Veto Thresholds Research Articles

The Feminisation of Poverty in European Union Countries—Myth or Reality?

The feminisation of poverty is a complex, multidimensional phenomenon related to gender inequality in various aspects of life. Women are disproportionately affected by the gender pay gap, unequal intra-household resource distribution, unpaid domestic work, caregiving responsibilities, single motherhood, employment or educational barriers, violence, gender discrimination, and period poverty. Combating poverty and inequality are among the main goals of the 2030 Agenda for Sustainable Development adopted by the United Nations General Assembly on 25 September 2015, and their great importance is further highlighted in the preamble of the resolution outlining the plan to transform our world by 2030. This study uses SDG indicators from the Eurostat database to assess the feminisation of poverty in the EU-27 member states in 2020 based on selected diagnostic characteristics mainly related to SDG 1 and SDG 5; they are also related to other goals due to the cross-cutting nature of the topic. The characteristics were transformed to reflect gender gaps and afterwards unitised with a veto threshold indicating gender balance. These were then used to calculate a synthetic taxonomic measure, allowing for linear ordering and classification of countries based on the feminisation of poverty levels. The study confirmed significant feminisation of poverty in the EU-27, with a few aspects showing masculinisation. High feminisation of poverty was observed in both emerging and advanced economies.

New optimization technique for group decision analysis with complex Pythagorean fuzzy sets

The striking theory of ELECTRE III approach, being a marvelous strategy to deal with pseudo criterion, prevails over the traditional variants of ELECTRE method and other decision-making approaches for veracious decision-making. The noticeable efficiency and broader space of complex Pythagorean fuzzy model make it more significant and dominant for modeling two dimensional imprecise knowledge. The remarkable contribution of this study is to present a high aptitude variant of ELECTRE method by taking the advantage of the flexible structure of complex Pythagorean fuzzy sets closely following the outranking principles of ELECTRE III method. The proposed complex Pythagorean fuzzy ELECTRE III method is accredited to employ the theory of ELECTRE III technique to excellently deal with pseudo criterion as well as the two dimensional imprecise data for authentic decision-making. The proposed methodology uses three different threshold values, including preference, indifference and veto threshold values, to check the preference relation between alternatives. The presented strategy is applied to a case study for material selection to get the befitting decision. The comparative study with Pythagorean fuzzy ELECTRE III method is also included in this article to verify its decision-making aptitude.

The design and performance of the XL-Calibur anticoincidence shield

The XL-Calibur balloon-borne hard X-ray polarimetry mission comprises a Compton-scattering polarimeter placed at the focal point of an X-ray mirror. The polarimeter is housed within a BGO anticoincidence shield, which is needed to mitigate the considerable background radiation present at the observation altitude of ∼40 km. This paper details the design, construction and testing of the anticoincidence shield, as well as the performance measured during the week-long maiden flight from Esrange Space Centre to the Canadian Northwest Territories in July 2022. The in-flight performance of the shield followed design expectations, with a veto threshold <100 keV and a measured background rate of ∼0.5 Hz (20–40 keV). This is compatible with the scientific goals of the mission, where %-level minimum detectable polarisation is sought for a Hz-level source rate.

An evolutionary approach for inferring the model parameters of the hierarchical Electre III method

Given a finite set of alternatives, the ranking problem statement builds a preference pre-order (partial or complete) on this set. In this paper, we are interested in multiple criteria ranking problems with a hierarchical structure of criteria; more precisely, we are interested in the existing hierarchical Electre III method. This method requires eliciting several preference parameters (namely, the weights and the veto thresholds). A direct elicitation of such parameters can be cognitively very demanding; thus, it is adequate to define the parameters in a way that requires much less cognitive effort from the decision-maker. The model parameters can be indirectly elicited by using holistic information provided by the decision-maker; this information can be given in the form of a ranking on a set of reference alternatives and some additional preference information. This paper proposes an aggregation-disaggregation approach for inferring the model parameters of the hierarchical Electre III based on an evolutionary algorithm. To verify the applicability and validity of the proposed preference disaggregation methodology, an illustrative example is addressed regarding the ranking of a set of universities.

