Choquet Integral Research Articles

A sustainability assessment model for industrial parks: A Choquet integral aggregation approach

This study deals with subject sustainability assessment for industrial parks which are seen as systems of interrelated companies and infrastructures. Although sustainability was introduced into mainstream policy discourse several decades ago, it remains complex to assess, and thus to improve in an integrated way. This is particularly true for such elaborate structures as industrial parks. However, the literature has made little effort to present tools for industrial parks managers to take decisions towards sustainability. The paper develops a sustainability assessment framework aimed at industrial parks' managers. The model is based on a multi-criteria compromise aggregation principle and relies on a preliminary systemic deployment of industrial park sustainability. The presented assessment uses a double aggregation mechanism using the weighted arithmetic mean (WAM) and the Choquet integral (CI) to account for the interrelations between stakeholders involved in an industrial park. This double aggregation results in two level of assessment, offering a more comprehensive view of the examined industrial park. A first level of assessment allows managers to control and improve the performance of their industrial parks in each pillar of sustainability. The second level is the assessment of the overall sustainability, which supports the managers' analysis of their strategy to achieve sustainability. As an illustration, the model is used to assess the sustainability of a Canadian industrial park. Application of the model shows that the completion of the studied industrial park's action plan results in reaching a 54% sustainability performance considering the managers' long-term sustainability strategy and that their vision of sustainability moderately favors the simultaneous satisfaction of economic criteria with environmental or social criteria. These results illustrates the capacity of the model to guide managers in the sustainable development of their industrial parks.

Application of the Choquet Integral: A Case Study on a Personnel Selection Problem

Personnel selection plays a decisive role in human resource management since it determines the input quality of personnel. One approach, fuzzy decision-making methods, has become popular in decision making for personnel selection, considering those methods provide a wide range of tools for dealing with uncertainty. Choquet integral is an aggregation operator, frequently used to unite interrelated information. Choquet integral, with respect to fuzzy, allows consideration of the phenomenon of dependence between criteria. In this paper, personnel selection was performed using the Choquet integral, based on a fuzzy measure. The problem of the evaluation of employees is performed with respect to the personal characteristics of the employees, task performance, employee–employee relationship approaches, and effectiveness of communication.

A non-linear risk assessment method for chemical clusters based on fuzzy measure and Choquet integral

The risk assessment of chemical clusters faces two challenges. First, the synergistic effects in chemical accidents introduce nonlinearity into the risk. The second challenge is the lack of cooperation and information exchange. A novel method for risk assessment in chemical clusters with the application of a Choquet integral and a multiple linear regression model, is proposed to overcome the challenges in this paper. This method is intended to achieve non-linear risk assessment and determine the distribution of individual risk in chemical clusters without significantly increasing the investment in cooperation and communication between companies. The application of the fuzzy measure and the Choquet integral enables the consideration of the synergistic effects. To evaluate the effectiveness of the method, a cluster of gas stations in Hefei, China, was used as a case study. The risk in chemical clusters was found to increase due to the domino and synergistic effects. The lack of cooperation and information exchange in such clusters leads to the disregard of the domino and synergistic effects and the underestimation of the risk. The new risk assessment method can provide guidance for the process safety, accident prevention, and land-use planning in chemical clusters.

On Risk Probability of Prefabricated Building Hoisting Construction Based on Multiple Correlations

With growing concern about environmental pollution and occupational safety in construction industry globally, prefabricated building has become a popular building model in sustainable society. In China, management specifications of prefabricated buildings are far from mature, and safety accidents occur frequently in construction. In order to comprehensively analyze risks in hoisting construction of prefabricated buildings, this study, in view of characteristics of hoisting construction process and correlations in complex system, summarizes risk factors and classifies them according to Wuli-Shili-Renli (WSR) system. From perspective of multiple correlations, evolution mechanism of multi-system correlation and multi-risk correlation is carried out, so as to explore risk probability of hoisting construction of prefabricated buildings. At the same time, this study extends Two Additive Choquet Integral (TACI) operator and Decision-making Trial and Evaluation Laboratory (DEMATEL) in dynamic stochastic environment to construct a two-stage model for risk probability research of hoisting construction, hoping to profoundly reveal influence of risk factors and their dynamic evolution. The results show that: (1) risk probability presented a seasonal, dynamic change trend, which meant rising first, then falling, and finally keeping rising, thus regular inspection and dynamic monitoring are required in hoisting construction in these regions in the first three quarters. (2) the influence of each risk factor demonstrated dynamic changes, and risk sources that need to prevent and defuse at different time points are varied, thus targeted measures catering to different risk sources are required. (3) the degree of risk controllability is in dynamic change, but classification of cause or result in the region at the period remains the same, thus necessitating targeted response measures aimed at various risk types. (4) Individual risks like hoisting job climated break out periodically, so the law of risk occurrence should be mastered and relative precautionary measures should be taken in advance.

