Choquet Integral Research Articles

Submodular financial markets with frictions

This paper studies arbitrage-free financial markets with bid-ask spreads whose super-hedging prices are submodular. The submodular assumption on the super-hedging price, or the supermodularity usually assumed on utility functions, is the formal expression of perfect complementarity, which dates back to Fisher, Pareto, and Edgeworth, according to Samuelson (J Econ Lit 12:1255–1289, 1974). Our main contribution provides several characterizations of financial markets with frictions that are submodular as a consequence of a more general study of submodular pricing rules. First, a market is submodular if and only if its super-hedging price is a Choquet integral and if and only if its set of risk-neutral probabilities is representable as the core of a submodular non-additive probability that is uniquely defined, called risk-neutral capacity. Second, a market is representable by its risk neutral capacity if and only if it is equivalent to a market, only composed of bid-ask event securities.

Extending Set Measures to Orthopair Fuzzy Sets

Yager have proposed the extending set measures to Pythagorean fuzzy sets, which is able to efficiently solve the problems of uncertain information representation in Pythagorean fuzzy environment. However, the Pythagorean fuzzy sets represent a limited range of fields, while the q-rung orthopair fuzzy sets can represent many fuzzy sets, including the Pythagorean fuzzy sets, Fermatean fuzzy sets, and intuitionistic fuzzy sets. In order to extend the extending set measures to Pythagorean fuzzy sets to a broader range, the paper proposes the extending set measures to orthopair fuzzy sets, which can extend the extending set measures to Pythagorean fuzzy sets to q-rung orthopair fuzzy environment. The extending set measures to orthopair fuzzy sets combined with level sets, measure, principle extension and Choquet Integral, which can greatly extend the ability of representing unknown information and processing unknown information. If the q-rung orthopair fuzzy sets degenerate into to Pythagorean fuzzy sets, then the extending set measures to orthopair fuzzy sets will be generated as the extending set measures to Pythagorean fuzzy sets. Numerical examples are designed to prove the effectiveness of the proposed models and the experimental results demonstrate that the proposed method can extend the extending set measures to Pythagorean fuzzy sets to q-rung orthopair fuzzy environment successfully and solve issues of decision making under q-rung orthopair fuzzy environment effectively.

A Computational Model for Multi-Criteria Decision Making in Traffic Jam Problem

In this paper, we apply a computational model for multi-criteria decision making in traffic jam problems. First, we propose a system to determine the optimal shortcut road by reading the number of cars in each street using Radio Frequency Identification (RFID). Then, we have processed the data of traffic jam problems using Choquet integral with writing algorithm and computer program as a working procedure.

Cosine and Cotangent Similarity Measures Based on Choquet Integral for Spherical Fuzzy Sets and Applications to Pattern Recognition

The notion of trigonometric similarity measure (SM) for spherical fuzzy sets (SFSs) has become very important in solving various problems in pattern recognition and medical diagnosis. This study proposes some trigonometric SMs with the help of Choquet integral for SFSs. The proposed trigonometric SMs clearly satisfy the axiomatic definition of classical SMs. We also perform these SMs in pattern recognition problems to examine a comparative analysis of the proposed trigonometric SMs with some existing SMs. Spearman’s rank correlation coefficient is utilized to demonstrate the effectiveness of the proposed SMs.

Möbius product-based constructions of aggregation functions

Möbius transforms of capacities or games were considered as a tool for extensions of capacities to particular aggregation functions in several papers. This is, for example, the case of the Lovász extension coinciding with the Choquet integral, or the Owen extension that is also known as multilinear extension. In this paper, a much deeper study of the links between the Möbius transforms of real-valued functions defined on finite bounded posets and aggregation functions is performed. We introduce a Möbius product of any two real-valued functions defined on an arbitrary finite bounded poset, and then, fixing the poset (2N,⊆), N={1,…,n}, we propose and discuss a construction method for n-ary aggregation functions based on the Möbius product of any capacity on N and a real-valued function gx, x∈[0,1]n, defined on 2N and determined by some appropriate n-ary aggregation function. We provide some necessary and some sufficient conditions for the introduced construction to yield an aggregation function for any capacity. For the binary case, a complete characterization of conditions under which our approach results in an aggregation function for each capacity m is given.

A sociotechnical approach to vaccine manufacturer selection as part of a global immunization strategy against epidemics and pandemics.