Learning the parameters of an outranking-based sorting model with characteristic class profiles from large sets of assignment examples

We address the problem of learning the parameters of the outranking-based multiple criteria sorting model from large sets of assignment examples. We focus on a recently devised method called Electre TRI-rC, incorporating a single characteristic profile to describe each decision class. We introduce four algorithms aimed at the problem. They use different optimization techniques, including an evolutionary algorithm, linear programming combined with a genetic approach, simulated annealing, and a dedicated heuristic. We present the results of the experiments carried out on both artificial and real-world data sets. They reveal an impact of the comparison and veto thresholds, various sorting rules, and ensembles on the classification accuracy of the proposed algorithms. From a broader perspective, we contribute to cross-fertilizing the fields of Multiple Criteria Decision Aiding and Machine Learning for supporting real-world decision-making.

ELECTRE tree: a machine learning approach to infer ELECTRE Tri-B parameters

PurposeThis paper presents an algorithm that can elicitate (infer) all or any combination of elimination and choice expressing reality (ELECTRE) Tri-B parameters. For example, a decision maker can maintain the values for indifference, preference and veto thresholds, and the study’s algorithm can find the criteria weights, reference profiles and the lambda cutting level. The study’s approach is inspired by a machine learning ensemble technique, the random forest, and for that, the authors named the study’s approach as ELECTRE tree algorithm.Design/methodology/approachFirst, the authors generate a set of ELECTRE Tri-B models, where each model solves a random sample of criteria and alternates. Each sample is made with replacement, having at least two criteria and between 10% and 25% of alternates. Each model has its parameters optimized by a genetic algorithm (GA) that can use an ordered cluster or an assignment example as a reference to the optimization. Finally, after the optimization phase, two procedures can be performed; the first one will merge all models, finding in this way the elicitated parameters and in the second procedure, each alternate is classified (voted) by each separated model, and the majority vote decides the final class.FindingsThe authors have noted that concerning the voting procedure, nonlinear decision boundaries are generated and they can be suitable in analyzing problems of the same nature. In contrast, the merged model generates linear decision boundaries.Originality/valueThe elicitation of ELECTRE Tri-B parameters is made by an ensemble technique that is composed of a set of multicriteria models that are engaged in generating robust solutions.

Two-Phase Group Decision-Aiding System using ELECTRE III Method in Pythagorean Fuzzy Environment

This paper is in the continuation of a well-established line of research in multi-criteria decision making, namely, the development of the basic ELECTRE methodology. In the present study, we make an attempt to enhance the influence of the ELECTRE III method, which was conceived in response to the deficiency that existing variants of the ELECTRE method did not provide a full ordering of the alternatives. ELECTRE III has been recently extended so as to make use of information in the form of intuitionistic fuzzy sets. Although this enhancement has been acclaimed by many scholars, it is nonetheless true that further progresses can be made in the quest of generality. In this research, we develop a two-phase Pythagorean fuzzy version of standard ELECTRE III method, called two-phase Pythagorean fuzzy ELECTRE III (PF-ELECTRE III) approach. It takes full advantage of the capabilities of Pythagorean fuzzy sets (PFS); a successful model that generalizes intuitionistic fuzzy sets in a practical and intuitive way. The group decision support system of PF-ELECTRE III first evaluates the performances of the alternatives characterized by Pythagorean fuzzy numbers. The second stage produces a complete ranking of the alternatives from their evaluations in the first phase. We formulate the approach by defining PF indifference threshold, preference threshold and veto threshold functions which provide a more reliable basis to construct outranking relations. The ranking module of the PF-ELECTRE III method is simplified by computing the concordance credibility, discordance credibility and net credibility degrees of each alternative. A diagrammatic representation of the group decision-supporting system is presented to justify the corresponding step-by-step approach for solving problems. Finally, the haze management problem is solved to verify the applicability of the approach proposed in this paper. The investigation of this model and its performance paves the way to additional generalizations by other models like q-rung orthopair fuzzy sets.

Interval-based extensions of two outranking methods for multi-criteria ordinal classification

We present two new interval-based extensions of ELECTRE TRI-nB and ELECTRE TRI-nC, in which the preference relations are built by using the interval outranking approach. The boundaries between adjacent classes (or categories) are described by a set of limiting profiles, whose criteria could take on values which are interval numbers. Compared to INTERCLASS (a recently proposed interval-based ordinal classification method), the assignments suggested by our first extension come from enhanced preference relations between the actions and limiting boundaries and are likely to be more appropriate. In addition, it can suggest assignments from a pseudo-conjunctive logic. In our second extension, each class is characterized by a set of representative actions, again allowing interval numbers as criterion scores. The outranking relations between actions and classes are enhanced by having several representative actions in each category. Both new extensions can handle imperfect knowledge of the model parameters (weights, veto thresholds, credibility threshold), even missing criterion scores. Some fundamental properties and results are proved to guarantee the consistency of the methods, which are also illustrated with some numerical examples.