The interval-valued Choquet-Sugeno-like operator as a tool for aggregation of interval-valued functions

We propose a novel mapping from a space of interval-valued functions defined on an arbitrary set to the family of closed subintervals of nonnegative extended real numbers, called the interval-valued Choquet-Sugeno-like operator. It is based on the notion of the Choquet-Sugeno-like operator and the interval-valued seminormed fuzzy operator introduced by Boczek et al. (2021) and generalizes many interval-valued operators known in the literature, such as n-ary interval-valued aggregation operators, interval-valued ordered weighting average operators, interval-valued seminormed fuzzy operators, and discrete interval-valued Choquet integral. We study its properties and show that it can be used to aggregate interval-valued data.

Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity

We establish general “collapse to the mean” principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and sharpen known results from the literature. However, our results also apply beyond the convex setting. We illustrate this by providing a complete account of the “collapse to the mean” for quasiconvex functionals. In the special cases of consistent risk measures and Choquet integrals, we can even dispense with quasiconvexity. In addition, we relate the “collapse to the mean” to the study of solutions of a broad class of optimisation problems with law-invariant objectives that appear in mathematical finance, insurance, and economics. We show that the corresponding quantile formulations studied in the literature are sometimes illegitimate and require further analysis.

Choquet-Integral-Based Data Envelopment Analysis with Stochastic Multicriteria Acceptability Analysis

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiencies of decision-making units (DMUs) by using a set of inputs and a set of outputs. However, traditional DEA models always assume that the inputs or outputs are independent of each other, which is unrealistic in practical problems. To reflect the interactions between inputs or outputs, the Choquet integral is employed in DEA models. The traditional DEA models are usually used to find some specific input and output weights of DMUs to optimize the efficiency score of DMUs, but the corresponding input and output weights for the optimal efficiency score of a DMU may not be distributed symmetrically, that is to say, the space of weights may be different for different DMUs. Instead of finding the self-efficiency score and the cross-efficiency score of a DMU in traditional DEA models based on some specific input and output weights, stochastic multicriteria acceptability analysis is used to explore the input or output evaluation space and weight space to calculate the Choquet-integral-based acceptability indices of DMUs. The proposed method considers the interactions between inputs or outputs, which can make more DMUs efficient and can also measure the acceptability of a DMU to become an efficient one by exploring the supporting information space. Examples are given to illustrate the proposed method.

Formula omitted]-Choquet integral on time scales with applications

The fundamental purpose of this work is to analyze Δ-Choquet integrals on time scales which is a special case of Choquet integral on abstract fuzzy (non-additive) measure space. We first present a Δ-Choquet integral with respect to non-additive Δ-measure or more precisely a distorted Lebesgue Δ-measure on an arbitrary time scale. Consequently, we come up with a more general integral than the standard Choquet integral of continuous and discrete calculus. Its use can be seen as convenient in economics, decision making, artificial intelligence, and many more. Particularly, in economics, most of the models are dynamic models (continuous and/or discrete), and those can be easily studied on time scales. Further, some basic essential results and properties of the general integral are studied. For instance, we discuss translation, homogeneity, linearity, and many more with respect to the functions and measures of the integral.Then, after that, we present some theorems for computing the integral. The findings agree to unify and extend a number of well-known results reported in the literature to a broader calculus, including continuous, discrete, and quantum calculus, among others. We also evaluate the integral on an invariant under the translation of time scales. Besides, a short note on Δ-Choquet integral with the Caputo-Fabrizio fractional derivative on the time scales is given. The significance of the outcomes is also further enhanced by a variety of interesting examples.Moreover, eventually, we stop findings after discussing an another way to calculate the Δ-Choquet integral on the time scales. To do this, we define Stieltjes distorted types-I and II Lebesgue Δ-measures on time scales which are accomplished with the help of distorted Lebesgue Δ-measure.

