Robust Ordinal Regression Research Articles

Robust ordinal regression for subsets comparisons with interactions

This paper is devoted to a robust ordinal method for learning the preferences of a decision maker between subsets. The decision model, derived from Fishburn and LaValle (1996) and whose parameters we learn, is general enough to be compatible with any strict weak order on subsets, thanks to the consideration of possible interactions between elements. Moreover, we accept not to predict some preferences if the available preference data are not compatible with a reliable prediction. A predicted preference is considered reliable if all the simplest models (Occam’s razor) explaining the preference data agree on it. Following the robust ordinal regression methodology, our predictions are based on an uncertainty set encompassing the possible values of the model parameters. We define a new ordinal dominance relation between subsets and design a procedure to determine whether this dominance relation holds. Numerical tests are provided on synthetic and real-world data to evaluate the richness and reliability of the preference predictions made.

Multiple criteria decision modeling in social networks: An application to identify opinion leaders in online public opinion events

For online public opinion events, the misconduct of opinion leaders can easily lead to the spread of negative public opinion, which in turn can adversely affect real society. In order to minimize this adverse impact to the greatest extent, this paper uses social network analysis to explore the attributes of individuals, features of network structure, and social relationships between decision makers (DMs). It constructs the structural system of evaluation criteria and a multiple criteria decision model to comprehensively and reasonably identify opinion leaders. It additionally considers the importance of criteria and the interaction among them. The hierarchical structure is combined with the evaluation level to construct a precise structural system of criteria. To handle the interaction, the Choquet integral is applied as the preference model. Based on the disaggregation principle, a generalized hierarchical level dependent Choquet integral is developed to reproduce additional preference information provided by decision analysts (DAs) and aggregate evaluation values of DMs on multiple interacting criteria. Then, the relevant indices of this integral and the preference information are applied to robust ordinal regression to mine rich preference relations among DMs. Furthermore, the hierarchical level dependent Choquet integral-driven multiple criteria decision model is proposed to rank DMs and identify opinion leaders. Finally, a numerical example and two real datasets validate the effectiveness and advantages of the proposed decision model.

The Elephant Queen: Can a nature documentary help to increase tolerance towards elephants?

Abstract Conflict between humans and elephants is one of the more complex examples of human‐wildlife conflict, a key challenge for wildlife conservation. While interventions exist to separate humans from elephants, few exist aimed at bringing the two species closer together. This study assesses if a natural history film, The Elephant Queen (TEQ), makes communities living around elephants more tolerant of conflict with elephants. Questionnaires and interviews were conducted before and after seeing the film screened on a mobile cinema in Southern Kenya. A double robust ordinal regression analysis using 357 matching specifications to measure the effect size of viewing TEQ on the six criteria identified as being drivers of tolerance of a wild animal by the Hazard Acceptance model. This study found that students aged between 16 and 18 gained knowledge (mean effect size = 0.27) and affection (mean effect size = 0.17) towards elephants and felt the benefits of elephants more keenly (mean effect size = 0.26) following viewing TEQ. Community members aged between 16–80 also gained knowledge (mean effect size = 0.21) and saw the benefits of elephants (mean effect size = 0.15) but felt the costs of living with elephants more profoundly after viewing TEQ (mean effect size = −0.11). After 90 days a follow‐up survey also showed a significant increase in community “affection” towards elephants (mean effect size = 0.11), however the costs, benefits and knowledge gained had been reduced to a statistically insignificant level compared to baseline. Our results suggest that natural history films can serve as a valuable tool in inspiring young minds. When shown to an adult audience, changes were more nuanced and some of the changes were short lived (<3 months). Read the free Plain Language Summary for this article on the Journal blog.

