Consensus reaching for social network group decision making by considering leadership and bounded confidence

Deep Learning Based Feature Selection and Ensemble Learning for Sintering State Recognition

Sintering is a commonly used agglomeration process to prepare iron ore fines for blast furnace. The quality of sinter significantly impacts the blast furnace ironmaking process. In the vast majority of sintering plants, the judgment of sintering quality still relies on the intuitive observation of the cross section at sintering machine tail by operators, which is susceptible to the external environment and the experience of operators. In this paper, we propose a new sintering state recognition method using deep learning based feature selection and ensemble learning. First, features from the infrared thermal images of sinter cross section at the tail of the sinterer are extracted based on ResNeXt. Then, to eliminate the irrelevant, redundant and noisy features, an efficient feature selection method based on binary state transition algorithm (BSTA) is proposed to find the truly useful features. Subsequently, an ensemble learning (EL) method based on group decision making (GDM) is proposed to recognize the sintering states. Novel combination strategies considering the varying performance of the base learners are designed to further improve recognition accuracy. Industrial experiments conducted at a steel plant verify the effectiveness and superiority of the proposed method.

An approach to prevent weight manipulation by minimum adjustment and maximum entropy method in social network group decision making

In social network group decision making (SN-GDM) problem, subgroup weights are mostly unknown, many approaches have been proposed to determine the subgroup weights. However, most of these methods ignore the weight manipulation behavior of subgroups. Some studies indicated that weight manipulation behavior hinders consensus efficiency. To deal with this issue, this paper proposes a theoretical framework to prevent weight manipulation in SN-GDM. Firstly, a community detection based method is used to cluster the large group. The power relations of subgroups are measured by the power index (PI), which depends on the subgroups size and cohesion. Then, a minimum adjustment feedback model with maximum entropy is proposed to prevent subgroups' manipulation behavior. The minimum adjustment rule aims for 'efficiency' while the maximum entropy rule aims for 'justice'. The experimental results show that the proposed model can guarantee the rationality of weight distribution to reach consensus efficiently, which is achieved by maintaining a balance between 'efficiency' and 'justice' in the mechanism of assigning weights. Finally, the detailed numerical and simulation analyses are carried out to verify the validity of the proposed method.

Density and node closeness based clustering method for community detection

In a real-world, networked system, the ability to detect communities or clusters has piqued the concern of researchers in a wide range of fields. Many existing methods are simply meant to detect the membership of communities, not the structures of those groups, which is a limitation. We contend that community structures at the local level can also provide valuable insight into their detection. In this study, we developed a simple yet prosperous way of uncovering communities and their cores at the same time while keeping things simple. Essentially, the concept is founded on the theory that the structure of a community may be thought of as a high-density node surrounded by neighbors of minor densities and that community centers are located at a significant distance from one another. We propose a concept termed “community centrality” based on finding motifs to measure the probability of a node becoming the community center in a setting like this and then disseminate multiple, substantial center probabilities all over the network through a node closeness score mechanism. The experimental results show that the proposed method is more efficient than many other already used methods.

A Large Group Decision Making Method Considering Experts’ Non-cooperative Behavior for Investment Selection of Renewable Energy Projects

The rapid expansion of renewable energy has attracted the attention of investors, which makes the evaluation of renewable energy projects a momentous issue. As the investment selection of renewable energy projects requires the joint discussion of experts from different professional backgrounds (such as energy, transportation, construction, economy, environment, etc.), it belongs to the category of large group decision-making (LGDM). Therefore, this paper is devoted to propose a novel LGDM method considering experts’ non-cooperative behavior for investment selection of renewable energy projects. First, considering that the complexity of renewable energy projects makes it difficult for experts to express their views in a single linguistic word, the hesitant fuzzy linguistic term set is used as the tool for expert evaluation in this paper. Second, since the assessment information provided by experts from different fields are often heterogeneous, a consensus-reaching process with a feedback mechanism is introduced which comprehensively considers three reliable sources: the experts’ trust relationship in the social trust network, the consensus contribution in the subgroup and the opinions’ similarity among experts. Further, to improve the efficiency and rationality of decision-making, an experts’ historical adjustment data-based non-cooperative behavior management method is proposed. Finally, the effectiveness and innovation of the proposed method are verified by a case of renewable energy power generation project investment selection in Qingdao, China and a series of comparative analysis.