Assessment of renewable energy sources for smart cities’ demand satisfaction using multi-hesitant fuzzy linguistic based choquet integral approach

With a sheer commitment to reduce carbon footprint, India refined its strategy towards meeting energy demands by adopting renewable energy policies in smart cities. In an event hosted by the Confederation of Indian Industry, the Chairman of the electricity board claimed that India has reached its renewable energy share of 26% and has rigorous plans to reduce carbon trace to adhere to the commitment made in the Paris Accord. Atal Mission for Rejuvenation and Urban Transformation (AMRUT) is an ambitious plan by India to create and manage smart cities with sustainable development plans. Under this plan, renewable energy usage plays a substantial role and the selection of appropriate energy options is a complex decision problem with competing criteria. Previous studies on renewable energy selection have paid subtle attention towards criteria interrelationships, managing of linguistic expressions, and relative importance of experts. Therefore, in this study, a new decision making approach is developed. Specifically, the hesitant fuzzy linguistic information (HFLI) is adopted. Then, attitudinal Choquet integral (AC) is proposed under HFLI context along with their fundamental properties. Besides, relative importance of criteria and experts are determined by evidence-based Bayesian approach and variance approach under HFLI context, respectively. A ranking algorithm is presented with the CRITIC technique. Finally, a case study in Tamil Nadu illustrates the usefulness of the integrated framework and the comparison provides grounding for the superiority of the framework.

Choquet capacity identification for multiple criteria sorting problems: A novel proposal based on Stochastic Acceptability Multicriteria Analysis

The Choquet integral is an aggregation operator widely used to deal with interacting criteria in multiple criteria decision analysis (MCDA). A practical problem regarding the use of the Choquet integral is the identification of its parameters, which are known as Choquet capacity. While capacity identification has received considerable attention in the context of ranking problems, it is difficult to find solutions tailored to sorting problems, which is the focus of this paper. We propose a novel method based on the Stochastic Acceptability Multicriteria Analysis (SMAA), by introducing the concept of feasible categorization scenarios. Moreover, two novel SMAA-based descriptive measures are proposed in order to provide valuable information for decision aiding, including the interpretation of the Choquet capacity and the possibility of exploiting the space of capacities by considering the decision makers’ initial preferences. Another feature of our proposal is the ability of dealing with unbalanced three-dimensional decision arrays. Numerical experiments with synthetic data were conducted to assess the proposed method. Furthermore, the applicability of our proposal is also attested to a case study related to the evaluation of research institutions.

The risk-neutral non-additive probability with market frictions

The fundamental theory of asset pricing has been developed under the two main assumptions that markets are frictionless and have no arbitrage opportunities. In this case the market enforces that replicable assets are valued by a linear function of their payoffs, or as the discounted expectation with respect to the so-called risk-neutral probability. Important evidence of the presence of frictions in financial markets has led to study market pricing rules in such a framework. Recently, Cerreia-Vioglio et al. (J Econ Theory 157:730–762, 2015) have extended the Fundamental Theorem of Finance by showing that, with markets frictions, requiring the put–call parity to hold, together with the mild assumption of translation invariance, is equivalent to the market pricing rule being represented as a discounted Choquet expectation with respect to a risk-neutral nonadditive probability. This paper continues this study by characterizing important properties of the (unique) risk-neutral nonadditive probability v_f associated with a Choquet pricing rule f, when it is not assumed to be subadditive. First, we show that the observed violation of the call–put parity, a condition considered by Chateauneuf et al. (Math Financ 6:323–330, 1996) similar to the put–call parity in Cerreia-Vioglio et al. (2015), is consistent with the existence of bid-ask spreads. Second, the balancedness of v_f—or equivalently the non-vacuity of its core—is characterized by an arbitrage-free condition that eliminates all the arbitrage opportunities that can be obtained by splitting payoffs in parts; moreover the (nonempty) core of v_f consists of additive probabilities below v_f whose associated (standard) expectations are all below the Choquet pricing rule f. Third, by strengthening again the previous arbitrage-free condition, we show the existence of a strictly positive risk-neutral probability below v_f, which allows to recover the standard formulation of the Fundamental Theorem of Finance for frictionless markets.