A Decision Support System for the Selection of Insulating Material in Energy Retrofit of Industrial Buildings: A New Robust Ordinal Regression Approach

The criteria for selecting insulating materials in the energy retrofitting of industrial buildings can often be conflicting, leading to a multicriteria decision-making problem. This is the first study to take an indirect elicitation approach to solving this selection problem, which is particularly applicable in the preliminary phases of negotiation with all of the decision-makers involved. We introduce a nonlinear indirect elicitation approach for PROMETHEE II that uses Bézier curves as nonlinear preference curves to fit the decision-maker's preferences, i.e., indifference and/or strict preferences for insulating materials that are taken as references. In our approach, no parameters need to be initially set, and thus, it has the advantage of setting both the preference curves on the criteria and the criteria weights when the decision-maker is not confident. The set of Bézier curves and criteria weights that best fits the preferences given by the decision-maker may thus be achieved and visualized, which provides managerial insights as it makes explicit the preference structure of the decision-maker. We use a case study to validate our proposal in a real setting and confirm that linear preference curves would have achieved less clear relations between the insulating materials used as references respect to Bèzier curves.

A robust ordinal regression feedback consensus model with dynamic trust propagation in social network group decision-making

This paper proposes a robust ordinal regression feedback consensus model based on trust relationships for social network group decision-making problems in intuitionistic fuzzy environment. The model consists of two main parts: (a) the construction of the complete trust matrix among decision makers (DMs) and (b) the design of a feedback mechanism formulated on robust ordinal regression. In Part (a), to complete the initial trust matrix between DMs, a dynamic trust propagation mode founded on maximum credibility is proposed to investigate indirect trust relationships between unfamiliar DMs from the perspective of overall optimization. In Part (b), when the group consensus does not reach the consensus threshold, the utility function compatible with the preference information of DMs is constructed through robust ordinal regression, and the most representative utility function is selected by maximizing the difference of the necessary weak preference relationship. In addition, the performance of DMs under four evaluation dimensions, individual consensus degree, individual comprehensive influence, individual opinion retention, and individual proximity centrality, is aggregated into a total utility value. In each iteration, the DM with the lowest total utility value is identified for opinion adjustments. Further, based on trust-similarity analysis, recommendations are designed for opinion adjustments to improve the group consensus. An illustrative example along with the related sensitivity analysis and comparative study is used to examine the effectiveness and advantages of the proposed model.

Non-additive robust ordinal regression: A multicriteria decision model based on hierarchical-level-bidirectional Choquet integral

In contrast to the stable development of the traditional face to face teaching, distance education has become a considerable portion in higher education today and it is still rapidly growing. The mixed modes in education promote a great challenge for the professors and administrators to accurately and fairly evaluate the performance of students. Indeed, students’ performance evaluation is a multicriteria decision problem. To obtain a robust auxiliary decision support scheme compatible with the preferences of decision maker (DM), challenges often confronted in multicriteria decision analysis include dealing with complex structure of criteria, handling interaction between criteria and reducing the cognitive efforts of the DM. Based on the disaggregation–aggregation principle, complex preference is refined into smaller, manageable modules from two dimensions of alternative evaluation and criteria hierarchy. Then, a hierarchical-level-bidirectional Choquet integral preference method is developed to reproduce the refined preference and obtain the comprehensive evaluation of the alternatives. Further, a class of non-additive robust ordinal regression is performed by utilizing the characteristic indicators of the new Choquet integral and the preference relations given by the DM. Moreover, a representative preference method is put forward to rule out some preconceived possible relations, which enriches the necessary relations among alternatives. Finally, an illustrative example is provided to verify the practicability of the above multicriteria decision support methods.

A contextual Choquet integral-based preference learning model considering both criteria interactions and the compromise effects of decision-makers

Preference learning has been widely employed to predict decision-makers’ preferences from historical information. This study develops a preference learning model for multiple criteria decision analysis where the decision-maker is supposed to be bounded rational and criteria are not completely independent of each other. The contextual Choquet integral is used as the aggregation function to address criteria interactions. The robust-ordinal-regression (ROR) technique is then applied to learn the preferences of decision-makers from the given preference data and provide robust decision recommendations. The proposed approach is illustrated by a numerical study concerning sustainable product evaluation.

