Intuitionistic Fuzzy Method Research Articles

An intuitionistic fuzzy grey-Markov method with application to demand forecasting for emergency supplies during major epidemics

PurposeForecasting demand of emergency supplies under major epidemics plays a vital role in improving rescue efficiency. Few studies have combined intuitionistic fuzzy set with grey-Markov method and applied it to the prediction of emergency supplies demand. Therefore, this article aims to establish a novel method for emergency supplies demand forecasting under major epidemics.Design/methodology/approachEmergency supplies demand is correlated with the number of infected cases in need of relief services. First, a novel method called the Intuitionistic Fuzzy TPGM(1,1)-Markov Method (IFTPGMM) is proposed, and it is utilized for the purpose of forecasting the number of people. Then, the prediction of demand for emergency supplies is calculated using a method based on the safety inventory theory, according to numbers predicted by IFTPGMM. Finally, to demonstrate the effectiveness of the proposed method, a comparative analysis is conducted between IFTPGMM and four other methods.FindingsThe results show that IFTPGMM demonstrates superior predictive performance compared to four other methods. The integration of the grey method and intuitionistic fuzzy set has been shown to effectively handle uncertain information and enhance the accuracy of predictions.Originality/valueThe main contribution of this article is to propose a novel method for emergency supplies demand forecasting under major epidemics. The benefits of utilizing the grey method for handling small sample sizes and intuitionistic fuzzy set for handling uncertain information are considered in this proposed method. This method not only enhances existing grey method but also expands the methodologies used for forecasting demand for emergency supplies.Highlights (for review)An intuitionistic fuzzy TPGM(1,1)-Markov method (IFTPGMM) is proposed.The safety inventory theory is combined with IFTPGMM to construct a prediction method.Asymptomatic infected cases are taken to forecast the demand for emergency supplies.

Intuitionistic fuzzy normalized weighted geometric Bonferroni means with reducibility and boundedness and application in decision making1

Bonferroni mean (BM) is an important aggregation operator in decision making. The desirable characteristic of the BM is that it can capture the interrelationship between the aggregation arguments or the individual attributes. The optimized weighted geometric Bonferroni mean (OWGBM) and the generalized optimized weighted geometric Bonferroni mean (GOWGBM) proposed by Jin et al in 2016 are the extensions of the BM. However, the OWGBM and the GOWGBM have neither the reducibility nor the boundedness, which will lead to the illogical and unreasonable aggregation results and might make the wrong decision. To overcome these existing drawbacks, based on the normalized weighted Bonferroni mean (NWBM) and the GOWGBM, we propose the normalized weighted geometric Bonferroni mean (NWGBM) and the generalized normalized weighted geometric Bonferroni mean (GNWGBM), which can not only capture the interrelationship between the aggregation arguments, but also have the reducibility and the boundedness. Further, we extend the NWGBM and the GNWGBM to the intuitionistic fuzzy decision environment respectively, and develop the intuitionistic fuzzy normalized weighted geometric Bonferroni mean (IFNWGBM) and the generalized intuitionistic fuzzy normalized weighted geometric Bonferroni mean (GIFNWGBM). Subsequently, we prove some properties of these operators. Moreover, we present a new intuitionistic fuzzy decision method based on the IFNWGBM and the GIFNWGBM. Two application examples and comparisons with other existing methods are used to verify the validity of the proposed method.

How to promote the sustainable development of strategic emerging industries: Evidence from Guangzhou

The strategic emerging industry (SEI) can effectively cope with high energy consumption, high pollution and low efficiency in traditional production mode, which attracts high attention. However, few studies quantitatively analyze the input-output relationships and the sustainable development level of SEIs. Moreover, existing method frameworks fail to consider both the current situation and development potential of SEIs. To deal with the above research gaps, a novel static-dynamic intuitionistic fuzzy evaluation framework integrating output-oriented data envelopment analysis model, improved Malmquist model, triangular intuitionistic fuzzy number, clustering method and Tobit regression model is first proposed. 120 SEIs from Guangzhou are selected for empirical study. Results reveal that all SEIs have almost no expected movement in operational cost but obvious redundancies in employee expenditure with a standard deviation of 1.771. It's urgent to optimize the employment, assessment and salary systems for staff. Moreover, SEI sustainable development scores vary from 0.473 to 1. It's necessary to strengthen cultivation of excellent SEIs and pay attention to supervision of the weak. Research findings can not only guide local government and industry associations to make scientific evaluation, but also help SEIs carry out self-inspections, which can further promote sustainable development of the entire industry.