These are unprecedented times while the world weathers the highly infectious respiratory pandemic caused by coronavirus disease-19 (COVID-19). Humanity has experienced other cataclysmic events, but something as novel as this pandemic cannot be easily described. A safe COVID-19 vaccine is often hailed as the only effective public health method to prevent the further spread of this virus. New vaccines’ cost has increased even as policymakers struggle with limited resources and budget constraints. Thus, more decision-support tools are needed to facilitate the selection of vaccine manufacturers as part of a global immunization strategy against COVID-19 or other epidemics and pandemics. This study sought to address this issue by combining three well-established operational research methods (i.e., cognitive mapping, decision-making trial and evaluation laboratory, and the Choquet integral). Based on the insights provided by a panel of experts on vaccination and infectious diseases, a vaccine manufacturer selection mechanism was developed that incorporates the World Health Organization’s guidelines. This approach facilitated the identification of multiple selection criteria regarding vaccine manufacturers, their allocation into six major clusters (i.e., soundness of scientific approach and technology used; speed of delivery; cost; liability and risk sharing; ability to supply sufficient quantities through production capacity development; and global solidarity), and subsequent analysis of the respective cause-and-effect relationships. The results of a real-life application of the proposed selection system were further consolidated by a member of Saint Francisco Xavier Hospital Infectious Diseases Unit in Lisbon, Portugal. The mechanism’s advantages and limitations are also discussed.

A Choquet integral based interval Type-2 trapezoidal fuzzy multiple attribute group decision making for Sustainable Supplier Selection

A new Choquet Integral based interval type-2 (IT2TrFS) trapezoidal fuzzy multiple attribute group decision making (GDM) for Sustainable Supplier Selection (SSS) is put forward in this article. It mainly consists of two aspects: (1) resolving the interaction between criteria (attributes); and (2) obtaining a consensual evaluation matrix acceptable to the group. The new partial order of IT2TrFS is proposed to better retain the original evaluation information of individual experts. Then, the Choquet integral with IT2TrFS is put forward to compute the criteria weight, so as to reflect interaction relationship between criteria. The distance of IT2TrFS is explored to calculate the consensus level, which is used to detect the inconsistencies among experts, and then a new feedback mechanism with considering benefit or cost criteria is developed to obtain the individual consensus evaluation matrix. Then, Shapley value based on fuzzy measure is used to determine weight of experts to reflect their global relationship. The final group evaluation matrix is obtained by integrating all individual consensus evaluation matrices. At last, a numerical case is presented to illustrate the effectiveness of the designed method.

On the Hartman–Wintner law of the iterated logarithm under sublinear expectation

In this article, we establish two types of the Hartman–Wintner law of the iterated logarithm under sublinear expectations, especially for pseudo-independent random variables with the finite quadratic Choquet expectations, which generalizes the existing results for independent and identically distributed sequences. But unlike the classical situation, one counterexample is provided to show that the Hartman–Wintner law of the iterated logarithm may fail on the sublinear expectation space only with the finite second moment condition.

The q-Rung orthopair fuzzy hamacher generalized shapley choquet integral operator and its application to multiattribute decision making

• The q-rung orthopair fuzzy Hamacher generalized Shapley Choquet integral (q-ROFHGSCI) operator is proposed as a tool for MADM. • The proposed q-ROFHSCI operator based on generalized Shapley function is a better alternative to existing Choquet integral operator with respect to fuzzy measure as it can reduce the complexity of solving the fuzzy measure on a large set of attributes. • A MADM model based on the q-ROFHGSCI operator is developed to deal with interrelationship among attributes under the q-rung orthopair fuzzy environment. The q -rung orthopair fuzzy sets ( q -ROFs) which are eminent extensions of the intuitionistic fuzzy sets and the pythagorean fuzzy sets can be considered as an efficient tool for modeling real life decision making problems involving uncertainty of information. In this paper, in order to reflect the correlation among the attributes of real decision making problems, the Choquet integral operator is extended to develop the q -rung orthopair fuzzy Hamacher generalized Shapley Choquet integral ( q -ROFHGSCI) operator under the q -rung orthopair fuzzy environment. Furthermore, some important properties and special cases of the q -ROFHGSCI operator are discussed. An approach for multiattribute decision making based on q -ROFHGSCI operator is developed. Finally, a numerical example is provided to illustrate the proposed approach.