Integrated Conceptual Mechatronic Design of a Delta Robot

In this paper, a conceptual design of a Delta robot is developed by means of a mechatronic design methodology. A fully integrated conceptual design, clarifying the recurrence of the conceptual design process using black-box/white-box analysis, is presented using the Model Based Systems Engineering (MBSE) paradigm and the SysML language as the formal modeling tool. Multiple designs proposals are then evaluated by the non-linear Choquet integral in order to choose the most appropriate according to a multicriteria requirement. For a preliminary conceptual design, structural parameters for the Delta robot are determined by defining and solving a nonlinear constrained optimization problem, which considers the kinematic model of the robot maximizing its workspace. Both the decision making and the optimization problem are integrated and automated into a common software framework for the design process, by using a standard genetic algorithm and Monte Carlo method to set the optimized conceptual design to be rendered in Computer Aided Design (CAD) software and in a physical prototype, satisfying the technical specifications.

A multinomial probit model with Choquet integral and attribute cut-offs

Several non-linear functions and machine learning methods have been developed for flexible specification of the systematic utility in discrete choice models. However, they lack interpretability, do not ensure monotonicity conditions, and restrict substitution patterns. We address the first two challenges by modeling the systematic utility using the Choquet Integral (CI) function and the last one by embedding CI into the multinomial probit (MNP) choice probability kernel. We also extend the MNP-CI model to account for attribute cut-offs that enable a modeler to approximately mimic the semi-compensatory behavior using the traditional choice experiment data. The MNP-CI model is estimated using a constrained maximum likelihood approach, and its statistical properties are validated through a comprehensive Monte Carlo study. The CI-based choice model is empirically advantageous as it captures interaction effects while maintaining monotonicity. It also provides information on the complementarity between pairs of attributes coupled with their importance ranking as a by-product of the estimation. These insights could potentially assist policymakers in making policies to improve the preference level for an alternative. These advantages of the MNP-CI model with attribute cut-offs are illustrated in an empirical application to understand New Yorkers’ preferences towards mobility-on-demand services.

Building the hierarchical Choquet integral as an explainable AI classifier via neuroevolution and pruning

Building the hierarchical Choquet integral as an explainable AI classifier via neuroevolution and pruning

Combination forecasting using multiple attribute decision making in tourism demand

Pronóstico combinado utilizando la toma de decisiones de atributos múltiples en la demanda turísticaPropósitoLa combinación de pronósticos en este estudio abordó tres cuestiones importantes para la situación del turismo: Reducir las restricciones que surgen con respecto a las estadísticas de datos disponibles, evaluar los pesos con un solo pronóstico, y considerar las relaciones no lineales entre las combinaciones con un único modelo de pronóstico.Diseño/metodología/enfoqueSe propuso un marco metodológico de tres etapas basado en MADM. Un solo pronóstico fue generado mediante modelos de predicción grises para la primera etapa. Se aplicó VIKOR para desarrollar un esquema de ponderación en la segunda etapa, y la integral de Choquet se usó para combinar los pronósticos de manera no lineal en la tercera etapa.RecomendacionesLos resultados empíricos de la demanda turística entrante en Taiwán mostraron que el método propuesto puede mejorar efectivamente la precisión en mayor medida que otros métodos combinados. Una buena práctica del pronóstico puede proporcionar aún más, mediante las previsiones y la estimación exante de pronósticos posteriores al COVID-19.Implicaciones practicesLos sectores públicos y privados de las economías con alta dependencia del turismo pueden beneficiarse del método propuesto al usar los pronósticos para ayudarlos a formular estrategias turísticas.Autenticidad/valorEste estudio contribuye a presentar un marco basado en MADM que avanza en el desarrollo de un método de combinación más preciso para la previsión del turismo.

Causality of circular business strategy under uncertainty: A zero-waste practices approach in seafood processing industry in Vietnam

This study contributes to the literature by investigating the causality of circular business strategy under uncertainty using a zero-waste practice approach in the seafood processing industry and recommending managerial implications for decision-makers. The circular business strategy has increasingly attracted more notice as a proper solution to address the environmental issues and accomplish economic as well as social benefit with the ultimate target of zero-waste. Yet, prior studies failed to determine circular business strategy attributes with the complete viewpoint and adequate measurement under qualitative information. Studies on zero-waste practices from the firm perspective are limited. To fulfill this gap, this study aims to determine the decisive circular business strategy attributes, their interrelationships in view of sustainable balanced scorecard and examine influential zero-waste practices from firm perspective. A combined method, including fuzzy Delphi method, fuzzy decision-making trial and evaluation laboratory, and Choquet integral is employed. From the original set of attributes, five aspects and 20 criteria are validated. The results present that collaborative circularity, strategic internal process, and technology competency are causal aspects with high involvement among the effect group. The decisive criteria for the seafood processing industry encompass resource consumption minimization, waste minimization, clean technology, by-product marketplace, network development, and coordination upgradation. From initial zero-waste practices of the industry's current status, two critical ones are identified including reuse and recycle.

