Rough set-based logics for multicriteria decision analysis

In this paper, we propose some decision logic languages for rule representation in rough set-based multicriteria analysis. The semantic models of these logics are data tables, each of which is comprised of a finite set of objects described by a finite set of criteria/attributes. The domains of the criteria may have ordinal properties expressing preference scales, while the domains of the attributes may not. The validity, support, and confidence of a rule are defined via its satisfaction in the data table.     

An approach for predicting and describing patient outcome using multicriteria decision analysis and decision rules

Patient outcome in brain trauma patients is affected by a multiplicity of factors, beginning with ambulatory transportation and routing, to the grade of the receiving facility and treatment therein, and finally the treatment and monitoring in definitive care (the brain trauma intensive care unit). Factors and events in each of these phases can be modeled as a multicriteria problem, where the objective is to optimize patient outcome; moreover, a more comprehensive model can embody the interactions of all three phases. This study focuses on modeling the factors that affect patient outcome in definitive care and on expressing these in machine readable format so that we can better describe or predict patient outcome using data mining tools. We use multicriteria decision analysis and decision rules for knowledge representation. Preliminary results suggest that the incorporation of a priori knowledge does help better predict or describe patient outcome when using decision tree induction.     

Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bellman–Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (X,M models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called X,R models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example.     

Aggregation of fuzzy preference relations to multicriteria decision making

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed fuzzy preference relation includes t-norms and t-conorms to take into account the relation between the criteria importance. Properties of the composition and new relation, giving a possibility to make a consistent choice or to rank the alternatives, are proved. An illustrative numerical study and comparative examples are presented.     

Multicriteria sorting using a valued preference closeness relation

To define a metric or a similarity relation with good properties is a crucial issue in most analogy and rule induction oriented methods for multicriteria sorting. Here, we propose a valued indifference (closeness) relation which is inspired on concordance and discordance measures. The criterion “weights” are obtained from the preferential information embedded in a reference set. This proposal performs very well in several practical problems.     

Visualizing preferences on spheres for group decisions based on multiplicative preference relations

Decision makers’ choices are often influenced by visual background information. One of the difficulties in group decision is that decision makers may bias their judgment in order to increase the possibility of a preferred result. Hence, the method used to provide visual aids in helping decision making teams both to observe the background context and to perceive outliers is an important issue to consider. This study proposes an extended Decision Ball model to visualize a group’s decisions. By observing the Decision Balls, each decision maker can: see individual ranking as well as similarities between alternatives, identify the differences between individual judgments and the group’s collective opinion, observe the clusters of alternatives as well as clusters of decision makers, and discover outliers. Thus, this method can help decision makers make a more objective judgment.     

Rough set based rule induction from two decision tables

We study rule induction from two decision tables as a basis of rough set analysis of more than one decision tables. We regard the rule induction process as enumerating minimal conditions satisfied with positive examples but unsatisfied with negative examples and/or with negative decision rules. From this point of view, we show that seven kinds of rule induction are conceivable for a single decision table. We point out that the set of all decision rules from two decision tables can be split in two levels: a first level decision rule is positively supported by a decision table and does not have any conflict with the other decision table and a second level decision rule is positively supported by both decision tables. To each level, we propose rule induction methods based on decision matrices. Through the discussions, we demonstrate that many kinds of rule induction are conceivable.     

Interpretation of association rules in multi-tier structures

Dealing with the large amount of data resulting from association rule mining is a big challenge. The essential issue is how to provide efficient methods for summarizing and representing meaningful discovered knowledge from databases. This paper presents a new approach called multi-tier granule mining to improve the performance of association rule mining. Rather than using patterns, it uses granules to represent knowledge that is implicitly contained in relational databases. This approach also uses multi-tier structures and association mappings to interpret association rules in terms of granules. Consequently, association rules can be quickly assessed and meaningless association rules can be justified according to these association mappings. The experimental results indicate that the proposed approach is promising.     

Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm

Most multicriteria decision methods need the definition of a significant amount of preferential information from a decision agent. The preference disaggregation analysis paradigm infers the model’s parameter values from holistic judgments provided by a decision agent. Here, a new method for inferring the parameters of a fuzzy outranking model for multicriteria sorting is proposed. This approach allows us to use most of the preferential information contained in a reference set. The central idea is to characterize the quality of the model by measuring discrepancies and concordances amongst (i) the preference relations derived from the outranking model, and (ii) the preferential information contained in the reference set. The model’s parameters are inferred from a multiobjective optimization problem, according to some additional preferential information from a decision agent. Once the model has been fitted, sorting decisions about new objects are performed by using a fuzzy indifference relation. This proposal performs very well in some examples.     