An interval extension of the outranking approach and its application to multiple-criteria ordinal classification

This paper presents a new outranking method whose main feature is its capacity to handle imperfect knowledge. This research is interested in two important sources of imperfect knowledge: 1) poorly known model parameters, and 2) imperfectly known (even missing) criterion values characterizing the actions. The use of interval numbers to model imperfect knowledge is suggested, and a new interval-based outranking method is proposed as an extension of the outranking approach to the interval framework. This method handles different sources of imperfect knowledge coming from model parameters (weights, veto thresholds, majority threshold) and from ill-determined, imprecise, uncertain, arbitrary (even missing) criterion values. The index of likelihood of the interval outranking is interpreted from a logical perspective, and could be used for choice, ranking and ordinal classification. Specifically, this paper proposes the method INTERCLASS for ordinal classification, which is inspired by ELECTRE TRI-B. Their assignment rules and structural properties are similar, but INTERCLASS is able to handle imprecisions in weights, veto thresholds, cutting level, and even in criteria defining limiting profiles.

Robustness Analysis of an Outranking Model Parameters’ Elicitation Method in the Presence of Noisy Examples

One of the main concerns in Multicriteria Decision Aid (MCDA) is robustness analysis. Some of the most important approaches to model decision maker preferences are based on fuzzy outranking models whose parameters (e.g., weights and veto thresholds) must be elicited. The so-called preference-disaggregation analysis (PDA) has been successfully carried out by means of metaheuristics, but this kind of works lacks a robustness analysis. Based on the above, the present research studies the robustness of a PDA metaheuristic method to estimate model parameters of an outranking-based relational system of preferences. The method is considered robust if the solutions obtained in the presence of noise can maintain the same performance in predicting preference judgments in a new reference set. The research shows experimental evidence that the PDA method keeps the same performance in situations with up to 10% of noise level, making it robust.

Finding the most sustainable wind farm sites with a hierarchical outranking decision aiding method

This paper considers the problem of finding suitable sites for wind farms in a region of Catalonia (Spain). The evaluation criteria are structured into a hierarchy that identifies several intermediate sub-goals dealing with different points of view. Therefore, the recent ELECTRE-III-H hierarchical multi-criteria analysis method is proposed as a good solution to help decision-makers. This method establishes an order among the set of possible sites for the wind farms for each sub-goal. ELECTRE-III-H aggregates these orders into an overall order using different parameters. The procedure is based on the construction and exploitation of a pairwise outranking relation, following the principles of concordance (i.e. majority rule) and discordance (i.e. respect for the minority opinions). This paper makes two main contributions. First, it contributes to the ELECTRE-III-H method by studying its mathematical properties for the construction of outranking relations. Second, the case study is solved and its results show that we can effectively represent and manage the overall influence of the various criteria on the global result at different levels of the hierarchy. The paper compares different scenarios with strict, normal, and optimistic preference, indifference and veto thresholds. Results show that the best site differs for technical, economic, environmental, and social intermediate criteria. Therefore, the best overall solution changes depending on the preference and veto thresholds fixed at the intermediate level of the hierarchy.

Green supplier evaluation in manufacturing systems: a novel interval-valued hesitant fuzzy group outranking approach

Green supplier selection problem has become a developing concept which could enhance the performance of companies regarding the environmental competencies. In order to deal with the uncertainty of green supplier selection problems, this paper proposes an extended elimination and choice translating reality (ELECTRE) method based on the interval-valued hesitant fuzzy set. In this method, the weight or relative importance of each expert is measured through the proposed interval-valued hesitant fuzzy extended preference selection index method. Also, the importance of each attribute is calculated using the developed maximizing deviation method so that loss of data will be prevented. Afterward, the weights of experts and attributes are used in the proposed interval-valued hesitant fuzzy extended ELECTRE (IVHFE-ELECTRE) method, and in so doing, calculation errors in the proposed algorithm decrease. In the classical approaches, the interval-valued hesitant fuzzy effective outranking matrix may not assist to rank the suppliers. Thus, a novel ranking index is proposed by considering indifference, preference and veto thresholds for each attribute to compare the equivalent ranking of green suppliers. In addition, a case study of the automobile manufacturing industry is used to evaluate the candidate suppliers regarding environmental competencies from the recent literature to verify the proposed IVHFE-ELECTRE method. Also, a comparative analysis based on two outranking methods from the recent literature is elaborated to represent the merits and advantages of the proposed approach. Finally, a sensitivity analysis and quite a few simulation-based experiments are prepared to sensitiveness and validation of the proposed method, respectively.