Application of GRA Method in Multi-Attribute Decision Making Problem Base on Picture Fuzzy Choquet Integral Information

Picture fuzzy set (PFS) is the generalize structure over existing structures of fuzzy sets to arrange uncertainty and imprecise information in the decision making problem. Picture fuzzy set is a direct extension of the intuitionistic fuzzy set (IFS) that can model uncertainty in situations with multiple types of answers, such as yes, no, abstain, and refuse. In this paper, we propose Choquet integral (CI) for the picture fuzzy set (PFS). Then, we defined some basic operational laws for picture fuzzy set. Also, based on the defined operational laws, we proposed picture fuzzy averaging (PFA) and picture fuzzy Choquet integral weighted averaging operator (PFCIWAO) along with their basic properties. Also, we propose the normalized Hamming distance and normalized Euclidean distance for the picture fuzzy numbers. Viewing the electiveness of the picture fuzzy set, we proposed a decision-making approach for the multi-criteria decision-making problems. We also propose the GRA method using Choquet integral for dealing uncertainty in decision making problems under picture fuzzy information. Lastly, we illustrate an example show the effectiveness and reliability of the proposed method.

Research on Normal Pythagorean Neutrosophic Set Choquet Integral Operator and Its Application

We first propose the normal Pythagorean neutrosophic set (NPNS) in this paper, which synthesizes the distribution of the incompleteness, indeterminacy, and inconsistency of the Pythagorean neutrosophic set (PNS) and normal fuzzy number. We also define some properties of NPNS. For solving the decision-making problem of the non-strictly independent and interacting attributes, two kinds of NPNS Choquet integral operators are proposed. First, the NPNS Choquet integral average (NPNSCIA) operator and the NPNS Choquet integral geometric (NPNSCIG) operator are proposed. Then, their calculating formulas are derived, their properties are discussed, and an approach for solving the interacting multi-attribute decision making based on the NPNS is studied. Finally, the two kinds of operators are applied to validate the stability of the new method.

Enhancing strategic management using a “quantified VRIO”: Adding value with the MCDA approach

• A quantified VRIO is presented. • The proposed approach overcomes some limitations of the traditional VRIO framework. • MCDA improves understanding of causal relationships between resources and capabilities. • The Choquet integral adds value to the Resource-based View. Strategic management has been popularized since the 1960s as a useful tool in the search for success factors in organizations’ internal and external environments. Strategic management researchers have observed and created strategies now considered to be essential pillars of contemporary management operations. This approach relies on managers’ ability to understand and evaluate contextual trends, but a variety of questions have been left unanswered, especially regarding analyses of combinations of quantitative and qualitative decision criteria. This study sought to enhance strategic management by developing a quantified valuable, rare, inimitable, and organized (VRIO) framework using the multiple-criteria decision analysis (MCDA) approach. To accomplish this objective, the proposed VRIO model was combined with the Choquet integral, and a real-life application was conducted to test this approach’s adequacy to support strategic management. The integrated methodology developed was shown to offer an innovative business improvement process. The perceived benefits and limitations are also presented and analyzed.

The Approach of Induced Generalized Neutrosophic Cubic Shapley Choquet Integral Aggregation Operators via the CODAS Method to Solve Distance‐Based Multicriteria Decision‐Making Problems

This study aims to define a conjecture that can handle complex frames of work more efficiently that occurs in daily life problems. In decision‐making theory inter‐relation of criteria, weights and choice decision‐making method subject to the given circumstances which are an important component for appropriate decisions. For this, we define neutrosophic cubic Shapley–Choquet integral (NCSCI) measure; combinative distance‐based assessment selection (CODAS) is accomplished over NCSCI and is implemented over a numerical example of a company foreign investment model as an application in decision‐making (DM) theory. The neutrosophic cubic set (NCS) is a hybrid of the neutrosophic set (NS) and interval neutrosophic set (INS), which provides a better plate form to handle inconsistent and vague data more conveniently. The novel CODAS method is based on Shapley–Choquet integral and Minkowski distance which contain more information measures than usual criteria weights and distances. The weights of criteria are measured by Shapley–Choquet integral and distance is evaluated by Minkowski distance. The Choquet integral considers the interaction among the criteria, and Shapley considers the overall weight criteria. Motivated by these characteristics NCSCI, we defined two aggregation operators’ induced‐generalized neutrosophic cubic Shapley–Choquet integral arithmetic (IGNCSCIA) and operators’ induced‐generalized neutrosophic cubic Shapley–Choquet integral geometric (IGNCSCIG) operators. To find the distance between two NC values, Minkowski distance is defined to evaluate neutrosophic cubic combinative distance‐based assessment selection (NCCODAS). To examine the feasibility of the proposed method, an example of company investment in a foreign country is considered. To check, the validity of the method, the comparative analysis of the proposed method with other methods is conducted.