A fuzzy multiobjective programming algorithm in decision support systems

Multicriteria analysis is one of the analytical functions in the problem processing system of decision support systems (DSS). In this paper, an interactive and iterative fuzzy programming method for solving a quasi-optimization problem in complex decisions under constraints involving a multiple objective function is proposed. Comparing with an adapted gradient search method, a surrogate worth tradeoff method, and a Zionts—Wallenius method, an approximate preference structure is emphasized in the proposed method.     

Multi-criteria classification – A new scheme for application of dominance-based decision rules

We are considering the problem of multi-criteria classification. In this problem, a set of “if … then …” decision rules is used as a preference model to classify objects evaluated by a set of criteria and regular attributes. Given a sample of classification examples, called learning data set, the rules are induced from dominance-based rough approximations of preference-ordered decision classes, according to the Variable Consistency Dominance-based Rough Set Approach (VC-DRSA). The main question to be answered in this paper is how to classify an object using decision rules in situation where it is covered by (i) no rule, (ii) exactly one rule, (iii) several rules. The proposed classification scheme can be applied to both, learning data set (to restore the classification known from examples) and testing data set (to predict classification of new objects). A hypothetical example from the area of telecommunications is used for illustration of the proposed classification method and for a comparison with some previous proposals.     

Multicriteria approach for intelligent decision support in supervisory control

In the framework of integrated automation, this work concerns the top level of the management and supervision of complex automated systems. When a process is being disturbed, the supervisory function modifies the established production planning, in accordance with different norms and constraints. The operator remains beside the regulated process controls to perform manual operations. The number of potential actions and the conflicting nature of some objectives make his task complex: he must reach quantitative and qualitative objectives with imperfect and temporal information. To assist him, we study a decision support model following a multicriteria approach involving the supervision problem. AI techniques and DSS are used to develop the aid tool. The Spinning Reserve problem encountered by Electricité de France is studied and used as support. To test our concepts, we develop the CASTART experimental support based on a synergy between the user, the problem, and the resolution models.This study is co-financed by the Conseil Régional Nord-Pas de Calais (France) and the University of Valenciennes.     

The impact of DSS use and information load on errors and decision quality

This paper uses a laboratory experiment to examine the effect of DSS use on the decision maker’s error patterns and decision quality. The DSS used in our experiments is the widely used Expert Choice (EC) implementation of the Analytic Hierarchy Process. Perhaps surprisingly, our experiments do not provide general support for the often tacit assumption that the use of a DSS such as EC improves decision quality. Rather, we find that, whereas a DSS can help decision makers develop a better understanding of the essence of a decision problem and can reduce logical error (especially if the information load is high), it is also susceptible to introducing accidental effects such as mechanical errors. In some cases, as in our study, the accidental errors may outweigh the benefits of using a DSS, leading to lower quality decisions.     

An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection

This paper presents a consensus model for group decision making with interval multiplicative and fuzzy preference relations based on two consensus criteria: (1) a consensus measure which indicates the agreement between experts’ preference relations and (2) a measure of proximity to find out how far the individual opinions are from the group opinion. These measures are calculated by using the relative projections of individual preference relations on the collective one, which are obtained by extending the relative projection of vectors. First, the weights of experts are determined by the relative projections of individual preference relations on the initial collective one. Then using the weights of experts, all individual preference relations are aggregated into a collective one. The consensus and proximity measures are calculated by using the relative projections of experts’ preference relations respectively. The consensus measure is used to guide the consensus process until the collective solution is achieved. The proximity measure is used to guide the discussion phase of consensus reaching process. In such a way, an iterative algorithm is designed to guide the experts in the consensus reaching process. Finally the expected value preference relations are defined to transform the interval collective preference relation to a crisp one and the weights of alternatives are obtained from the expected value preference relations. Two numerical examples are given to illustrate the models and approaches.     

Using decision rules to achieve mass customization of airline services

This paper uses the Dominance-based Rough Set Approach (DRSA) to formulate airline service strategies by generating decision rules that model passenger preference for airline service quality. DRSA could help airlines eliminate some services associated with dispensable attributes without affecting passenger perception of service quality. DRSA could also help airlines achieve mass customization of airline services and generate additional revenues by active or passive targeting of quality services to passengers.     