Methodology for teaching quality evaluation of college volleyball training with probabilistic double hierarchy linguistic information

The physical education teaching quality evaluation is a very important part of the current physical education teaching reform in colleges and universities, and many experts and scholars have achieved fruitful results in this area, which has played a role in promoting the development of physical education teaching evaluation theory and practice. But at the same time, it should be soberly recognized that, with the deepening reform of physical education teaching in colleges and universities, the current teaching quality evaluation system can no longer meet the needs of the current education situation, and there are still many problems that need to be further studied and improved. The teaching quality decision evaluation of college volleyball training is looked as the MAGDM. Thus, a useful MAGDM process is needed to cope with it. The information entropy is used for determination of target weight. Based on the grey relational analysis (GRA) and probabilistic double hierarchy linguistic term sets (PDHLTSs), this paper constructs the PDHLTS-GRA for MAGDM issues. Finally, an example for teaching quality evaluation of college volleyball training is used to illustrate the designed method.

A probabilistic linguistic opinion dynamics method based on the DeGroot model for emergency decision-making in response to COVID-19

Emergency decision-making entails a multi-criteria problem with a short period and urgent events, which creates difficulties for decision makers to undertake an optimal decision. To ensure the validity and rationality of decision results, the probabilistic linguistic term set is adopted to represent the evaluation information of experts because it can assign different probabilities or importance to different linguistic terms, which is closely related to human cognition. In addition, to portray the dynamic changes in the emergency decision-making process, this study develops a new dynamics method based on the DeGroot model with probabilistic linguistic information. First, to simulate the transition matrix of probabilistic linguistic opinions, the basic operational rules are defined based on the transformation function and expectation function. Next, three forms of influence matrices incorporating similarity, self-persistence, and authority degrees are constructed, and the consensus conditions of the models are discussed. Then, considering the social networks and incomplete trust relationships between experts, a fourth trust-based influence matrix is devised. A case study of emergency decision-making for assessing response plans to COVID-19 is performed to verify the feasibility and effectiveness of the dynamic method. Furthermore, a sensitivity analysis is conducted. Finally, comparisons with classical methods are performed to illustrate the superiorities of the proposed algorithms.

Cross-platform opinion dynamics in competitive travel advertising: A coupled networks’ insight

Social media platforms have become an important tool for travel advertisement. This study constructs the bounded confidence model to build an improved cross-platform competitive travel advertising information dissemination model based on open and closed social media platforms. Moreover, this study examines the evolution process of group opinions in cross-platform information dissemination with simulation experiments. Results reveal that based on strong relationships, the closed social media platform opinion leaders better guide in competitive travel advertising and can bring more potential consumers to follow. However, being an opinion leader on an open social media platform will not result in more consumer following.

A multiple attribute decision-making three-way model at four-branch fuzzy environment

Three-way decisions (TWDs) theory is one of the core ideas of decision-theoretic rough sets (DTRSs). Reviewing the existing research results, we find that TWDs provides us with more flexible decision choices. And the traditional fuzzy number does not take into account the absence of information (indifference) in the evaluation process. In order to construct a new model which can get flexible decision results in complex decision environment, we introduce four-branch fuzzy numbers (FBFNs) to describe the evaluation information, so that the decision-makers can express the evaluation information more comprehensively. In this paper, a novel TWDs model in four-branch fuzzy environment is proposed to solve multiple-attribute decision-making (MADM) problem. The first challenge is to construct a TWDs model based on FBFNs and to develop a new linguistic interpretation of the loss functions. Then, we extend a method for aggregating the loss functions obtained from the attribute evaluation values. Finally, we use the nonlinear solution to solve the threshold, and apply TOPSIS method to solve the conditional probability of FBFNs. The effectiveness of this method is illustrated by an example, and the decision results are compared with a MADM method based on OWGA operator.

Deep Learning-Based Consensus Control of a Multi-Agents System with Unknown Time-Varying Delay

Despite the enormous progress in consensus control of a multi-agents system (MAS), amodel-based consensus control is valid only when the assumption on the system environment and on the model is valid. To overcome this limitation, several deep learning (DL) based consensus controls directly learn how to generate a control signal from the model-based control. Depending on the exploitation of knowledge from the model-based control structure, four different deep learning models were considered. Numerical simulations of MAS with unknown time-varying delays and disturbance verify that, while providing comparable performance to the model-based control for many different system configurations, the DL-based controls with explicit knowledge of the control signal structure are preferred to that with implicit knowledge of the control signal or no knowledge, which shows the promising potential of DL-based control with supervised learning.

