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

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.

Approaches for inequity-averse sorting

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

Context-dependent DEASort: A multiple criteria sorting method for ecological risk assessment problems

In Multi-Criteria Decision Aiding, one of the current challenges involves the proper integration and tuning of the preference models in real-life contexts. In this article, we consider the multi-criteria sorting problem where the decision maker’s preferences fall within the outranking paradigm. Following recent advances on extensions of classical majority-rule sorting models, we propose a methodology for adapting them to the perspective of the decision maker. We illustrate the application of the methodology on a real-world problem linked to the evaluation of contributors within Free/Libre Open Source Software communities. The experiments that we have carried out show that the various considered model extensions appear to be useful from the perspective of decision makers in a real-life preference elicitation process, and that the proposed methodology gives useful indications that can serve as guidelines for analysts involved in other elicitation processes.

Preference disaggregation for multiple criteria sorting with partial monotonicity constraints: Application to exposure management of nanomaterials

Rough sets proved to be very useful for analysis of decision problems concerning objects described in a data table by a set of condition attributes and by a set of decision attributes. In practical applications, however, the data table is often not complete because some data are missing. To deal with this case, we propose an extension of the rough set methodology. The adaptation concerns both the classical rough set approach based on indiscernibility relations and the new rough set approach based on dominance relations. While the first approach deals with multi-attribute classification problems, the second approach deals with multi-criteria sorting problems. The adapted relations of indiscernibility or dominance between two objects are considered as directional statements where a subject is compared to a referent object having no missing values. The two rough set approaches handling the missing values boil down to the original approaches when the data table is complete. The rules induced from the rough approximations are robust in a sense that each rule is supported by at least one object with no missing values on condition attributes or criteria used by the rule.

Decision makers are often interested in assigning alternatives to preference classes under multiple criteria instead of choosing the best alternative or ranking all the alternatives. Firms need to categorize suppliers based on performance, credit agencies need to classify customers according to their risks, and graduate programs need to decide who to admit. In this article, we develop an interactive Bayesian algorithm to aid a decision maker (DM) with a multicriteria sorting problem by learning about her preferences and using that knowledge to sort alternatives. We assume the DM has a linear value function and value thresholds for preference classes. Our method specifies an informative prior distribution on the uncertain parameters. At each stage of the process, we compare the expected cost of stopping with the expected cost of continuing to consult the DM. If it is optimal to continue, we select an alternative to present to the DM and, given the DM’s response, we update the prior distribution using Bayes’ Theorem. The goal of the algorithm is to minimize expected total cost. We develop lower bounds on the optimal cost and study the performance of a heuristic policy that presents the DM alternatives with the highest expected cost of misplacement.

In recent years, multi-criteria sorting problems have become an interesting topic for researchers working on multi-criteria decision-making. ELimination and Choice Expressing REality (ELECTRE)-TRI and FlowSort are well-known approaches suggested for such a classification. The current study aimed to implement ELECTRE-TRI and FlowSort methods in the stock portfolio selection (SPS) as one of the most popular and important decision-making subjects and compare the outcomes of each method to understand how these methods perform in SPS problems. In this study, the best–worst method was applied to determine the weights of criteria. Four approaches for ELECTRE-TRI and 15 approaches for FlowSort were considered. Finally, 19 different approaches were considered to select stocks from a large pool of stocks. Results indicated that the model parameter should be properly defined to minimize inconsistencies and improve the power of the model.

Multi-criteria sorting problems have gained significant importance across various fields. However, when experts express their opinions using linguistic terms and quantitative evaluation criteria are not feasible, the fuzzy set theory proves to be a suitable framework. Moreover, in such scenarios, the use of hesitant fuzzy sets becomes necessary because each criterion might have multiple values compared with other alternatives. This paper introduces a novel method called Hesitant Triangular Fuzzy Sorting (HTFFS), which is a variation of the fuzzy FlowSort method based on the preference ranking organisation method for enrichment evaluation (PROMETHEE). The HTFFS method incorporates the theory of fuzzy sets and establishes theoretical foundations for calculating the degree of superiority of each alternative over others. This calculation uses mathematical operators specifically designed for uncertain fuzzy sets and uncertain triangular fuzzy numbers. To demonstrate the effectiveness and practicality of the proposed HTFFS method, two numerical examples are presented. The results obtained from these examples showcase the applicability and validity of the HTFFS method in handling multi-criteria sorting problems.

Rough sets methodology is a useful tool for analysis of decision problems concerning a set of objects described in a data table by a set of condition attributes and by a set of decision attributes. In practical applications, however, the data table is often not complete because some data are missing. To deal with this case, we propose an extension of the rough set methodology to the analysis of incomplete data tables. The adaptation concerns both the classical rough set approach based on the use of indiscernibility relations and the new rough set approach based on the use of dominance relations. While the first approach deals with the multi-attribute classification problem, the second approach deals with the multi-criteria sorting problem. In the latter, condition attributes have preference-ordered scales, and thus are called criteria, and the classes defined by the decision attributes are also preference-ordered. The adapted relations of indiscernibility or dominance between a pair of objects are considered as directional statements where a subject is compared to a referent object. We require that the referent object has no missing data The two adapted rough set approaches boil down to the original approaches when there are no missing data. The rules induced from the newly defined rough approximations defined are either exact or approximate, depending whether they are supported by consistent objects or not, and they are robust in a sense that each rule is supported by at least one object with no missing data on the condition attributes or criteria represented in the rule.

This work defines various stakeholder roles (or strategies) to overcome the barriers to implementing Education 4.0 (EDUC4), which were recently identified in the domain literature. The stakeholder roles are evaluated against these barriers, and such evaluation is structured as a multicriteria sorting problem. To this end, an integrated entropy‐based CRITIC‐CODAS‐SORT under a Fermatean fuzzy (FF) environment addresses epistemic uncertainties inherent in decision‐making. The FF CRITIC assigns the priority weights of the barriers, while the FF CODAS‐SORT determines the high‐priority stakeholder roles. A case of an HEI evaluating 57 possible roles of 5 stakeholders is demonstrated here. Findings suggest the lack of collaboration, apprehensive stakeholders, cybersecurity threats, health issues, and cost as crucial barriers to the HEI. The sorting process yields 13 high‐priority roles, encompassing those within the influence of the government (i.e., cybersecurity awareness, allocation of necessary funds, designing more aligned curricula, and streamlining the basic education agenda), university management (i.e., investing in efficient technologies and forging extensive stakeholder collaboration), human resource function (i.e., implementing periodic skills training for educators), and educators (i.e., engaging in continuous learning about cybersecurity threats, integrating awareness of applicable laws against cyberbullying, devising alternative cost‐efficient teaching strategies, taking part in initiatives to improve curricula, efficient preparation of learning materials, and participating in skills development initiatives). Various managerial insights are offered as inputs to the design of initiatives in EDUC4 implementation.