An Intuitionistic Fuzzy Decision Support for Agile Project Selection Problem

In the early 1990s, organizations started to use information technology and software engineering, which encouraged the companies for employing project management methodologies to survive and then advance in competitive technologic environment. Use of project management methodologies provides efficient planning, budgeting and scheduling processes and high management quality for companies. A lot of different methodologies were developed and used to reach better ways of defining the project requirements, analyzing the problem, and implementing it in a systematic manner. In 2001, agile project management methodology came forward in response to cope with waterfall project methodology’s limitations that arise from unpredictability of technology evolution, customer requirements, and unstable business environments. In this study, intuitionistic fuzzy COPRAS method, which aims to obtain a solution relative to the ideal solution, is used to rank agile project alternatives and identify the best performing one among them. Intuitionistic fuzzy sets are used to deal with loss of information and hesitation in data that may occur in operations with fuzzy numbers. The application of the proposed intuitionistic fuzzy decision-making approach is illustrated by conducting a case study.

Novel evaluation model of teaching quality based on the improved IVIF-BWM and IVIFWMSM

The evaluation of teaching quality plays a crucial role in promoting the improvement of education quality and ensuring the healthy development of education. This study presents a novel teaching quality evaluation model based on improved interval-valued intuitionistic fuzzy Best-Worst method (IVIF-BWM) and interval-valued intuitionistic fuzzy weighted Maclaurin symmetric mean operators (IVIFWMSM). The study is divided into three parts. Firstly, to derive the optimal interval-valued intuitionistic fuzzy weights of criteria, we develop an improved IVIF-BWM by establishing a goal programming model based on the multiplicative consistent interval-valued intuitionistic fuzzy preference relation(IVIFPR), and then we propose the new consistency index (CI) and the consistency ratio (CR) under interval-valued intuitionistic fuzzy environment to verify the reliability of the derived results. Secondly, with regard to the importance and interaction relationships among criteria, IVIFWMSM is used to aggregate evaluation values of alternatives on each evaluation criteria in multi-criteria decision making process. Finally, the proposed teaching quality evaluation model is applied to a case of teaching quality evaluation in higher education and a comparison study with other existing methods are performed. The results demonstrate that the proposed teaching quality evaluation model not only overcomes the shortcomings of previous methods, but also is more accuracy, effective and reasonable for dealing with the teaching quality evaluation under the intuitionistic fuzzy environments.

A novel interactive intuitionistic fuzzy approach to find satisfactory Pareto-optimal solutions for general bilevel multi-followers programming

This paper focuses on the approach for solving the satisfactory Pareto-optimal solutions of the general form of bilevel multi-followers programming(BMFP), including the BMFP with partial shared variables among followers, the so-called referential-uncooperative BMFP, the uncooperative BMFP, and the cooperative BMFP. Without losing generality, the BMFP with partial shared variables among followers will be taken as a representative to explain the universal applicability of the proposed generic interactive intuitionistic fuzzy method. Based on the theory of intuitionistic fuzzy set, the new definition of satisfactory Pareto-optimal solutions is introduced by means of membership function, non-membership function, and score function. In order to obtain satisfactory Pareto-optimal solutions of BMFP with partial shared variables among followers, a prior minimization optimization problem and a series of corresponding auxiliary maximization optimization problems are formulated, and we strictly prove that the optimal solution of the prior minimization optimization problem is not necessarily the satisfactory Pareto-optimal solutions, but at least one satisfactory Pareto optimal solution can be derived by further solving these auxiliary maximization optimization problems. Then, a detailed interactive intuitionistic fuzzy algorithm framework that consider both the balance of satisfactory degree between the leader and the followers and the balance of satisfactory degree among all followers is proposed. In the part of numerical experiments, four examples(including a linear BMFP problem with partial shared variables among followers, a BMFP model of a road network problem, an uncooperative BMFP problem, and a nonlinear BMFP problem with partial shared variables among followers) are illustrated to demonstrate the applicability, effectiveness and superior performance of the proposed technique.