A hybrid decision making aided framework for multi-criteria decision making with R-numbers and preference models

As a risk modeling about fuzzy numbers, R-numbers have successfully extended to multi-criteria decision making (MCDM) methods for the real-life decision making problems involving the risk and uncertainties associated with fuzzy numbers. To obtain more reliable and robust multi-criteria ranking alternatives in these uncertain situations, a hybrid decision making aided framework involving stochastic multiobjective acceptability analysis (SMAA), robust ordinal regression (ROR), and multi-attributive border approximation area comparison (MABAC) is proposed for MCDM problems with risk factors and preference models. Firstly, some novel operations of the R-numbers associated with triangular fuzzy numbers are proposed to explore a broader application scope. Secondly, a novel MABAC method combined with the R-numbers is proposed for MCDM problems which focus on uncertainty and error of triangular fuzzy numbers. Thirdly, a hybrid decision making aided framework which applies SMAA and ROR into the novel MABAC method is proposed for obtaining robust multi-criteria ranking alternatives through two binary relations, and two measures complement each other. Moreover, a Monte Carlo simulation of the framework is performed. Lastly, an application of assessment of wind energy potential and comparative analysis is provided to illustrate the efficiency and superiority of the proposed framework.

Dimensionality reduced robust ordinal regression applied to life cycle assessment

Life Cycle Assessment quantifies the multi-dimensional impact of goods and services and can be handled by Multi-Criteria Decision Analysis. In Multi-Criteria Decision Analysis, Robust Ordinal Regression manages all the compatible preference functions at once when assessing a set of alternatives and a group of preferences on reference alternatives. Robust Ordinal Regression is thus a versatile method of reducing the cognitive effort required by decision makers for eliciting their preference structures in Life Cycle Assessment, although it does not directly operate on noisy alternatives and requires Stochastic Multicriteria Acceptability Analysis to deal with such scenarios.We propose integrating a dimensionality reduction technique, Principal Component Analysis, and Robust Ordinal Regression methods, to reduce the problem dimensionality and ensure the actual problem features are considered.A generated dataset, a dataset from literature and a Life Cycle Assessment case study are used to test the effectiveness of the proposed methods.

Robust Ordinal Regression: User Credit Grading with Triplet Loss-Based Sampling

With the development of social media sites, user credit grading, which served as an important and fashionable problem, has attracted substantial attention from a slew of developers and operators of mobile applications. In particular, multi-grades of user credit aimed to achieve (1) anomaly detection and risk early warning and (2) personalized information and service recommendation for privileged users. The above two goals still remained as up-to-date challenges. To these ends, in this article, we propose a novel regression-based method. Technically speaking, we define three natural ordered categories including BlockList , GeneralList , and AllowList according to users’ registration and behavior information, which preserve both the global hierarchical relationship of user credit and the local coincident features of users, and hence formulate user credit grading as the ordinal regression problem. Our method is inspired by KDLOR ( kernel discriminant learning for ordinal regression ), which is an effective and efficient model to solve ordinal regression by mapping high-dimension samples to the discriminant region with supervised conditions. However, the performance of KDLOR is fragile to the extreme imbalanced distribution of users. To address this problem, we propose a robust sampling model to balance distribution and avoid overfit or underfit learning, which induces the triplet metric constraint to obtain hard negative samples that well represent the latent ordered class information. A step further, another salient problem lies in ambiguous samples that are noises or located in the classification boundary to impede optimized mapping and embedding. To this problem, we improve sampling by identifying and evading noises in triplets to obtain hard negative samples to enhance robustness and effectiveness for ordinal regression. We organized training and testing datasets for user credit grading by selecting limited items from real-life huge tables of users in the mobile application, which are used in similar problems; moreover, we theoretically and empirically demonstrate the advantages of the proposed model over established datasets.