Fuzzy preference orderings in group decision making

In this paper, some use of fuzzy preference orderings in group decision making is discussed. First, fuzzy preference orderings are defined as fuzzy binary relations satisfying reciprocity and max-min transitivity. Then, particularly in the case where individual preferences are represented by utility functions (utility values), group fuzzy preference orderings of which fuzziness is caused by differences or diversity of individual opinions are defined. Those orderings might be useful for proceeding the group decision making process smoothly, in the same manner as the extended contributive rule method.     

Multi-criteria supplier segmentation using a fuzzy preference relations based AHP

One of the strategic activities of a firm is supplier segmentation, whereby a firm creates groups of suppliers to handle them differently. Existing literature provides several typologies of suppliers, each of which uses different dimensions/variables. In this paper, different typologies are combined by distinguishing two overarching dimensions, the capabilities and the willingness of suppliers to cooperate with a particular firm. These dimensions cover almost all the existing supplier segmentation criteria mentioned in existing literature. For each particular situation, these dimensions can be specified using a multi-criteria decision-making method. A methodology is proposed that includes a fuzzy Analytic Hierarchy Process (AHP) which uses fuzzy preference relations to incorporate the ambiguities and uncertainties that usually exist in human judgment. The proposed methodology is used to segment the suppliers of a broiler company. The result is a segmentation of suppliers based on two aggregated dimensions. Finally some strategies to handle different segments are discussed and concluding remarks and suggestions for future research are provided.     

Application of consistent fuzzy preference relations in predicting the success of knowledge management implementation

The implementation of knowledge management (KM) involves innovation and reformation for organizations. KM implementation requires not only a substantial investment, but also changes the organization culture and structure. Before embarking on KM, thorough planning is crucial to ensure the implementation achieves the intended objectives of accruing profit and enhancing competitiveness for organisations. Therefore, this study proposes an analytic hierarchical prediction model based on the reciprocal additive consistent fuzzy preference relations to help the organizations become aware of the essential factors affecting the KM implementation, forecasting the chance of successful KM initiative, as well as identifying the actions necessary before implementing KM. Pairwise comparisons are used to determine the priority weights of influential factors and the ratings of two possible outcomes (success and failure) amongst decision makers. The subjectivity and vagueness in the prediction procedures are dealt with using linguistic terms quantified in an interval scale [0, 1]. By multiplying the weights of influential factors and the ratings of possible outcomes, predicted success/failure values are obtained to enable organizations to decide whether to initiate knowledge management, inhibit adoption or take remedial actions to increase the possibility of successful KM project. This proposed approach is demonstrated with a real case study assessed by eleven evaluators solicited from a Liquid Crystal Display (LCD) manufacturing corporation located in Taiwan.     

Optimal aggregation of fuzzy preference relations with an application to broadband internet service selection

This paper investigates the aggregation of multiple fuzzy preference relations into a collective fuzzy preference relation in fuzzy group decision analysis and proposes an optimization based aggregation approach to assess the relative importance weights of the multiple fuzzy preference relations. The proposed approach that is analytical in nature assesses the weights by minimizing the sum of squared distances between any two weighted fuzzy preference relations. Relevant theorems are offered in support of the proposed approach. Multiplicative preference relations are also incorporated into the approach using an appropriate transformation technique. An eigenvector method is introduced to derive the priorities from the collective fuzzy preference relation. The proposed aggregation approach is tested using two numerical examples. A third example involving broadband internet service selection is offered to illustrate that the proposed aggregation approach provides a simple, effective and practical way of aggregating multiple fuzzy preference relations in real-life situations.     

A least deviation method for priority derivation in group decision making with incomplete reciprocal preference relations

In this paper, based on the transfer relationship between reciprocal preference relation and multiplicative preference relation, we proposed a least deviation method (LDM) to obtain a priority vector for group decision making (GDM) problems where decision-makers' (DMs') assessments on alternatives are furnished as incomplete reciprocal preference relations with missing values. Relevant theorems are investigated and a convergent iterative algorithm about LDM is developed. Using three numerical examples, the LDM is compared with the other prioritization methods based on two performance evaluation criteria: maximum deviation and maximum absolute deviation. Statistical comparative study, complexity of computation of different algorithms, and comparative analyses are provided to show its advantages over existing approaches.