Handling incomplete information in the framework of THESEUS multicriteria sorting method

Lexicographic optimization-based approaches to learning a representative model for multi-criteria sorting with non-monotonic criteria

Integrating machine learning models to learn potentially non-monotonic preferences for multi-criteria sorting from large-scale assignment examples

Some recent works have established the importance of handling abundant reference information in multi-criteria sorting problems. More valid information allows a better characterization of the agent’s assignment policy, which can lead to an improved decision support. However, sometimes information for enhancing the reference set may be not available, or may be too expensive. This paper explores an automatic mode of enhancing the reference set in the framework of the THESEUS multi-criteria sorting method. Some performance measures are defined in order to test results of the enhancement. Several theoretical arguments and practical experiments are provided here, supporting a basic advantage of the automatic enhancement: a reduction of the vagueness measure that improves the THESEUS accuracy, without additional efforts from the decision agent. The experiments suggest that the errors coming from inadequate automatic assignments can be kept at a manageable level.

A novel hybrid simplified group BWM and multi-criteria sorting approach for stock portfolio selection

Performance Evaluation of Artificial Neural Network Algorithms: A Case of Classification Problem

We consider the multi-criteria sorting problem where alternatives that are evaluated on multiple criteria are assigned into ordered categories. We focus on the sorting problem with category size restrictions, where the decision maker (DM) may have some concerns or constraints on the number of alternatives that should be assigned to some of the categories. We develop an approach based on the UTADIS method that fits an additive utility function to represent the decision maker’s preferences. We introduce additional variables and constraints to enforce the restrictions on the sizes of categories. The new formulation reduces the number of binary variables and hence decreases the computational effort compared to the existing approaches in the literature. We further improve the computational efficiency by developing lower and upper bounds on the rank of each alternative in order to narrow down the set of categories that each alternative can be assigned to. We demonstrate our approach on two applications from practice.

Multicriteria sorting problem arises, among other things, when it is necessary to construct the base of Decision Maker's rules for a classification/diagnostic Decision Support System (DSS). Advantages and drawbacks of existing methods for multicriteria sorting based on the Verbal Decision Analysis are analyzed. To overcome such drawbacks, it is proposed to apply to multicriteria sorting the main features of the VDA-based STEPCLASS method.

The exploitation of non timber forest products (NTFPs), are the main source of income for rural populations in the Pô region of Burkina Faso. However, the potential of NTFP-providing species is not always exploited in a way that provides greater profitability for rural populations. This is mainly due to the fact that several criteria must be taken into account and aggregated in agreement with the various stakeholders. The aim of this work is to propose a prioritization of NTFP-providing species based on their ability to provide greater profitability for local populations. To this end, a proposition of a methodology based on the joint use of the KEMIRA-sort and ELECTRE Tri multi-criteria sorting methods to assign NTFP-providing species to ordered categories of profitability is made. The application of this methodology enabled to identify a median categorization made up of three categories of NTFP-providing species according to their profitability in the Pô area. The best category is made up of one specie (tamarind), while the second best category is made up of four species (shea, baobab, moringa, mango) and the last of five species (nere, detarium, jujube, resin and liana). The concordance of these results with the estimate of the expert, playing the role of decision maker, at the very start of our study, validate empirically the proposed approach, prefiguring its successful application to other context of multiple criteria sorting problems in the future (e.g. prioritizing areas at risk of the spread of a given disease in public health). Our approach also shows the complementary use of a total aggregation method (KEMIRA-sort) and an outranking method (ELECTRE Tri) in solving a multi-criteria sorting problem.

We introduce the concept of variable-consistency monotonic decision tree induced from preference-ordered data concerning a multicriteria sorting (classification) problem. Given the data in form of an information table including some sorting examples, we propose to induce a decision tree using an inductive learning algorithm. The decision tree can be considered as a preference model of a decision maker who supplied the sorting examples. Moreover, a partial violation of the dominance principle is admitted and controlled by an index called consistency level. The monotonic decision trees with variable consistency can be applied to a wide range of possible applications, for instance, financial rating, bank creditworthiness, medical diagnosis, and the like.

The original version of the rough sets theory has proved to be particularly useful in the analysis of multiattribute classification problems under inconsistency following from information granulation, i.e. objects having the same description but belonging to different classes. It fails, however, when attributes with preference-ordered domains (criteria) have to be taken into account. In order to deal with problems of multicriteria decision analysis (MCDA), such as sorting, choice or ranking, the authors have extended the original rough sets theory in a number of directions. The main extension is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered decision classes in multicriteria sorting. Second extension was necessary to approximate preference relations in multicriteria choice and ranking problems; it requires substitution of the data table by a pairwise comparison table, where each row corresponds to a pair of actions described by binary relations on particular criteria. In all these MCDA problems, the extended rough set approach ends with a set of “if..., then...” decision rules playing the role of a preference model. It is more general than the classical functional or relational model and more understandable for the users. These rules have a more general syntax than the rules following from the original rough set approach and they are able to handle two kinds of inconsistencies, one with respect to indiscernibility and another with respect to dominance, instead of the first one only. In the extended rough set approach, discretization of quantitative attributes is not necessary and it is possible to consider attributes and criteria within the same decision problem. The paper summarizes these extensions and concentrates on description of the rough set approach to the multicriteria sorting problem, illustrated by a case study of airline company financial ratings.