Robust stochastic sorting with interacting criteria hierarchically structured

In this paper we propose a multiple criteria decision aiding method to deal with sorting problems in which alternatives are evaluated on criteria structured in a hierarchical way and presenting interactions. The underlying preference model is the Choquet integral, while the hierarchical structure of the criteria is taken into account by applying the Multiple Criteria Hierarchy Process. Considering the Choquet integral based on a 2-additive capacity (non additive weights for considered criteria), we present a procedure to find all minimal sets of pairs of interacting criteria representing the preference information provided by the Decision Maker (DM). Robustness concerns are also addressed applying the Robust Ordinal Regression and the Stochastic Multicriteria Acceptability Analysis. Even if in different ways, both of them provide recommendations on the hierarchical sorting problem at hand by exploring the whole set of capacities compatible with the preferences provided by the DM. The applicability of the considered method to real world problems is demonstrated by an example regarding rating of European countries evaluated on economic, governmental and financial data provided by Standard & Poor’s Global Inc.

Towards sustainability: An assessment of an urbanisation bubble in China using a hierarchical - Stochastic multicriteria acceptability analysis - Choquet integral method

Urbanisation bubbles have become an increasingly serious problem. Attention has been paid to the speed of urbanisation; however, the issue of quality has been neglected, particularly in the case of China. Therefore, the aim of this research is to evaluate China’s urbanisation bubbles by employing a hierarchical - stochastic multicriteria acceptability analysis (SMAA) - Choquet integral method. In order to highlight regional disparities, we measure the urbanisation bubbles at a provincial level. Our study aggregates the urbanisation bubble indices using the Choquet integral preference model, and considers the interactions between various indicators. Furthermore, robust ordinal regression and SMAA are applied to resolve the robustness issues associated with the entire set of weights assigned to the urbanisation bubble composite indicator. In addition, by employing a multiple criteria hierarchy process, the study aggregates urbanisation bubble indices not only at the comprehensive level, but also at the intermediate levels of the hierarchy. Our findings suggest that the ranking of urbanisation bubbles is positively related to the level of regional development. This study contributes to the evaluation of regional urbanisation and sustainable development.

Towards sophisticated decision models: Nonadditive robust ordinal regression for preference modeling

This paper addresses a methodology for decision support under multiple and correlated decision criteria. Nonadditive robust ordinal regression (NAROR) aims to build capacities that fit the decision makers’ explicit preferences and pairwise rankings of some alternatives. The capacities provide great flexibility to model decision problems accounting for interactions among the decision criteria. The feasible set of capacities helps identifying all the necessary and possible dominance relations among all the decision alternatives. In this paper we enhance the NAROR method by identifying optimal capacities through entropy maximisation. We formulate suitable optimisation problems and provide avenues for capacity simplification based on k-interactivity. We also consider the situation of large number of sparse constraints, for which we formulate a linear program based on Renyi entropy. We deal with preferences inconsistency by using multiple goal linear programming technique. The results show that the k-interactivity is an efficient way to reduce the complexity of capacities while preserving their expressiveness and representation ability, and that optimal capacities can be found by standard mathematical programming techniques.

As simple as possible but not simpler in Multiple Criteria Decision Aiding: the robust-stochastic level dependent Choquet integral approach

The level dependent Choquet integral has been proposed to handle decision making problems in which the importance and the interaction of criteria may depend on the level of the alternatives’ evaluations. This integral is based on a level dependent capacity, which is a family of single capacities associated to each level of evaluation for the considered criteria. We present two possible formulations of the level dependent capacity where importance and interaction of criteria are constant inside each one of the subintervals in which the interval of evaluations for considered criteria is split or vary with continuity inside the whole interval of evaluations. Since, in general, there is not only one but many level dependent capacities compatible with the preference information provided by the Decision Maker, we propose to take into account all of them by using the Robust Ordinal Regression (ROR) and the Stochastic Multicriteria Acceptability Analysis (SMAA). On one hand, ROR defines a necessary preference relation (if an alternative a is at least as good as an alternative b for all compatible level dependent capacities), and a possible preference relation (if a is at least as good as b for at least one compatible level dependent capacity). On the other hand, considering a random sampling of compatible level dependent capacities, SMAA gives the probability that each alternative reaches a certain ranking position as well as the probability that an alternative is preferred to another. A real-world decision problem on rankings of universities is provided to illustrate the proposed methodology.