Veto Override Requirements and Executive Success

Presidential systems around the world vary in the proportion of legislators required to override an executive veto. We argue that the nature of the override provision affects executive influence in policymaking; as the proportion needed to override a veto increases, so should executive influence. We leverage varying override requirements across the US states to conduct a comparative study of executive influence over budgetary outcomes. Using governors’ budget requests and enacted appropriations for fiscal years 1987–2011, we provide evidence that state legislatures better accommodate budgetary requests in states with higher override requirements. Further, governors whose preferences are extreme relative to the legislature are more likely to have their budgetary goals met in states with a higher veto threshold.

A Fuzzy Multicriteria Categorization of Water Scarcity in Complex Water Resources Systems

Although water scarcity is a well-understood concept, it is difficult to define it precisely and furthermore, to address the water scarcity which requires a complicated set of water actions. In this work, with the aim to face the complexity of water scarcity, we propose the establishment of several categories in order to characterize the water scarcity. These categories are guided by the corresponding roadmap so as to address the water scarcity. Consequently, the considered categories are used to characterize the scarcity are non-ordered. The methodology is based on a developed fuzzy multi-criteria filtering approach. The Water Demand Satisfaction, Water Reliability, Management Effectiveness and Water Sustainability, are selected as criteria. Each category is characterized by reference to a fictitious alternative, the prototype. Τhe water scarcity categorization process is based on the fuzzy binary comparison between the water scarcity evaluation of the criteria in the watersheds and the prototype of each category. This binary comparison over all criteria consists of the concordance and non-discordance principle. The use of fuzzy analysis enables us to express the grey region of the monocriterion comparison between the basins and the prototypes and furthermore, to achieve a suitable aggregation of the achieved monocriterion comparison between the basins and the prototypes. Eventually, the use of the veto thresholds and discordance indices of the fuzzy aggregation allowing compensation, are to be avoided when criteria are strongly conflicting, which is a very useful property in classification problems. The described methodology was applied to the Ebro river basin, identifying the existing problems.

Uwagi do unitaryzacji zmiennych w referencyjnym systemie granicznym

The article is a polemic with the proposal of Strahl and Walesiak (1997) concerning unitarisation variables in the border reference system. Shown are adverse implications of the unitarisation model proposed by Strahl and Walesiak. To be able to modify formulas for unitarisation in the border reference system, the key issue is to clarify what is the veto threshold. According to the author, one can distinguish the following variants of the veto thresholds: 1. The veto threshold means that the object does not meet the minimum requirements. 2. The veto threshold does not implicate additional consequences. Here you can consider two situations: a) transgression of the veto threshold does not bring additional benefi ts, b) transgression of the veto threshold does not cause additional losses. 3. Transgression of the veto threshold means a signifi cant deterioration in the attractiveness of the object. The above variants of veto thresholds may occur alone or together. This possibility, in combination with the three possible types of variables (a stimulant, destimulant, nominant) causes that each situation Uwagi do unitaryzacji zmiennych w referencyjnym systemie granicznym 167 requires a separate description with the use particular formulas. The author postulates that in each situation following conditions should be met: 1. Continuity of unitarisation transformation. 2. Transformation of the interval [xmin, xmax] to the interval [0, 1]. 3. Best / optimal values are assigned a value of 1, and the worst values of 0. For the above terms the author proposes new models in the case of presence of veto thresholds. The proposal is illustrated by an empirical example.

