Multicriteria Sorting Research Articles

Predictive Modelling for Sensitive Social Media Contents Using Entropy-FlowSort and Artificial Neural Networks Initialized by Large Language Models

This work offers an integrated methodological framework that integrates the capabilities of large language models (LLMs), rules-based reasoning, multi-criteria sorting, and artificial neural networks (ANN) in developing a predictive model for classifying the intensity of sensitive social media contents. The current literature lacks a holistic consideration of multiple attributes in evaluating social media contents, and the proposed framework intends to bridge such a gap. Three actions constitute the development of the framework. First, LLMs (i.e., GPT4) evaluate the social media contents under a predefined set of attributes, leveraging the power of LLMs in content analytics. Second, rules-based reasoning and multi-criteria sorting (i.e., entropy-FlowSort) determine the categories of social media contents. Lastly, the two previous actions produced a complete dataset that can be used to train a predictive model using ANN to classify sensitive social media contents. With 1100 randomly extracted social media contents and the predefined categories of violations against community standards set by Facebook, the proposed integrated methodology produces an ANN-based classification model with 86.36% prediction accuracy. Comparative analysis using Decision Trees, k-nearest neighbors, Linear Discriminant Analysis, Random Forest, and Naive Bayes classification yields the highest performance of ANN. The predictive model can be used as a decision-support tool to design moderation actions on social media contents.

Strategic behavior in multi-criteria sorting with trust relationships-based consensus mechanism: Application in supply chain risk management

Strategic behavior is common in multi-criteria sorting, where manipulated alternatives are allocated to the target category to achieve the intended goal. Engaging in such strategic behavior in sorting consensus often comes at a cost, which is closely tied to the degree of preference adjustments and the level of trust relationships among decision makers. This study investigates strategic behavior using piecewise cost-based consensus mechanism in social trust network. Firstly, the trust relationship dependent piecewise cost is formally defined and formulated by considering the impact of trust relationship on the preference adjustments willingness to achieve sorting consensus. Then, based on the trust relationship dependent piecewise cost, a preference strategic manipulation model is proposed to achieve strategic behavior in sorting consensus, which is implemented by minimizing the cost of strategically guiding decision makers in adjusting their preferences. Considering that social trust network affects strategic manipulation, a preference-network collaborative strategic manipulation model is further proposed, which is designed to strategically guide decision makers in adjusting both their preferences and social trust networks. Moreover, the practicality of proposed strategic manipulation models is exemplified through a case study on supply chain risk management and their performance is validated via simulation analysis.

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

Learning preferences from assignment examples has attracted considerable attention in the field of multi-criteria sorting (MCS). However, traditional MCS methods, designed to infer decision makers’ preferences from small-scale assignment examples, encounter limitations when confronted with large-scale data sets. Additionally, the presence of decision makers’ non-monotonic preferences for certain criteria in MCS problems necessitates accounting for potential non-monotonicity when devising preference learning methods. To address this, this paper proposes some new models to learn potentially non-monotonic preferences for MCS problems from large-scale assignment examples by leveraging machine learning models. Specifically, we first introduce the Piecewise-Linear Neural Network (PLNN) model, which leverages the threshold-based value-driven sorting procedure as the underlying sorting model and integrates a perceptron-based model to establish piecewise-linear marginal value functions to approximate real ones. On this basis, we address MCS problems with criteria interactions and extend the PLNN model to develop the Piecewise-Linear Factorization Machine-based Neural Network (PLFMNN) model by incorporating the factorization machine to factorize interaction coefficients. Training these models allows us to learn potentially non-monotonic preferences of decision makers. To illustrate the proposed models, we apply them to a red wine quality classification problem. Furthermore, we assess the performance of the proposed models through computational experiments on both artificial and real-world data sets. Additionally, we conduct statistical tests to ascertain the significance of the performance differences. Experimental results reveal that the proposed models are comparable to the multilayer perceptron model and outperform other baseline models on most data sets, thus affirming their efficacy. Finally, we conduct some sensitivity analysis to assess the impact of certain parameters on the performance of the proposed models and compare them with existing studies from a theoretical perspective, further demonstrating their effectiveness.

