore, based on the derived probabilities, an algorithm is developed to rank the alternatives. Finally, a numerical example is used to illustrate the feasibility and validity of the proposed method.