A Novel Hotel Selection Decision Support Model Based on the Online Reviews from Opinion Leaders by Best Worst Method

Hotel selection is an important decision in making travel plans. Since hotel selection is a typical non-expert decision, online reviews provide people with information about the hotels and travel destinations they never went to. Several studies construct the decision model based on online reviews with the subjective weights of criteria but ignore the objective weight of criteria derived by opinion leaders, which contributes to the review helpfulness. This study proposes a decision-making model based on online reviews for satisfactory hotel selection. Firstly, an RFMP model is proposed to extract the online reviews of opinion leaders, and the Word2vec method is used to extract the criteria from the online review of opinion leaders. Secondly, obtain the objective weight of criteria from the online reviews of opinion leaders by Word2Vec. Meanwhile, obtain the subjective weight of criteria by the best worst method(BWM) method. Thus, the weight of the hotel selection criteria can be obtained by a linear weighting of objective and subjective weight with a parameter. Thirdly, the hotel selection process based on TOPSIS is employed. Finally, a case study of 8 alternative hotels on Mafengwo.com is applied to verify the proposed model. Comparison experiments and sensitivity analysis are given to illustrate the reasonableness and advantage of the proposed model.

A consensus building model in group decision making with non-reciprocal fuzzy preference relations

Group decision making (GDM) is a wisdom extracting process where a group of decision makers (DMs) could reach a consensus on the optimal solution to the choice problem with a finite set of alternatives. This paper reports a consensus model in GDM, where the opinions of experts are expressed as fuzzy preference relations (FPRs) without additively reciprocal property to cope with the existing uncertainty. The concept of non-reciprocal fuzzy preference relations (NrFPRs) is proposed to capture the considered situation. A novel additive consistency index is constructed to quantify the inconsistency degree of NrFPRs using the relationship of two column/row vectors. An optimization model is constructed, where a new fitness function is proposed by considering the consistency degrees of NrFPRs and the consensus level of a group of experts. A novel concept of acceptable consensus standard is proposed to characterize the acceptance of the consensus process. The particle swarm optimization (PSO) algorithm is utilized to solve the constructed optimization problem. As compared to the existing models, numerical results show that the proposed model can be used to effectively reach an optimal solution to a GDM problem with NrFPRs.

Research on the optimal aggregation method of fuzzy preference information based on spatial Steiner-Weber point

In view of the present situation that most aggregation methods of fuzzy preference information are extended or mixed by classical aggregation operators, which leads to the aggregation accuracy is not high. The purpose of this paper is to develop a novel method for spatial aggregation of fuzzy preference information. Thus we map the fuzzy preference information to a set of three-dimensional coordinate and construct the spatial aggregation model based on Steiner-Weber point. Then, the plant growth simulation algorithm (PGSA) algorithm is used to find the spatial aggregation point. According to the comparison and analysis of the numerical example, the aggregation matrix established by our method is closer to the group preference matrices. Therefore, the optimal aggregation point obtained by using the optimal aggregation method based on spatial Steiner-Weber point can best represent the comprehensive opinion of the decision makers.

Housing affordability evaluation based on the third-generation prospect theory and the improved VIKOR method

Housing affordability is an important issue and can be measured by an increasing number of indicators. Different urban settings may lead to different housing affordability criteria. This study incorporates the third-generation prospect theory and improved VIKOR method to construct a novel, comprehensive evaluation model for assessing housing affordability. The housing price to income and rent to income ratios were chosen as evaluation indicators, and the yearly median value of each indicator was taken as a dynamic reference point. The housing affordability indicators’ realistic prospect value matrix for large- and medium-sized Chinese cities were obtained for the study period’s duration. The comprehensive housing affordability prospect values were ranked using the improved VIKOR with entropy weight method. The novel proposed approach’s rationality and effectiveness were examined by comparing the original and prospect values, performing sensitivity analysis on the prospect value parameters, contrasting the ordinary and improved VIKOR methods, and comparing the proposed approach with the TOPSIS method. The results demonstrate that the proposed method can consider the decision maker’s psychological factors, endow housing affordability evaluation criteria with dynamic characteristics, overcome the problem of order reversal, and ensure the optimal compromise solution. Therefore, the proposed approach is suitable for housing affordability evaluation.