This study offers an integrated evaluation methodology for construction project delay causes viewed as a multicriteria sorting (MCS) problem. Time, cost, and quality were the three project management factors considered as criteria to evaluate 38 identified delay causes. The priority weights were extracted using the integration of Weighted Influence Non-linear Gauge Systems (WINGS) and Level-Based Weight Assessment (LBWA) to capture the inherent interdependencies of the criteria. The sorting of 38 delay causes was performed using FlowSort. To handle the uncertainty and vagueness of the judgments of the decision makers in the evaluation process, q-rung fuzzy orthopair fuzzy sets (q-ROFS) were integrated within the proposed computational framework. The proposed novel q-ROF–WINGS–LBWA–FlowSort method was applied in an actual case study in residential construction projects. The delay causes were categorized under three categories of construction firm vulnerability into four levels of impact. In highly vulnerable construction firms, thirty-five delay causes have a high impact, two have a moderate impact, and one has the least impact. In moderately vulnerable and least-vulnerable construction firms, 32 and 28 delay causes have a medium impact, respectively. The results may provide insights for decision makers in highly vulnerable construction firms, i.e., small companies with limited resources and networks. Layers of sensitivity and comparative analyses were put forward to test the robustness of the approach.

This paper explores possibilities for recognizing and analytically using culturally-specific understandings of artefacts and spaces at an ancient Maya archaeological site. In the case study that we present, we use Classic Maya material categories – derived from hieroglyphic texts – to re-envision our representations of artefactual distributions and accompanying interpretations. We take inspiration from countermapping as an approach that recognizes the positionality of spatial representations and makes space for multiple/alternative spatial perspectives. We present spatial analyses based on our work at the Classic Maya archaeological site of Say Kah, Belize, juxtaposing modern modes of visualizing the results of multiple seasons of excavations with visualizations that instead draw upon reconstructed elements of ancient inhabitants’ perspectives on the site, its spaces, and usages (based on information drawn from Classic Maya textual ‘property qualifiers’). We argue that even incomplete information, such as that available for archaeological contexts, allows us to reimagine past spatial perspectives and experiences. Furthermore, doing so represents a move towards inclusion that changes our understanding of sites in terms of ancient experience and usage. The outcome is a shifted perspective on the spaces of the site that decentres the modern, archaeological vision, accompanied by a more reflexive awareness of the processes we use to construct our interpretations. We end with larger reflections useful for archaeologists curious about translating these ideas to other cultural settings.

The rough sets theory has been proposed by Z. Pawlak in the early 80’s to deal with inconsistency problems following from information granulation. It operates on an information table composed of a set U of objects (actions) described by a set Q of attributes. Its basic notions are: indiscernibility relation on U, lower and upper approximation of a subset or a partition of U, dependence and reduction of attributes from Q, and decision rules derived from lower approximations and boundaries of subsets identified with decision classes. The original rough sets idea has proved to be particularly useful in the analysis of multiattribute classification problems; however, it was failing when preferential ordering of attributes (criteria) had to be taken into account In order to deal with problems of multicriteria decision making (MCDM), like sorting, choice or ranking, a number of methodological changes to the original rough sets theory were necessary. The main change is the substitution of the indiscernibility relation by a dominance relation (crisp or fuzzy), which permits approximation of ordered sets in multicriteria sorting In order to approximate preference relations in multicriteria choice and ranking problems, another change is necessary: substitution of the information table by a pairwise comparison table, where each row corresponds to a pair of objects described by binary relations on particular criteria. In all those MCDM problems, the new rough set approach ends with a set of decision rules, playing the role of a comprehensive preference model. It is more general than the classic functional or relational model and it is more understandable for the users because of its natural syntax. In order to workout a recommendation in one of the MCDM problems, we propose exploitation procedures of the set of decision rules. Finally, some other recently obtained results are given: rough approximations by means of similarity relations (crisp or fuzzy) and the equivalence of a decision rule preference model with a conjoint measurement model which is neither additive nor transitive.

A new approach to classification problems with incomplete information is described. The decision rule is designed considering the similarity of recognized objects. Designing a decision rule with the help of a general generalized variable is the basis of the approach.

Machine learning (ML) applications have been thriving recently, largely attributed to the increasing availability of data. However, inconsistency and incomplete information are ubiquitous in real-world datasets, and their impact on ML applications remains elusive. In this paper, we present a formal study of this impact by extending the notion of Certain Answers for Codd tables, which has been explored by the database research community for decades, into the field of machine learning. Specifically, we focus on classification problems and propose the notion of "Certain Predictions" (CP) --- a test data example can be certainly predicted (CP'ed) if all possible classifiers trained on top of all possible worlds induced by the incompleteness of data would yield the same prediction. We study two fundamental CP queries: (Q1) checking query that determines whether a data example can be CP'ed; and (Q2) counting query that computes the number of classifiers that support a particular prediction (i.e., label). Given that general solutions to CP queries are, not surprisingly, hard without assumption over the type of classifier, we further present a case study in the context of nearest neighbor (NN) classifiers, where efficient solutions to CP queries can be developed --- we show that it is possible to answer both queries in linear or polynomial time over exponentially many possible worlds. We demonstrate one example use case of CP in the important application of "data cleaning for machine learning (DC for ML)." We show that our proposed CPClean approach built based on CP can often significantly outperform existing techniques, particularly on datasets with systematic missing values. For example, on 5 datasets with systematic missingness, CPClean (with early termination) closes 100% gap on average by cleaning 36% of dirty data on average, while the best automatic cleaning approach BoostClean can only close 14% gap on average.