A Method to Handle the Missing Values in Multi-Criteria Sorting Problems Based on Dominance Rough Sets

The handling of missing attribute values remains a challenging and problematic issue in data analysis. Imputation techniques are key procedures used to deal with missing attribute values. However, although these methods are widely used, they cause data bias. Rough set theory, a unique mathematical tool for decision making under uncertainty, overcomes this problem by properly adjusting the relationships. Rough sets are often preferred in both classification and sorting problems. The aim of sorting problems is to sort the objects in the decision table (DT) from best to worst and/or to select the best one. For this purpose, it is necessary to obtain a pairwise comparison table (PCT) from the DT. However, in the presence of missing values, the transformation from DT to PCT is not feasible because there are no ranking methods in the literature for sorting problems based on rough sets. To address this limitation, this paper presents a way to transform from DT to PCT and introduces a generalization of the relation belonging to the “do not care” type of missing values in the dominance-based rough set approach (DRSA) to the decision support tool jRank. We also adapted the DomLem algorithm to enable it to work in PCT with missing values. We applied our method step by step to a decision table with 11 objects and investigated the effect of missing values. The experimental results showed that our proposed approach captures the semantics of `do not care’ type missing values.

Enhancing resource allocation in drought mitigation through a group multicriteria sorting model: a case study of Rio Grande do Norte, Brazil

ABSTRACT Drought is a natural phenomenon that poses a significant threat to water resources in affected regions. The detrimental effects of this extreme weather event, regardless of its type, have had an impact, necessitating concrete resource allocation projects to mitigate drought. From this perspective, our research proposes a group multicriteria sorting model to support resource allocation for drought mitigation. A multicriteria sorting model was developed based on the PROMSORT method to assist the government in evaluating 14 municipalities of the Apodi-Mossoró river basin in the Rio Grande do Norte State in Brazil. This model classifies the municipalities into high, moderate, and low-priority categories, enabling targeted attention and allocation of resources for drought mitigation efforts. The research findings demonstrate that the proposed model can effectively support strategic public policies, allocate resources, and facilitate the implementation of appropriate actions, thereby focusing efforts on the cities most severely affected by drought and alleviating the adverse effects of this natural disaster

An adaptive consensus model for multi-criteria sorting under linguistic distribution group decision making considering decision-makers’ attitudes

Group multiple criteria sorting (MCS) has become a trend in dealing with a variety of practical problems. During the process of managing group MCS, it is critical to reduce conflicts among decision-makers (DMs). Given the key role of DMs’ attitudes in affecting consensus level, this study aims to propose a novel consensus-based approach to solve group MCS problems considering DMs’ attitudes with flexible expression linguistic distribution assessments (LDAs) that can capture massive DMs’ qualitative preferences. To achieve this goal, first, a minimum adjustment-based optimization model is built to guide individuals in revising their preferences, and a maximum assignment interval-based optimization model is constructed to derive consistent and possible assignments of each alternative while maintaining the accuracy levels of the original assignments. An attitudinal consensus index is then defined to measure the group consensus level, by which group DMs’ attitudes can be well considered in MCS problems. A sophisticated adaptive feedback adjustment mechanism is also developed and inserted into the consensus model, which provides support for consensus-reaching based on the advantages of both types of adaptive feedback adjustment mechanism strategies. Afterwards, to generate more straightforward and scientific assignment solutions, this study proposes a minimum information loss-based optimization model to identify the final categories of each alternative. Finally, an illustrative example for evaluating livable cities, followed by sensitivity and comparative analyses, is presented to demonstrate the applicability and advantages of the proposed MCS approach.