Bifurcation in the evolution of certainty in a small decision-making group by consensus

In a previous paper, the evolution of certainty measured during a consensus-based small-group decision process was shown to oscillate to an equilibrium value for about two-thirds of the participants in the experiment. Starting from the observation that experimental participants are split into two groups, those for whom the evolution of certainty oscillates and those for whom it does not, in this paper we perform an analysis of this bifurcation with a more accurate model and answer two main questions: what is the meaning of this bifurcation, and is this bifurcation amenable to the approximation method or numerical procedure? Firstly, we have to refine the mathematical model of the evolution of certainty to a function explicitly represented in terms of the model parameters and to verify its robustness to the variation of parameters, both analytically and by computer simulation. Then, using the previous group decision experimental data, and the model proposed in this paper, we run the curve-fitting software on the experimental data. We also review a series of interpretations of the bifurcated behaviour. We obtain a refined mathematical model and show that the empirical results are not skewed by the initial conditions, when the proposed model is used. Thus, we reveal the analytical and empirical existence of the observed bifurcation. We then propose that sensitivity to the absolute value of certainty and to its rate of change are considered as potential interpretations of this split in behaviour, along with certainty/uncertainty orientation, uncertainty interpretation, and uncertainty/certainty-related intuition and affect.

A Fuzzy Collaborative Intelligence Approach to Group Decision-Making: a Case Study of Post-COVID-19 Restaurant Transformation

In a fuzzy group decision-making task, when decision makers lack consensus, existing methods either ignore this fact or force a decision maker to modify his/her judgment. However, these actions may be unreasonable. In this study, a fuzzy collaborative intelligence approach that seeks the consensus among experts in a novel way is proposed. Fuzzy collaborative intelligence is the application of biologically inspired fuzzy logic to a group task. The proposed methodology is based on the fact that a decision maker must make a choice even if he/she is uncertain. As a result, the decision maker’s fuzzy judgment matrix may not be able to represent his/her judgment. To solve such a problem, the fuzzy judgment matrix of each decision maker is decomposed into several fuzzy judgment submatrices. From the fuzzy judgment submatrices of all decision makers, a consensus can be easily identified. The proposed fuzzy collaborative intelligence approach and several existing methods have been applied to the case of the post-COVID-19 transformation of a Japanese restaurant in Taiwan. Because such transformation was beyond the expectation of the Japanese restaurant, the employees lacked consensus if existing methods were applied to identify their consensus. The proposed methodology solved this problem. The optimal transformation plan involved increasing the distance between tables, erecting screens between tables, and improving air circulation. In a fuzzy group decision-making task, an acceptable decision cannot be made without the consensus among decision makers. Ignoring this or forcing decision makers to modify their preferences is unreasonable. Identifying the consensus among experts from another point of view is a viable treatment.

Managing consistency and consensus measures and adjustment strategies in group decision making with probabilistic linguistic preference relations

The use of probabilistic linguistic preference relations (PLPRs) in pairwise comparisons enhances the flexibility of quantitative decision making. To promote the application of probabilistic linguistic term sets (PLTSs) and PLPRs, this paper introduces the consistency and consensus measures and adjustment strategies to guarantee the rationality of preference information utilized in the group decision making process. First of all, a novel entropy-based similarity measure is developed with PLTSs. Hereafter an improved consistency measure is defined on the basis of the proposed similarity measure, and a convergent algorithm is constructed to deal with the consistency improving process. Furthermore, a similarity-based consensus measure is developed in a given PLPR, and the consensus reaching process is presented to deal with the unacceptable consensus degree. The proposed consistency improving and consensus reaching processes follow a principle of minimum information loss, called a local adjustment strategy. In particular, the presented methods not only overcome the deficiencies in existing studies but also enhance the interpretation and reduce the complexity of the group decision making process. Finally, the proposed consistency measure and improving process, as well as consensus measure and reaching process are verified through a numerical example for the medical plan selection issue. The result and in-depth comparison analysis validate the feasibility and effectiveness of the proposed methods.

An integrated approach to site selection for a big data center using PROMETHEE-MCGP methodology

In today’s economy, information technology (IT) is vitally important, and the increasing use of the Internet, telecommunications services, and internal IT networks in organizations have led to rapid growth in the demands on big data processing. In general, site selection is a fundamental part of the design of a big data center (BDC), and a poor site decision can affect the sustainability of the facility. To construct a comprehensive assessment framework for a BDC, the following three categories of indicators are determined based on the “Specification for Design of Data Center” in GB50174-2017 of China: economic factors, natural climate environment factors, and energy resources factors. After explaining the rationality of choosing these indicators in detail, an integrated method that combines the multi-criteria decision-making (MCDM) method and the multi-choice goal programming (MCGP) model is proposed. The proposed approach uses two phases to conduct the decision procedure. First, the preference ranking organization method for enrichment evaluation (PROMETHEE) method is applied to evaluate the economic factors. Then, the evaluation results are added to the MCGP model as one of the goals of multi-objective programming. Second, the remaining five sub-indicators and the evaluation results generated from the first phase are formulated as a complete MCGP model. Finally, an empirical study on the site selection for the BDC is implemented based on the proposed method. The result shows that Guiyang is the most suitable place for locating a BDC in China.