Digital technology of centralized procurement organization

The article is devoted to the development of models framework for digital transformation of processes in corporate and public procurement systems. In particular, the solution of the problem of multicriteria choice in economic systems described by the three-part graph "producer — resource — consumer" is considered. A mathematical model for the optimal distribution of a homogeneous resource from suppliers to consumers in a centralized procurement system is proposed. This model is reduced to a transport problem with intermediate points. Optimization is aimed at achieving maximum compliance in terms of the totality of technical and commercial characteristics of a homogeneous resource. To set the requirements for these characteristics on the part of the consumer, it is proposed to use fuzzy variables. This provides the consumer with a flexible mechanism for describing resource requirements based on his preferences. An operator of aggregation of local correspondences concerning a set of characteristics is proposed in the form of a discrete Choquet integral with a fuzzy measure. Using the example of production equipment, it is shown how it is possible to formalize the parameters of the model, and then to optimize and automate the process of distributing equipment by solving a transport problem with intermediate points in such a way, that the maximum correspondence in its characteristics is achieved. The developed models and algorithms can be used to create information services on electronic trading platforms, including the of public procurement.

A multi-criterion group decision-making method based on regret theory under 2-tuple linguistic environment

PurposeThe purpose of this paper is to develop a multi-criterion group decision-making (MCGDM) method by combining the regret theory and the Choquet integral under 2-tuple linguistic environment and apply the proposed method to deal with the supplier selection problem.Design/methodology/approachWhen making a decision, the decision-maker is more willing to choose the alternative(s) which is preferred by the experts so as to avoid the regret. At the same time, the correlative relationships among the criterion set can be sufficiently described by the fuzzy measures, later the evaluations of a group of criteria can be aggregated by means of the Choquet integral. Hence, the authors cope with the MCGDM problems by combining the regret theory and the Choquet integral, where the fuzzy measures of criteria are partly known or completely unknown and the evaluations are expressed by 2-tuples. The vertical and the horizontal regret-rejoice functions are defined at first. Then, a model aiming to determine the missing fuzzy measures is constructed. Based on which, an MCGDM method is proposed. The proposed method is applied to tackle a practical decision-making problem to verify its feasibility and the effectiveness.FindingsThe vertical and the horizontal regret-rejoice functions are defined. The relationships of the fuzzy measures are expressed by the sets. A model is built for determining the fuzzy measures. Based on which, an MCGDM method is proposed. The results show that the proposed method can solve the MCGDM problems within the context of 2-tuple, where the decision-maker avoids the regret and the criteria are correlative.Originality/valueThe paper proposes an MCGDM method by combining the regret theory and the Choquet integral, which is suitable for dealing with a variety of decision-making problems.

On quadruplets of nonadditive integrals

The definition of the well-known Choquet integral of a nonnegative random variable is based on a survival (decumulative distribution) function. A quadruplet of Choquet integrals is obtained by extending this idea also to a (cumulative) distribution function for real random variables. The concept includes the asymmetric and symmetric Choquet integrals as well as their complementary versions. These four integrals coincide for any additive measure. For a finite measure, the complementary integrals are related to the original asymmetric and symmetric Choquet integrals via dual measure. Duality also plays a key role in the study of basic integral properties. An alternative way to look at Choquet integral goes via the area of a survival function subgraph. Substituting the Lebesgue planar measure with an arbitrary planar (fuzzy) measure we generalize the introduced quadruplet concept in which the Sugeno and the Shilkret integral quadruplets are involved. This gives a new insight into a common generalization of the three most known nonadditive integrals of Choquet, Sugeno and Shilkret as well as their symmetric, asymmetric and complementary versions.