A semi-supervised multi-criteria sorting approach to constructing social vulnerability composite indicators

A semi-supervised multi-criteria sorting approach to constructing social vulnerability composite indicators

Estimating relative importance of criteria by post-processing dominance-based rough set approach’s outputs

The dominance-based rough set approach (DRSA) is one of the rare multicriteria sorting methods that does not require a priori values for the relative importance of criteria. This method therefore is cognitively less demanding. However, the decision-maker may lack some valuable information that is needed to explain and justify final decisions to stakeholders. The relative importance of criteria can instead be estimated based on the characteristics of the outputs of the DRSA, which are mainly decision rules and attribute reducts. The estimated values can then be used to understand the role played by each criterion and justify the final decisions to stakeholders. This paper first reviews and improves the decision rule attractiveness measure and the relative importance measures that are based on decision rules and attribute reducts, which were all proposed in the authors’ previous work. It also introduces new measures that rely on the marginal contributions and entropy of the criteria. This paper also extends these measures to estimate the relative importance of criteria with respect to specific unions of classes. The proposed measures have been applied to Brexit referendum and bankruptcy risk assessment datasets. Both applications showed that the proposed measures generally lead to different results. This can be explained by the diversity of the knowledge on which these measures rely and also by the multiplicity of the analytical perspectives associated with them. The results also showed that the marginal contribution-based measure is a good estimator of both Shapley and Banzhaf values.

A novel group multi-criteria sorting approach integrating social network analysis for ability assessment of health rumor-refutation accounts

Blooming social media platforms provide breeding ground for health rumors. Despite the establishment of accounts by numerous organizations to counter health rumors, the effectiveness of these endeavors exhibits considerable variability. Thus, there exists a pressing need to refine the framework and operation of rumor-refutation accounts. Aiming at enhancing the proficiency of accounts in refuting health rumors on social media platforms and exploring the factors affecting it, this paper proposes a novel group multi-criteria sorting approach integrating social network analysis (SNA) to classify accounts’ health rumor-refutation ability. To commence, an evaluation indicator system for accounts’ health rumor-refutation ability is established using SNA. Subsequently, the indicator values are computed, incorporating methods such as triangular fuzzy number (TFN), a lite bert (ALBERT) pre-trained language model, and PageRank. Furthermore, hesitant fuzzy linguistic term set (HFLTS) and triangular intuitionistic fuzzy number (TIFN) are used to determine the expert weights and indicator weights. After that, on the basis of original best worst method-sort (BWM-Sort), classification boundaries are discovered creatively using optimal clustering (OC), and minimum discrimination information (MDI) is adopted as the objective function for priority assignment. Consequently, an OC-MDI-BWM-Sort method is newly proposed which offers distinct advantages in computational efficiency, information integration, decision-making objectivity, and result effectiveness. Lastly, regarding to four cases of widely circulated rumors, health rumor-refutation ability of 35 accounts on Weibo platform is classified using the proposed method. The findings underscore that merely 8.57% of accounts exhibit stable and good health rumor-refutation ability, while up to 28.57% and 80.00% display poor and inconsistent ability in certain instances. Tailored to accounts with excellent or good, satisfactory or fair, and poor health rumor-refutation ability, respectively, managerial suggestions are provided regarding information expression standards, account operator proficiency, and account cooperation, and all accounts are advised to watch audience behavior.

Hesitant triangular fuzzy FlowSort method: the multi-criteria decision-making problems

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.

A family of fuzzy multi-criteria sorting models FTOPSIS-Sort: Features, case study analysis, and the statistics of distinctions

A family of fuzzy multi-criteria sorting models, FTOPSIS-Sort, as a fuzzy extension of Multi-Criteria Decision Analysis (MCDA) ordinary method TOPSIS, is introduced and analyzed. Models from this family differ by approaches to determining functions of fuzzy numbers (approximate computations, standard fuzzy arithmetic, and transformation method) and by methods for ranking of fuzzy numbers (two defuzzification based ranking methods are considered). The features of developing and adjusting Fuzzy TOPSIS (FTOPSIS) models to sorting problematic are presented. The developed models are implemented in the case study on a healthcare supply chain alternative selection problem. For exploring distinctions in sorting alternatives by FTOPSIS-Sort models, the special algorithms have been developed along with their integrating with Monte Carlo simulation of a large number of input scenarios, each of which is a separate (and independent of the others) multicriteria problem on sorting alternatives. The results of such an analysis demonstrate a significant distinction in sorting alternatives by different FTOPSIS-Sort models. The latter has theoretical, methodological, and applied significance within the use of Fuzzy TOPSIS (Fuzzy MCDA) sorting models.