Multi-source heterogeneous data fusion model based on fuzzy mathematics

Sensors as the sensing end of intelligent control can be used to collect various data instead of human beings. In the context of technological development, the variety of sensors leads to multiple and structurally unequal data sources, and fusion of these data becomes a problem for consideration. The study constructs an intuitionistic fuzzy transformation method to handle data with various attributes with the help of fuzzy mathematical concepts, which characterizes the data based on the hesitancy and ideal solutions under Gaussian distribution. Simulations of classical classification data show that the intuitionistic fuzzy transformation method can effectively differentiate the affiliation of data points in the dataset, and the results of 800 simulations show that the qualitative accuracy of the algorithm can reach 89%, while the causes of abnormal data are explored and it is found that the attributes of the dataset based on Gaussian distribution are too close to each other as the cause of misclassification; the algorithm is also optimized from multi-dimensional considerations, and a An optimization operator based on the distance method of superior and inferior solutions was constructed and simulated for several optimization paths. The results show that the study uses an optimization scheme that is significantly better than the existing fuzzy operator, and 800 times can improve the accuracy rate up to 95.23%, which is 14.01% higher than that of a single attribute. This indicates that the intuitionistic fuzzy algorithm of this study has some rationality and is able to fuse the data of multiple attributes of the sensor for determination and provide the necessary basis for decision making.

Interval-valued intuitionistic fuzzy best-worst method with additive consistency

Best-worst method (BWM) has received extensive attention because of its fewer pairwise comparisons and maintenance of consistency. Extending it to various fuzzy environments has become a hot research spot. This paper initiates a new interval-valued intuitionistic fuzzy (IVIF) BWM with additive consistency. Firstly, an IVIF fuzzy preference relation (IVIFPR) is viewed as a directed graph with IVIF weights. An approach is offered to distinguish the best and worst criteria by the defined score out-degree and accuracy out-degree of criteria. The concept of IVIF reference comparisons is introduced. The additive consistency of IVIF reference comparisons is acquired by that of IVIFPR using its left and right intuitionistic fuzzy preference relations. We derive the relationship between the IVIF reference comparisons and the IVIF priority weight vector. Based on this relationship, a linear goal programming model is constructed to generate the IVIF priority weights. Two consistency indexes are analytically obtained and the consistency ratio is then defined to check the consistency of IVIF reference comparisons. For the unacceptably additive consistency, a new approach is put forward to enhance the consistency. Thereby, the proposed IVIF BWM is summarized step by step. Three examples of applications are furnished to demonstrate its effectiveness and validation.

Archimedean [formula omitted]-norm and [formula omitted]-conorm based intuitionistic fuzzy WASPAS method to evaluate health-care waste disposal alternatives with unknown weight information

Health-care waste (HCW) contains numerous hazardous, infectious, and radioactive contents that may cause serious health issues for society and drastic environmental problems. Therefore, it is crucial to dispose of HCW safely and appropriately. Four commonly used HCW disposal methods are incineration, steam sterilization, microwave, and landfill disposal. To select an appropriate HCW disposal method, there are several conflicting criteria. Furthermore, when information is lacking due to uncertainty and criteria weighing conditions are also unknown, the decision to choose an appropriate HCW disposal method becomes more challenging. So, the objective of this paper is to introduce a novel integrated multi-criteria group decision-making (MCGDM) approach to evaluate HCW disposal methods in which incomplete information is quantified using intuitionistic fuzzy sets (IFSs), unknown criteria weights are evaluated using the maximizing deviation method, and the evaluation of HCW disposal methods is done by applying the Archimedean t-norm and t-conorm-based interactive intuitionistic fuzzy weighted aggregated sum product assessment (WASPAS) method. Herein, the Archimedean t-norm and t-conorm cover a wide range of t-norms and t-conorms, including the Algebraic, Einstein, Hamacher, and Frank, etc., by adopting prescribed combinations of additive generators. The proposed MCGDM approach has been applied to evaluate the above-listed four HCW disposal methods for a case study conducted by Mishra et al. (2020) in the context of India. A sensitivity analysis is performed to examine the impact of changes in the parameters involved in the proposed MCGDM approach. A comparative study is also performed with some well-known multi-criteria decision making(MCDM) and MCGDM methods to demonstrate the consistency and stability of the proposed approach. Findings suggest that the newly developed MCGDM approach is more general, flexible, and provides realistic results to evaluate HCW disposal methods under uncertainty and unknown criteria weight information.