Nonadditive robust ordinal regression with nonadditivity index and multiple goal linear programming

Nonadditive robust ordinal regression (NAROR) is a widely adopted approach to analyze and reveal the dominance relationships among all decision alternatives based on nonadditive measures, called capacities. In this paper, we first investigate some advantages of the nonadditivity index as an explicit interaction index, as compared with the traditional probabilistic simultaneous interaction indices, and show that nonadditivity index can serve as an equivalent representation of a capacity. Then we enhance the NAROR method by using nonadditivity index as well as multiple-goal linear programming, where the former is used to replace the traditional interaction index to more naturally represent the decision maker's preferences, and the latter aims to replace the 0 to 1 mixed integer programming to enhance the ability to detect and adjust contradictory and redundant preference information. The updated NAROR's steps are constructed and discussed in detail and illustrated with a practical example.

Predictors of self-care activities of outpatient diabetic residents in Harar and Dire Dawa: A hospital-based cross-sectional study.

Objectives:Diabetes mellitus is a metabolic disorder of major public health importance due to its prevalence and potential health complication. The success of long-term maintenance therapy of diabetes patients depends largely on their ability to adherence to self-care practices. Africa’s most populous country, Ethiopia, has the highest burden of diabetes mellitus. However, studies on self-care activities of diabetic patients are limited. Therefore, this study measures the level of self-care activities of diabetic patients in a follow-up clinic of public hospitals in Harar and Dire Dawa, Eastern Ethiopia.Methods:A hospital-based cross-sectional study was conducted on 320 randomly selected diabetic patients in Harar and Dire Dawa. A standard diabetic self-care activity interview tool was used to collect the data. Data were entered into Epi-data v 3.1 and STATA v 14.2 was used for analysis. Our outcome variable, self-care activities, has three ordered categories and a robust Ordinal logistic regression was used to identify predictors. All statistical tests with p-value <0.05 were considered as statistically significant.Results:The self-care activities of study participants were rated good for 38.1% (95% confidence interval: 32.94, 43.60). Being rural residents (adjusted odds ratio = 0.38, 95% confidence interval: 0.17, 0.82), attended secondary education (adjusted odds ratio = 2.96, 95% confidence interval: 1.51, 5.78), uncontrolled blood glucose (adjusted odds ratio = 1.68, 95% confidence interval: 1.02, 2.79), and had diabetic complications (one, adjusted odds ratio = 1.91, 95% confidence interval: 1.08, 3.38; two or more, adjusted odds ratio = 4.71, 95% confidence interval: 1.81, 12.25) were significantly associated with the better diabetes mellitus self-care activities.Conclusion:Significant number of diabetes mellitus patients living in rural areas did not adhere to diabetic self-care activities. This is more evident among participants who have limited or no formal education and patients with controlled blood glucose level. Therefore, individualized diabetic lifestyle education programs in follow-up clinics should target these population groups to improve self-care.

Rational preference and rationalizable choice

We study a decision maker characterized by two binary relations. The first reflects his judgments about well-being, his mental preferences. The second describes the decision maker’s choice behavior, his behavioral preferences. We propose axioms that describe a relation between these two preferences, so between mind and behavior, thus disentangling two different perspectives on preferences: a description of tastes (and attitudes) and a way to organize behavioral data. We obtain two representations: one in which mental preferences uniquely determine choice behavior, another for which mental preferences direct behavior but room remains for biases and framing effects. Our results also provide a foundation for a decision analysis procedure called robust ordinal regression and proposed by Greco et al. (Eur J Oper Res 191:416–436, 2008).