A Bayesian model for multicriteria sorting problems

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.

An Integrated Multicriteria Sorting Methodology with q-Rung Orthopair Fuzzy Sets for Evaluating the Impacts of Delays on Residential Construction Projects

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.

FUZZY LINEAR PROGRAMMING MODEL FOR INVERSE MULTIPLE CRITERIA SORTING PROBLEM: AN APPLICATION IN A PUBLIC TRANSPORTATION COMPANY

Multi-criteria decision making (MCDM) techniques are among the methods used by the decision maker in the decision phase in practice, as in the literature. MCDM problems are grouped as classifications and sorting problems according to the type of inclusion or ranking in existing classes. Inverse multi-criteria sorting problem, a new topic in recent years, is defined as choosing among existing actions in order to improve the status of alternatives. In this study, in order to find out which action plan should be chosen for providing the minimum cost for the improvement of public transportation vehicles in case the boundaries of the classes to be assigned are uncertain, the inverse multi-criteria ranking problem is used. Because the boundaries of the classes to be assigned are fuzzy, fuzzy linear programming method will be used to solve the problem.

Multicriteria sorting method based on global and local search for supplier segmentation

AbstractThe aim of this research is to develop a robust multicriteria method to classify suppliers into ordered categories and its validation in real contexts. The proposed technique is based on a property of net flows of the PROMETHEE method and uses global and local search concepts, which are common in the optimisation field. The results obtained are compared to those from the most cited sorting algorithm, and an empirical validation and sensitivity analysis is performed using real supplier evaluation data. Furthermore, it does not require additional information from decision‐makers as other sorting algorithms do for assigning incomparable or indifferent alternatives to groups. An extension of the silhouette concept from data mining is also contributed to measure the quality of ordered classes. Both contributions are easy to apply and integrate into decision support systems for automated decisions in the supply chain management. Finally, this practical approach is also useful to classify customers and any type of alternatives or actions into ordered categories, which have an increasing number of real applications.

PL-MACONT-I: A Probabilistic Linguistic MACONT-I Method for Multi-Criterion Sorting

Multi-criterion sorting (MCS) problems aim to assign alternatives to corresponding categories according to multiple criteria. Various MCS methods have been proposed. However, these methods need to preset reference profile of each category to arrange alternatives, which may be difficult for decision makers. To circumvent this issue, this study proposes an MCS method without setting reference profiles of categories. The mixed aggregation by comprehensive normalization technique (MACONT) method, as a recently-developed multi-criterion decision-making method, can obtain a multi-aspect and comprehensive solution for choice and ranking problems. To solve multi-criteria sorting problems, this study introduces an MACONT-I method in which the deck of card method (DCM) is applied to derive criteria weights. Furthermore, to enhance the applicability of the proposed method in decision-making with uncertain information, we extend the DCM and the proposed MACONT-I method to probabilistic linguistic context and propose a PL-MACONT-I method for multi-criterion sorting. An illustrative example is provided to demonstrate the practicality of the proposed method. Through sensitivity analysis and comparative analysis, the merits of the proposed method are emphasized.

Class Thresholds Pre-Definition by Clustering Techniques for Applications of ELECTRE TRI Method

The sorting problem in the Multi-criteria Decision Analysis (MCDA) has been used to address issues whose solutions involve the allocation of alternatives in classes. Traditional multi-criteria methods are commonly used for this task, such as ELECTRE TRI, AHP-Sort, UTADIS, PROMETHEE, GAYA, etc. While using these approaches to perform the sorting procedure, the decision-makers define profiles (thresholds) for classes to compare the alternatives within these profiles. However, most such applications are based on subjective tasks, i.e., decision-makers’ expertise, which sometimes might be imprecise. To fill that gap, in this paper, a comparative analysis using the multi-criteria method ELECTRE TRI and clustering algorithms is performed to obtain an auxiliary procedure to define initial thresholds for the ELECTRE TRI method. In this proposed methodology, K-Means, K-Medoids, Fuzzy C-Means algorithms, and Bio-Inspired metaheuristics such as PSO, Differential Evolution, and Genetic algorithm for clustering are tested considering a dataset from a fundamental problem of sorting in Water Distribution Networks. The computational performances indicate that Fuzzy C-Means was more suitable for achieving the desired response. The practical contributions show a relevant procedure to provide an initial view of boundaries in multi-criteria sorting methods based on the datasets from specific applications. Theoretically, it is a new development to pre-define the initial limits of classes for the sorting problem in multi-criteria approach.