MAGDM Model Using an Intuitionistic Fuzzy Matrix Energy Method and Its Application in the Selection Issue of Hospital Locations

Matrix energy is a valid mathematical tool for representing collective information. However, it is not used in the existing literature for fuzzy sets, intuitionistic fuzzy sets, and multi-attribute group decision making (MAGDM) problems, which highlights research gaps. Motivated by both matrix energy and the research gaps, this study aims to extend matrix energy to the energy of an intuitionistic fuzzy matrix (IFM) and to utilize the IFM energy method in the MAGDM problem, which fully contains all the IFM information on attribute weights, decision maker weights, and attribute values. To achieve these objectives, this paper first proposes IFM energy in terms of the true matrix energy and false matrix energy; then, it develops a MAGDM model using the IFM energy method and the score and accuracy equations of IFM energy. Then, the developed MAGDM model is applied to the selection problem of hospital locations in Shaoxing City, China to demonstrate the practicality and validity of the developed model. Compared with existing intuitionistic fuzzy MAGDM methods, the developed MAGDM model using the IFM energy method reveals its superiority and novelty in complete IFM information expressions and the MAGDM method because the existing MAGDM methods containing intuitionistic fuzzy set information have difficulty tackling MAGDM problems containing all the IFM information on attribute weights, decision maker weights, and attribute values.

TOPSISort-L: An extended likelihood-based interval-valued intuitionistic fuzzy TOPSIS-sort method and its application to multi-criteria group decision-making

In real-world multi-criteria group decision making challenges, decision makers typically provide imprecise or ambiguous information due to a lack of knowledge, time constraints, or restrictions regarding information disclosure. In order to deal with this sort of imprecision caused by experts' subjective evaluation, fuzzy sets have been suggested. When compared to traditional fuzzy sets, interval-valued intuitionistic fuzzy sets, also known as IVIFSs, are superior when it comes to dealing with subjective ambiguity and incomplete information. For these reasons, this work provides a novel extension for the TOPSIS technique by employing likelihoods of IVIFSs, and introduces a methodology named as TOPSISort-L that is capable of classifying alternatives under a variety of circumstances. We begin by developing the conventional fuzzy TOPSIS technique by using a newly proposed decision matrix, a novel selection mechanism for ideal solutions, and a generalized likelihood-based closeness metric for the purpose of alternative ranking. After that, the TOPSISort-L algorithms are presented to obtain an accurate classification for the alternatives when there are information about the characteristic profiles, and also obtain an approximate classification when information about the characteristic profiles is missing. Eventually, by contrasting the approach with various different methodologies now in use, we exhibit the validity and adaptability of the method.

An Intuitionistic Fuzzy Decision Aid for Neuromarketing Technology Selection Problem

Neuromarketing, which uses neuroimaging technologies for marketing initiatives, is represented as the application of neuroscientific methods for analysing and understanding consumer behaviour with regard to marketing objectives. Medical diagnostic devices for brain imaging are used by marketers as neuromarketing technologies. In this study, the intuitionistic fuzzy COPRAS method, which aims to obtain a solution relative to the ideal solution, is used to rank neuromarketing technology alternatives and identify the best-performing one among them. Intuitionistic fuzzy sets are used to deal with the loss of information and hesitation in data that may occur in operations with fuzzy numbers. The application of the proposed intuitionistic fuzzy decision-making approach is illustrated by conducting a case study

Renewable energy generation forecasting in Turkey via intuitionistic fuzzy time series approach

Recently, renewable energy generation (REG) forecasting has become a challenging task for effective energy management. To date, a number of time-series models utilizing physical models, statistical techniques, and artificial intelligence algorithms have been proposed to deal with this problem. Fuzzy time series (FTS) models stand out among these methods since they do not need extensive historical data or some statistical assumptions like the normal distribution. Because intuitionistic fuzzy sets incorporate non-membership values in addition to membership values, they provide more information than conventional fuzzy sets do. In this regard, this paper recommends a hybrid methodology that combines the intuitionistic FTS method with the intuitionistic fuzzy c-means method for REG forecasting of Turkey between the years 2000–2020. According to the empirical results, it can be concluded that the presented integrated model showed good performance in terms of accuracy. The suggested framework is a useful tool not only for REG forecasting but also for other time series forecasting problems.