Video conferencing software selection based on hybrid MCDM and cumulative prospect theory under a major epidemic

The video conferencing software is regarded as a significant tool for social distancing and getting incorporations up and going. Due to the indeterminacy of epidemic evolution and the multiple criteria, this paper proposes a video conferencing software selection method based on hybrid multi-criteria decision making (HMCDM) under risk and cumulative prospect theory (CPT), in which the criteria values are expressed in various mathematical forms (e.g., real numbers, interval numbers, and linguistic terms) and can be changed with natural states of the epidemic. Initially, the detailed description of video conferencing software selection problem under an epidemic are given. Subsequently, a whole procedure for video conferencing software selection is conducted, the approaches for processing and normalizing the multi-format evaluation values are presented. Furthermore, the expectations provided by DMs under different natural states of the epidemic are considered as the corresponding reference points (RP). Based on this, the matrix of gains and losses is constructed. Then, the prospect values of all criteria and the perceived probabilities of natural states are calculated according to the value function and the weighting function in CPT respectively. Finally, the proposed method is illustrated by an empirical case study, and the comparison analysis and the sensitivity analysis for the loss aversion parameter are conducted to prove the effectiveness and robustness. The results show that considering the psychological characteristics of DMs in selection decision is beneficial to avoid the unacceptable and potential loss risks. This study could provide a useful guideline for managers who intend to select appropriate video conferencing software.

A Consensus-Reaching Approach to the Evaluation of Product Design Alternatives with Multiple Preference Structures

With interdisciplinarity being an important characteristic of contemporary product design, the evaluation of design alternatives also involves multiple disciplines, and the evaluator group usually consists of evaluators from different fields and with obvious heterogeneous characteristics. To effectively satisfy the heterogeneous needs of evaluators and improve the credibility of evaluation results, the paper introduces a consensus-reaching approach that incorporates multiple preferences to the evaluation of product design alternatives. First, in order to obtain individual preference information, each evaluator is asked to evaluate all the design alternatives using a preference structure that he/she is familiar with. Second, we use a transfer function to uniform the evaluation information obtained from various preference structures into a complementary judgment matrix. Then, we use the Hybrid Weighted Averaging (HWA) operator weight determination model to aggregate the preference information and obtain the group preference information. Then, we measure the consensus degree between individual evaluators and the group using a consensus measurement method. After that, we use the feedback mechanism to instruct individual evaluators to modify their preferences until a consensus is achieved. We explain the application steps and the feasibility of this approach through the evaluation of the design alternatives of multichannel fluorescence immunochromatography analyzers (MFIAs).

Interval-valued intuitionistic pure linguistic entropy weight method and its application to group decision-making

In recent years, the problem of complex multi-attribute group decision-making (MAGDM) in uncertain environments has received increasing attention. In evaluating MAGDM problems, obtaining the objective attribute weights is very important. Considering the excellent performance of intuitive fuzzy linguistic sets in dealing with uncertain information, this paper introduces a new interval-valued intuitionistic pure linguistic entropy weight (IVIPLEW) method for determining attribute weights and evaluating MAGDM problems. The IVIPLEW method considers the cases of missing values, and uses the conventional interval-valued intuitionistic pure linguistic (IVIPL) expectations to supplement the missing values. This method of dealing with missing values not only considers the expectations of experts, but also prevents fluctuations in linguistic variables from impacting the decision results. This paper establishes an analysis framework that allows the IVIPLEW method to be applied to MAGDM problems, and presents a practical case study that illustrates the practicality and effectiveness of IVIPLEW. The results are quite satisfactory. The effectiveness of the proposed method is demonstrated through a comparison with the IVIPL information aggregation method. Furthermore, the robustness of the IVIPLEW method is verified through a sensitivity analysis. The results presented in this paper show that the IVIPLEW method is applicable to a wide range of MAGDM problems.