AGGREGATION OPERATORS VISUALIZATION USING 3D COGNITIVE GRAPHICS

To solve social dilemmas in multi-agent reinforcement learning it is necessary to formalize the corresponding reward functions in the form of aggregation operators. Such formalization encounters difficulties associated with the lack of an intuitive vision of the aggregation process among many practitioners. Various visualization methods have been proposed to overcome these difficulties. The proposed methods have disadvantages that prevent their wide application. The method proposed in the article differs from the existing ones by the use of a three-dimensional cognitive image which corresponds to a physical object with a well-developed intuitive spatial and physical perception. This method is based on the use of 3D cognitive graphics. The properties of the aggregation operator are directly related to the properties of the physical object which has a well-developed intuitive representation. An absolutely solid plane fixed on the support line by springs acts as such an object. The result of aggregation corresponds to the angle of deviation of the plane from the horizon. By placing loads that meet the criteria and indices of their interaction on this plane it is possible to simulate the corresponding operator including by means of virtual reality. A preliminary asessment of the formal properties of the proposed method was carried out in comparison with existing visualization methods using the example of the Choquet integral of the 2nd order. Based on the results of this assessment conclusions were drawn about the advantages of a three-dimensional balance model over existing visualization methods and the feasibility of continuing work in this direction.

Multi-Criteria Analysis and Sustainable Accounting. Defining Indices of Sustainability under Choquet’s Integral

The assessment of sustainability—in its three meanings: economic, social, and environmental ones—needs to be supported by specific econometric and statistical methodologies in order to be properly considered in policymaking processes. In the current literature the use of specific indices, capable of summarizing the three fields of sustainability, is a proven operational practice to express judgments on the convenience and the feasibility of investment in cities. It is necessary to specify that most sustainability indices are ordinarily calculated as arithmetic and geometric means of sub-dimensions. However, these two approaches do not allow investigation of the potential interactions between the various dimensions considered and, specifically, the geometric mean fails to smooth out unbalanced links. The research carried out here is aimed at implementing the use of the Choquet integral, as a non-additive and flexible aggregation model, to calculate evaluation indices able to consider the relationships between the different sustainable dimensions to be used in urban transformation projects. The methodology was tested on a case study, concerning an analysis—under economic, social, and environmental points of view—of different European countries. The evaluation frame based on the Choquet integral is referred to a ranking case aimed to establish the most sustainable country under the economic, environmental, and social point of view. The results obtained from the index processing show that the geometric mean scores and arithmetic ones are rather homogeneous, while the variations obtained among the three dimensions are moderately large. In the synoptic picture obtained with Choquet’s integral, countries with balanced results across dimensions are in higher positions. Therefore, the Choquet integral allows positive interactions to be taken into account across sustainable dimensions, and it is able to detect unbalanced achievements.

Algorithms for multiple attribute decision making with dual hesitant Pythagorean fuzzy information and their application to supplier selection

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the Hamacher aggregation operators and Choquet integral with dual Pythagorean hesitant fuzzy information. Then, motivated by the ideal of Hamacher operation and Choquet integral, we have developed some Hamacher correlated operators for aggregating dual hesitant Pythagorean fuzzy information. The prominent characteristic of these proposed operators is studied. Then, we have utilized these two operators to develop some approaches to solve the dual hesitant Pythagorean fuzzy MADM problems. Finally, a practical example for supplier selection in supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.

An Integrated Model of BWM and Choquet Integral for Determining Fuzzy Measures in Interacting Criteria

Decision-making is one of the significant and inevitable issues in the most real-world problems. Decision criteria interact in many of these problems, and traditional aggregation techniques, which are usually linear methods, cannot be exploited to consider these interactions and exert correlations between criteria. In such cases, nonadditive aggregation methods have attracted the attention of many researchers. This study presents a novel model based on the best-worst method (BWM) and the multi-criteria fuzzy Choquet integral technique to apply the interaction between the criteria. In the proposed model, we have reduced the effect of the inconsistency rate detected on the fuzzy measure (or Choquet capacity) by taking into account the positive or negative interaction between the criteria.