Measuring the comparative advantage of camping businesses: A multicriteria sorting methodology

The adoption of appropriate strategies is an obligation for firms to gain in competitiveness. This paper develops a camping comparative advantage measure methodology by composing an operational definition of this concept and by implementing an assessment method. The paper first undertakes a literature review concerning competitiveness and performance measurement in tourism and hospitality. Secondly, it develops a multi-criteria framework to evaluate comparative advantage of camping businesses. This framework is then applied to French firms by using the ELECTRE TRI methodology. The article has management implications in relation to the usefulness of the proposed methodology to real-world situations. Its results have theoretical significances: the paper extends the literature regarding hospitality firms’ competitiveness and specifies criteria concerning camping businesses advantage against competitors. Findings reveal three homogeneous categories. To ensure the relevance of these categories, the investment strategies and then the camping manager feedbacks are detailed. In terms of limitations, the adopted approach recalls to an accumulation of resources, and this does not automatically equate to competitiveness as exposed the resource quality or capabilities to manage these large number of resources.

Inferring Preferences for Multi-Criteria Ordinal Classification Methods Using Evolutionary Algorithms

Multicriteria sorting involves assigning the objects of decisions (actions) into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> priori known ordered classes considering the preferences of a decision maker (DM). Two new multicriteria sorting methods were recently proposed by the authors. These methods are based on a novel approach called interval-based outranking which provides the methods with attractive practical and theoretical characteristics. However, as is well known, defining parameter values for methods based on the outranking approach is often very difficult. This difficulty arises not only from the large number of parameters and the DM’s lack of familiarity with them, but also from imperfectly known (even missing) information. Here, we address: i) how to elicit the parameter values of the two new methods, and ii) how to incorporate imperfect knowledge during the elicitation. We follow the preference disaggregation paradigm and use evolutionary algorithms to address it. Our proposal performs very well in a wide range of computational experiments. Interesting findings are: i) the method restores the assignment examples with high effectiveness using only three profiles in each limiting boundary or representative actions per class; and ii) the ability to appropriately assign unknown actions can be greatly improved by increasing the number of limiting profiles.

Proposed Intuitionistic Fuzzy Entropy Measure Along With Novel Multicriteria Sorting Techniques

Recently, the major environmental change and a pandemic called COVID-19 have heavily impacted the economy, business, and health of each country. Moreover, the climatic changes and COVID-19 are calamities to human life. In other words, these two aspects threaten the existence of humans and the sustenance of the overall development of a country. These two factors particularly influence the tourism sector, so a strategy balancing environmental quality and dealing with the ill effects of COVID-19 is formulated to uplift the economic sectors. Atannasov’s intuitionistic fuzzy domain is used to model the environmental quality and COVID-19 due to the involvement of hesitancy and uncertainty. The precise measurement of the imprecision in the information is obtained with the help of entropy measure. The paper analyzes the two aspects using a novel entropy measure based on multiple criteria sorting (MCS). Here, the two MCS problems are solved with the help of two proposed techniques: TOPSIS-GREY-sort and ENTROPY-TOPSIS-GREY-sort. A case study showing the impact of COVID-19 in the Philippines and the environmental quality of Tehran (the capital city of Iran) are considered to validate the functioning of the proposed techniques. We use “A novel sorting method TOPSIS-SORT: an application for Tehran environmental quality evaluation (2016), Ekonomica a management,” and “Current Issues in Tourism 25.2(2022): 168–178, Taylor and Francis” for the comparative analysis.