A Multistakeholder Approach to the Airport Gate Assignment Problem: Application of Fuzzy Theory for Optimal Performance Indicator Selection

Airport gate assignment performance indicator selection is a complicated decision-making problem with strong subjectivity and difficulty in measuring the importance of each indicator. A better selection of performance indicators (PIs) can greatly increase the airport overall benefit. We adopt a multicriteria decision-making approach to quantify qualitative PIs and conduct subsequent selection using the fuzzy clustering method. First, we identify 21 commonly used PIs through literature review and survey. Subsequently, the fuzzy analytic hierarchy process technique was employed to obtain the selection criteria weights based on the relative importance of significance, availability, and generalisability. Further, we aggregated the selection criteria weights and experts' score to evaluate each PI for the clustering process. The fuzzy-possibilistic product partition c-means algorithm was applied to divide the PIs into different groups based on the three selection criteria as partitioning features. The cluster with highest weights of the centre was identified as the very high-influence cluster, and 10 PIs were identified as a result. This study revealed that the passenger-oriented objective is the most important performance criterion; however, the relevance of the airport/airline-oriented and robustness-oriented performance objectives was highlighted as well. It also offers a scientific approach to determine the objective functions for future gate assignment research. And, we believe, through slight modifications, this model can be used in other airports, other indicator selection problems, or other scenarios at the same airport to facilitate policy making and real situation practice, hence facilitate the management system for the airport.

Approximations of pythagorean fuzzy sets over dual universes by soft binary relations

 Yager introduced the Pythagorean Fuzzy Set (PFS) to deal with uncertainty in real-world decision-making problems. Binary relations play an important role in mathematics as well as in information sciences. Soft binary relations give us a parameterized collection of binary relations. In this paper, lower and upper approximations of PFSs based on Soft binary relations are given with respect to the aftersets and with respect to the foresets. Further, two kinds of Pythagorean Fuzzy Topologies induced by Soft reflexive relations are investigated and an accuracy measure of a PFS is provided. Besides, based on the score function and these approximations of PFSs, an algorithm is constructed for ranking and selection of the decision-making alternatives. Although many MCDM (multiple criteria decision making) methods for PFSs have been proposed in previous studies, some of those cannot solve when a person is encountered with a two-sided matching MCDM problem. The proposed method is new in the literature. This newly proposed model solved the problem more accurately. The proposed method focuses on selecting and ranking from a set of feasible alternatives depending on the two-sided matching of attributes and determines a ranking based solution for a problem with conflicting criteria to help the decision-maker in reaching a final course of action.

Using a fuzzy multiple criteria decision-making method to evaluate personal diversity perception to work in a diverse workgroup

Understanding employees’ perceptions in team collaboration may help managers select and develop effective teamwork and efficient job completion. Numerous criteria, including qualitative and quantitative, and their importance weights must be considered in evaluating individual diversity perception; therefore, evaluating individual diversity perception is a fuzzy multiple criteria decision-making (MCDM) problem. The purpose of this paper is to use a fuzzy MCDM method to evaluate the personal perception of working in a diverse workgroup. A ranking method using the mean of relative values is proposed to rank the final fuzzy values to complete the model. Formulas of the ranking procedure are derived to help execute the decision-making procedure and a numerical comparison is conducted to demonstrate the advantage of the proposed ranking method. In addition, a survey about personal diversity perception and willingness to work verifies the feasibility and validity of the proposed mean of relative values based fuzzy MCDM method. The results indicate that decision-makers prefer to work in a different countries-same working field group. More experienced decision-makers, unlike students, prefer to work in the same working sector group.

(α, β)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making

Pawlak’s rough set theory based on single granulation has been extended to multi-granulation rough set structure in recent years. Multi-granulation rough set theory has become a flouring research direction in rough set theory. In this paper, we propose the notion of (α, β)-multi-granulation bipolar fuzzified rough set ((α, β)-MGBFRSs). For this purpose, a collection of bipolar fuzzy tolerance relations has been used. In the framework of multi-granulation, we proposed two types of (α, β)-multi-granulation bipolar fuzzified rough sets model. One is called the optimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) o-MGBFRSs) and the other is called the pessimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) p-MGBFRSs). Subsequently, a number of important structural properties and results of proposed models are investigated in detail. The relationships among the (α, β)-MGBFRSs, (α, β) o-MGBFRSs and (α, β) p-MGBFRSs are also established. In order to illustrate our proposed models, some examples are considered, which are helpful for applying this theory in practical issues. Moreover, several important measures associated with (α, β)-multi-granulation bipolar fuzzified rough set like the measure of accuracy, the measure of precision, and accuracy of approximation are presented. Finally, we construct a new approach to multi-criteria group decision-making method based on (α, β)-MGBFRSs, and the validity of this technique is illustrated by a practical application. Compared with the existing results, we also expound its advantages.