Solving land-use suitability analysis and planning problem by a hybrid meta-heuristic algorithm

The aim of Land-use Suitability Analysis and Planning Problem (LSAPP) is to identify the most suitable parcels of land for future land-uses considering several conflicting criteria. LSAPP can be modeled using a variant of a well-known combinatorial optimization problem called Quadratic Assignment Problem (QAP). In this paper, a multi-objective mathematical model is developed for LSAPP based on QAP modeling. The large-size instances of the proposed multi-objective mathematical model are difficult to solve in a reasonable CPU time using exact algorithms. So, an efficient three-phase hybrid solution procedure is proposed. In the first phase, the compensatory objectives are integrated using Analytic Hierarchy Process (AHP) and Decision-Making Trial and Evaluation Laboratory. Then, based on the aforementioned suitability objective function and other spatial objectives and constraints, a multi-objective LSAPP is constructed. Finally, a hybrid multiple objective meta-heuristic algorithm is proposed to solve the LSAPP. The core of the proposed algorithm is based on Scatter Search while Tabu Search and Variable Neighborhood Search are also utilized. The proposed algorithm is equipped with the concepts of Pareto optimality and Veto Threshold, which improve its efficacy. The proposed algorithm is applied on a real LSAPP case study, in ‘Persian Gulf Knowledge Village’, wherein its performance is compared with a well-known evolutionary computation algorithm called Vector Evaluated Genetic Algorithm (VEGA) using comprehensive statistical analysis. A survey on time complexity of the proposed algorithm is also accomplished. The results show that MOSVNS is significantly superior to VEGA both in single and in multi-objective modes. Furthermore, analysis of time complexity of the proposed algorithm shows that it is of polynomial time and can be applied to significantly larger problems with multiple compensatory and non-compensatory objectives.

A new view to uncertainty in Electre III method by introducing interval numbers

Article history: Received March 29, 2012 Accepted 18 June 2012 Available online June 19 2012 The Electre III is a widely accepted multi attribute decision making model, which takes into account the uncertainty and vagueness. Uncertainty concept in Electre III is introduced by indifference, preference and veto thresholds, but sometimes determining their accurate values can be very hard. In this paper we represent the values of performance matrix as interval numbers and we define the links between interval numbers and concordance matrix .Without changing the concept of concordance, in our propose concept, Electre III is usable in decision making problems with interval numbers. © 2012 Growing Science Ltd. All rights reserved.

Eliciting Electre Tri category limits for a group of decision makers

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.

An Evolutionary Approach to Preference Disaggregation in a MURAME-Based Credit Scoring Problem

In this paper we use an evolutionary approach in order to infer the values of the parameters (weights of criteria, preference, indifference and veto thresholds) for developing the multicriteria method MURAME. According to the logic of preference disaggregation, the problem consists in finding the parameters that minimize the inconsistency between the model obtained with those parameters and that one connected with a given reference set of decisions revealed by the decision maker; in particular, two kinds of functions are considered in this analysis, representing a measure of the model inconsistency compared to the actual preferential system. In order to find a numerical solution of the mathematical programming problem involved, we adopt an evolutionary algorithm based on the Particle Swarm Optimization (PSO) method, which is an iterative heuristics grounded on swarm intelligence. The proposed approach is finally applied to a creditworthiness evaluation problem in order to test the methodology on a real data set provided by an Italian bank.

ELECTRE GKMS: Robust ordinal regression for outranking methods

We present a new method, called ELECTRE GKMS, which employs robust ordinal regression to construct a set of outranking models compatible with preference information. The preference information supplied by the decision maker (DM) is composed of pairwise comparisons stating the truth or falsity of the outranking relation for some real or fictitious reference alternatives. Moreover, the DM specifies some ranges of variation of comparison thresholds on considered pseudo-criteria. Using robust ordinal regression, the method builds a set of values of concordance indices, concordance thresholds, indifference, preference, and veto thresholds, for which all specified pairwise comparisons can be restored. Such sets are called compatible outranking models. Using these models, two outranking relations are defined, necessary and possible. Whether for an ordered pair of alternatives there is necessary or possible outranking depends on the truth of outranking relation for all or at least one compatible model, respectively. Distinguishing the most certain recommendation worked out by the necessary outranking, and a possible recommendation worked out by the possible outranking, ELECTRE GKMS answers questions of robustness concern. The method is intended to be used interactively with incremental specification of pairwise comparisons, possibly with decreasing confidence levels. In this way, the necessary and possible outranking relations can be, respectively, enriched or impoverished with the growth of the number of pairwise comparisons. Furthermore, the method is able to identify troublesome pieces of preference information which are responsible for incompatibility. The necessary and possible outranking relations are to be exploited as usual outranking relations to work out recommendation in choice or ranking problems. The introduced approach is illustrated by a didactic example showing how ELECTRE GKMS can support real-world decision problems.