Associated probabilities aggregations in multistage investment decision-making

PurposeThe attributes that influence the selection of applicants and the relevant crediting decisions are naturally distinguished by interactions and interdependencies. A new method of possibilistic discrimination analysis (MPDA) was developed for the second stage to address this phenomenon. The method generates positive and negative discrimination measures for each alternative applicant in relation to a particular attribute. The obtained discrimination pair reflects the interaction of attributes and represents intuitionistic fuzzy numbers (IFNs). For the aggregation of applicant's discrimination intuitionistic fuzzy assessments (with respect to attributes), new intuitionistic aggregation operators, such as AsP-IFOWA and AsP-IFOWG, are defined and studied. The new operators are certain extensions of the well-known Choquet integral and Yager OWA operators. The extensions, in contrast to the Choquet aggregation, take into account all possible interactions of the attributes by introducing associated probabilities of a fuzzy measure.Design/methodology/approachFor optimal planning of investments distribution and decreasing of credit risks, it is crucial to have selected projects ranked within deeply detailed investment model. To achieve this, a new approach developed in this article involves three stages. The first stage is to reduce a possibly large number of applicants for credit, and here, the method of expertons is used. At the second stage, a model of improved decisions is built, which reduces the risks of decision making. In this model, as it is in multi-attribute decision-making (MADM) + multi-objective decision-making (MODM), expert evaluations are presented in terms of utility, gain, and more. At the third stage, the authors construct the bi-criteria discrete intuitionistic fuzzy optimization problem for making the most profitable investment portfolio with new criterion: 1) Maximization of total ranking index of selected applicants' group and classical criterion and 2) Maximization of total profit of selected applicants' group.FindingsThe example gives the Pareto fronts obtained by both new operators, the Choquet integral and Yager OWA operators also well-known TOPSIS approach, for selecting applicants and awarding credits. For a fuzzy measure, the possibility measure defined on the expert evaluations of attributes is taken.Originality/valueThe comparative analysis identifies the applicants who will receive the funding sequentially based on crediting resources and their requirements. It has become apparent that the use of the new criterion has given more credibility to applicants in making optimal credit decisions in the environment of extended new operators, where the phenomenon of interaction of all attributes was also taken into account.

Minimization interchange theorem on posets

Interchange theorems between minimization and integration are useful in optimization, especially in optimal control and in stochastic optimization. In this article, we establish a generalized minimization interchange theorem, where integration is replaced by a monotone mapping between posets (partially ordered sets). As an application, we recover, and slightly extend, classical results from the literature, and we tackle the case of the Choquet integral. Our result provides insight on the mechanisms behind existing interchange results.

Recognition of Electroencephalography-Related Features of Neuronal Network Organization in Patients With Schizophrenia Using the Generalized Choquet Integrals.

In this study, we focused on the verification of suitable aggregation operators enabling accurate differentiation of selected neurophysiological features extracted from resting-state electroencephalographic recordings of patients who were diagnosed with schizophrenia (SZ) or healthy controls (HC). We built the Choquet integral-based operators using traditional classification results as an input to the procedure of establishing the fuzzy measure densities. The dataset applied in the study was a collection of variables characterizing the organization of the neural networks computed using the minimum spanning tree (MST) algorithms obtained from signal-spaced functional connectivity indicators and calculated separately for predefined frequency bands using classical linear Granger causality (GC) measure. In the series of numerical experiments, we reported the results of classification obtained using numerous generalizations of the Choquet integral and other aggregation functions, which were tested to find the most appropriate ones. The obtained results demonstrate that the classification accuracy can be increased by 1.81% using the extended versions of the Choquet integral called in the literature, namely, generalized Choquet integral or pre-aggregation operators.

Choquet Integral and Coalition Game-Based Ensemble of Deep Learning Models for COVID-19 Screening From Chest X-Ray Images.

Under the present circumstances, when we are still under the threat of different strains of coronavirus, and since the most widely used method for COVID-19 detection, RT-PCR is a tedious and time-consuming manual procedure with poor precision, the application of Artificial Intelligence (AI) and Computer-Aided Diagnosis (CAD) is inevitable. Though, some vaccines have now been authorized worldwide, it will take huge time to reach everyone, especially in developing countries. In this work, we have analyzed Chest X-ray (CXR) images for the detection of the coronavirus. The primary agenda of this proposed research study is to leverage the classification performance of the deep learning models using ensemble learning. Many papers have proposed different ensemble learning techniques in this field, some methods using aggregation functions like Weighted Arithmetic Mean (WAM) among others. However, none of these methods take into consideration the decisions that subsets of the classifiers take. In this paper, we have applied Choquet integral for ensemble and propose a novel method for the evaluation of fuzzy measures using coalition game theory, information theory, and Lambda fuzzy approximation. Three different sets of fuzzy measures are calculated using three different weighting schemes along with information theory and coalition game theory. Using these three sets of fuzzy measures, three Choquet integrals are calculated and their decisions are finally combined. Besides, we have created a database by combining several image repositories developed recently. Impressive results on the newly developed dataset and the challenging COVIDx dataset support the efficacy and robustness of the proposed method. Our experimental results outperform many recently proposed methods.