A method based on TODIM technique for multi-criteria two-sided matching and its application in person-position matching

It is impossible for agents on both sides to achieve complete rationality in the decision-making process of two-sided matching (TSM). The TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method considering the psychological behavior of decision-makers is well applied in the multiple criteria decision making (MCDM) problems. The TSM is a MCDM problem. Therefore, in this paper, a method based on TODIM technique is introduced to solve the TSM problem, in which the intuitionistic linguistic numbers are utilized to describe the mutual evaluation between candidates and hiring managers. The focus of this paper is to develop a method for the multi-criteria TSM problem under intuitionistic linguistic environment. First, the evaluation matrices of each agent with respect to each criterion are provided by agents on the opposite side, and the weight assigned to each criterion is determined according to the importance of the evaluation criterion to the matching agent. Then, the dominance measurement of each agent over another one can be calculated based on the intuitionistic linguistic TODIM method. Next, a bi-objective optimization model which aims to maximize the overall satisfaction degree of agents on both sides is constructed to attain the optimal matching pair. Furthermore, the feasibility of the solution method is verified by a case study of person-position matching (PPM), and the matching result demonstrates that the proposed method is effective in dealing with multi-criteria PPM problem. Finally, the sensitivity of parameters and some comparative studies are discussed.

Representing a probabilistic linguistic term set with an interval type-2 fuzzy set and the application in green supplier selection

The use of probabilistic linguistic term sets (PLTSs) means the process of computing with words. The existing methods computing with PLTSs mainly use symbolic model. To provide a semantic model for computing with PLTSs, we propose to represent a PLTS by using an interval type-2 fuzzy set (IT2FS). The key step is to compute the footprint of uncertainty of the IT2FS. To this aim, the upper membership function is computed by aggregating the membership functions of the linguistic terms contained in the PLTS, and the lower membership function is obtained by moving the upper membership function downward with the step being total entropy of the PLTS. The comparison rules, some operations, and an aggregation operator for PLTSs are introduced. Based on the proposed method of computing with PLTSs, a multi-criteria group decision making model is introduced. The proposed decision making model is then applied in green supplier selection problem to show its feasibility.

An approach to MCGDM based on multi-granulation Pythagorean fuzzy rough set over two universes and its application to medical decision problem

Exploring efficiency approaches to solve the problems of decision making under uncertainty is a mainstream direction. This article explores the rough approximation of the uncertainty information with Pythagorean fuzzy information on multi-granularity space over two universes combined with grey relational analysis. Based on grey relational analysis, we present a new approach to calculate the relative degree or the attribute weight with Pythagorean fuzzy set and give a new descriptions for membership degree and non-membership. Then, this paper proposes a multi-granulation rough sets combined with Pythagorean fuzzy set, including optimistic multi-granulation Pythagorean fuzzy rough set, pessimistic multi-granulation Pythagorean fuzzy rough set and variable precision Pythagorean fuzzy rough set. Several basic properties for the established models are investigated in detail. Meanwhile, we present an approach to solving the multiple-criteria group decision making problems with fuzzy information based on the proposed model. Eventually, a case study of psychological evaluation of health care workers in COVID-19 show the principle of the established model and is utilized to verify the availability. The main contributions have three aspects. The first contribution of an approach of calculating the attribute weight is presented based on Grey Relational Analysis and gives a new perspective for the Pythagorean fuzzy set. Then, this paper proposes a mutli-granulation rough set model with Pythagorean fuzzy set over two universes. Finally, we apply the proposed model to solving the psychological evaluation problems.

Rough approximations of bipolar soft sets by soft relations and their application in decision making

The rough set theory is an effective method for analyzing data vagueness, while bipolar soft sets can handle data ambiguity and bipolarity in many cases. In this article, we apply Pawlak’s concept of rough sets to the bipolar soft sets and introduce the rough bipolar soft sets by defining a rough approximation of a bipolar soft set in a generalized soft approximation space. We study their structural properties and discuss how the soft binary relation affects the rough approximations of a bipolar soft set. Two sorts of bipolar soft topologies induced by soft binary relation are examined. We additionally discuss some similarity relations between the bipolar soft sets, depending on their roughness. Such bipolar soft sets are very useful in the problems related to decision-making such as supplier selection problem, purchase problem, portfolio selection, site selection problem etc. A methodology has been introduced for this purpose and two algorithms are presented based upon the ongoing notions of foresets and aftersets respectively. These algorithms determine the best/worst choices by considering rough approximations over two universes i.e. the universe of objects and universe of parameters under a single framework of rough bipolar soft sets.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