Choice architecture for architecture choices: Evaluating social housing initiatives putting together a parsimonious AHP methodology and the Choquet integral

Choice architecture concerns different forms and procedures to present and handle a decision problem. It is a paradigm around which many theoretical results have been collected within behavioural psychology and experimental economics and many successful applications have been implemented in the domains of health, finance and social choices. In this work, we propose an application of the basic idea of architecture choice that is designing decision support procedures for complex problems, with a focus on housing realm. We consider a real-world problem in which 21 Social Housing initiatives sited in the Piedmont region (Italy) had to be evaluated taking into account several criteria and, to this aim, we propose a decision analysis methodology for supporting assessment in such complex problems. Our main preoccupations in designing the decision aiding procedure were related to build a model that, on one hand, permits to take into consideration the many delicate points of the problem, while, on the other hand, requires to the Decision Maker (DM) an affordable cognitive burden in terms of preference elicitation and interpretation of the obtained results. Since synergy and redundancy of criteria constitute important aspects of the decision problem, we aggregated evaluations on considered criteria by means of the Choquet integral. To maintain the preference information asked to the DM simple and not too requiring, we put together a recently proposed parsimonious approach of the Analytical Hierarchy Process (AHP) and the Non-Additive Robust Ordinal Regression (NAROR). The Parsimonious AHP permitted to assign a value on a common scale to the performances of all criteria, while the NAROR permitted to elicit the importance and the interaction of criteria taking into account all the possible values for the preference parameters compatible with the preference information supplied by the DM. Our methodology allowed a fruitful interaction with the DM that had the possibility to update the preference information during the decision process until he/she felt convinced and satisfied of the obtained result. The suitability and the interest of the proposed methodology were confirmed by the subjective final appreciation of the DM as well as by the objective absence of specific inconsistencies in the AHP procedure and in the non-additive robust ordinal regression, which witnessed the beneficial contribution of our approach.

Robust ordinal regression induced by l-centroid

Abstract Ordinal regression (OR) is an important research topic in machine learning and has attracted extensive attention due to its wide applications. So far, a variety of methods have been proposed to perform OR, in which the class-center-induced threshold methods (like KDLOR and MOR) have received more attention, for their simplicity and promising performance. The class-center-induced ORs typically calculate the ordinal thresholds with class centers, which are typically derived from the l2-norm. Unfortunately, in such a way, the class means may be biased when the data is corrupted with outliers (i.e., non-i.i.d. noises) such that the resulting OR accuracy will be deteriorated. Motivated by the success of lp-norm in applications against noises, in this paper we propose a novel type of class centroid derived from the lp-norm (coined as lp-centroid) to overcome the drawbacks above, and provide an optimization algorithm and corresponding convergence analysis for computing the lp-centroid. To evaluate the effectiveness of lp-centroid in OR context against noises, we then combine the lp-centroid with two representative class-center-induced ORs, namely discriminant learning based and manifold learning based ORs. Finally, extensive OR experiments on synthetic and real-world datasets demonstrate the effectiveness and superiority of the proposed methods to related existing methods.

Robust sustainable development assessment with composite indices aggregating interacting dimensions: The hierarchical-SMAA-Choquet integral approach

The evaluation of sustainable development –and, in particular, rural development– through composite indices requires taking into account a plurality of indicators, which are related to economic, social, and environmental aspects. The points of view evaluated by these indices are naturally interacting: thus, a bonus has to be recognized to units performing well on synergic criteria, whereas a penalisation has to be assigned on redundant criteria. An additional difficulty of the modelization is the elicitation of the parameters for the composite indices, since they are typically affected by some imprecision. In most approaches, all these critical points are usually neglected, which in turn yields an unpleasant degree of approximation in the computation of indices. In this paper we propose a methodology that allows one to simultaneously handle these delicate issues. Specifically, to take into account synergy and redundancy between criteria, we suitably aggregate indicators by means of the Choquet integral. Further, to obtain recommendations that take into account the space of fluctuation related to imprecision in non-additive weights (capacity of the Choquet integral), we adopt the Robust Ordinal Regression (ROR) and the Stochastic Multicriteria Acceptability Analysis (SMAA). Finally, to study sustainability not only at a comprehensive level (taking into account all criteria) but also at a local level (separately taking into account economic, social, and environmental aspects), we apply the Multiple Criteria Hierarchy Process (MCHP). We illustrate the advantages of our approach in a concrete example, in which we measure the rural sustainability of 51 municipalities in the province of Catania, the largest city of the East Coast of Sicily (Italy).