An evidence theory based approach for group decision making under uncertainty

With the changing business environment and the active participation of various stakeholders in the decision making process, it plays an increasingly important role to the weight of decision makers and the preference information given by decision makers. This paper presents a novel approach for group decision making under uncertainty with the involvement of the third-party evaluator in the decision making process. Recognizing the challenge in adequately determining the weight of decision makers in group decision making, the evidence theory is appropriately used with the involvement of the third-party evaluator. To effectively model the uncertainty and imprecision in the decision making process, fuzzy preference relations are used for better representing the subjective assessment of individual decision makers. To adequately determine the ranking of available alternatives, the logarithmic least square method is applied for appropriately aggregating the fuzzy preference relation of individual decision makers. A group consensus index is developed for facilitating consensus building in group decision making. This leads to better group decisions being made. A real-world application is presented that shows the proposed approach is effective in solving group decision making problems under uncertainty.

Extended TOPSIS method based on the entropy measure and probabilistic hesitant fuzzy information and their application in decision support system

Probabilistic hesitant fuzzy Set (PHFs) is the most powerful and comprehensive idea to support more complexity than developed fuzzy set (FS) frameworks. In this paper a novel and improved TOPSIS-based method for multi-criteria group decision making (MCGDM) is explained through the probabilistic hesitant fuzzy environment, in which the weights of both experts and criteria are completely unknown. Firstly, we discuss the concept of PHFs, score functions and the basic operating laws of PHFs. In fact, to compute the unknown weight information, the generalized distance measure for PHFs was defined based on the Probabilistic hesitant fuzzy entropy measure. Second, MCGDM will be presented with the PHF information-based decision-making process.

Multicriteria decision making approach using an efficient novel similarity measure for generalized trapezoidal fuzzy numbers

Multicriteria Decision Making (MCDM) has a huge role to play while ruling out one suitable alternative among a pool of alternatives governed by predefined multiple criteria. Some of the factors like imprecision, lack of information/data, etc., which are present in traditional MCDM processes have showcased their lack of efficiency and hence eventually it has paved the ways for the development of Fuzzy multicriteria decision making (FMCDM). In FMCDM processes, the decision makers can model most of the real-life phenomena by fuzzy information-based preferences. The availability of a wide literature on similarity measure (SM) emphasizes the vital role of SM of generalized fuzzy numbers (GFNs) to conduct accurate and precise decision making in FMCDM problems. Despite having few advantages, most of the existing approaches possessed a certain degree of counter intuitiveness and discrepancies. Thus, we have attempted to propose a novel SM for generalized trapezoidal fuzzy numbers (GTrFNs) which could deliberately overcome the impediments associated with the earlier existing approaches. Moreover, a meticulous comparative study with the existing approaches is also presented. This paper provides us with an improved method to obtain the similarity values between GTrFNs and the proposed SM consists of calculating the prominent features of fuzzy numbers such as expected value and variance. We use fourteen different sets of GTrFNs, to compare the fruition of the present approach with the existing SM approaches. Furthermore, to show the utility and applicability of our proposed measure, we illustrate few practical scenarios such as the launching of an electronic gadget by a company, a problem of medical diagnosis and finally, a proper anti-virus mask selection in light of the recent COVID-19 pandemic. The obtained results with our proposed SM, for the mentioned FMCDM problems, are analytically correct and they depict the efficiency and novelty of the present article.

Ranking Road Sections Based on MCDM Model: New Improved Fuzzy SWARA (IMF SWARA)

Traffic management is a significantly difficult and demanding task. It is necessary to know the main parameters of road networks in order to adequately meet traffic management requirements. Through this paper, an integrated fuzzy model for ranking road sections based on four inputs and four outputs was developed. The goal was to determine the safety degree of the observed road sections by the methodology developed. The greatest contribution of the paper is reflected in the development of the improved fuzzy step-wise weight assessment ratio analysis (IMF SWARA) method and integration with the fuzzy measurement alternatives and ranking according to the compromise solution (fuzzy MARCOS) method. First, the data envelopment analysis (DEA) model was applied, showing that three road sections have a high traffic risk. After that, IMF SWARA was applied to determine the values of the weight coefficients of the criteria, and the fuzzy MARCOS method was used for the final ranking of the sections. The obtained results were verified through a three-phase sensitivity analysis with an emphasis on forming 40 new scenarios in which input values were simulated. The stability of the model was proven in all phases of sensitivity analysis.