Solving multi-objective linear fractional decentralized bi-level decision-making problems through compensatory intuitionistic fuzzy mathematical method

This study has focused on developing a new method for solving the multi-objective linear fractional decentralized bi-level decision-making (MOLF-DBLDM) problem in an intuitionistic fuzzy decision environment. The main motivation behind this study is to determine a solution approach algorithm that is effective and simple to apply while taking actual decision-making circumstances into account. Real-world decision-making situations involve a bi-level of several decision-makers who use various decision-making processes such as agree, not certain, and disagree. By considering such real-world conditions here, all uncertain coefficients of objectives, constraint functions, and resources are portrayed as trapezoidal intuitionistic fuzzy numbers, and their crisp form is obtained through the (α,β)-cut (confidence level) concept. In the suggested method, we have transformed the crisp (α,β)-MOLF-DBLDM problem into a single objective linear decentralized bi-level decision-making (SOL-DBLDM) model using a modified linearized approach. Additionally, the upper level specified a tolerance region for its decision variables to regulate the lower levels in order to prevent decision lock. Then, the SOL-DBLDM problem is expressed as a single-level model using a new scalar function of membership and non-membership degree for each objective function at all decision-makers and upper level decision control variables. The key advantage of this method over others is that it produces an alternate, preferable compromise solution to the problem of imprecise hierarchical-level optimization. Finally, comparisons to the current methodology and appropriate numerical examples are used to demonstrate the superiority and effectiveness of the suggested method.

Assessing the environmental impact of industrial pollution using the complex intuitionistic fuzzy ELECTREE method: a case study of pollution control measures

Environmental pollution has become a major issue in today’s world, and controlling it is crucial for the sustainable development of our planet. Industries play a significant role in environmental pollution, and their impact must be controlled and minimized. In this paper, we present a novel approach, the complex intuitionistic fuzzy ELECTREE method (CIF–ELECTREE), for environmental impact assessment of industries. The method combines the principles of CIF sets and the ELECTREE method to provide a comprehensive and reliable assessment of the environmental impact of industries. The proposed method has been applied to real-world data, and the results obtained demonstrate the effectiveness of the CIF–ELECTREE method in controlling and reducing the environmental impact of industries. The results show that the CIF–ELECTREE method can provide a more accurate assessment of the environmental impact of industries compared to traditional methods. This study contributes to the existing literature by introducing a novel approach for environmental impact assessment and highlights the importance of considering both the uncertainty and vagueness in real-world data for reliable decision making.

Intuitionistic fuzzy multiple attribute decision making method based on a parametric piecewise score function

The score function and aggregation operator provide the theoretical basis for intuitionistic fuzzy multiple attribute decision making (MADM), where the role of the score function is to compare and rank the intuitionistic fuzzy numbers (IFNs), and the role of the aggregation operator is to integrate the evaluation information. In view of that, this paper proposes a new score function and aggregation operator, and a new intuitionistic fuzzy MADM method. It first constructs a parametric piecewise score function and discusses the influence of hesitancy degree and the parameter λ on it. Moreover, some properties of the constructed score function are discussed, including the monotonicity, maximum, minimum, and range. Then, it introduces a intuitionistic fuzzy modified Einstein aggregation (IFMEWA) operator and proves monotonicity, idempotency and boundedness of IFMEWA operator. Finally, combined with the constructed score function and IFMEWA operator, it proposes a new intuitionistic fuzzy MADM method.

Correction to: Interval-valued intuitionistic fuzzy symmetric point criterion-based MULTIMOORA method for sustainable recycling partner selection in SMEs

Correction to: Interval-valued intuitionistic fuzzy symmetric point criterion-based MULTIMOORA method for sustainable recycling partner selection in SMEs

Hybrid Intuitionistic Fuzzy Entropy-SWARA-COPRAS Method for Multi-Criteria Sustainable Biomass Crop Type Selection

To select a biomass crop type of the highest sustainability for the purpose of producing biofuel is recognized as a problem of the multi-criteria decision analysis (MCDA) type, as it comprises different conflicting criteria. To effectively address this problem, the present paper introduces a novel integrated approach using the complex proportional assessment (COPRAS) method under the intuitionistic fuzzy sets (IFSs). The proposed approach works based on the IFSs operators as well as an innovative process utilized in evaluating the attributes’ weights. To evaluate these weights, the subjective weights using the step-wise weight assessment ratio analysis (SWARA) model are integrated with the objective weights achieved using an entropy-based approach in order to attain more realistic weights. As MCDA problems inevitably suffer from different degrees of uncertainty, the proposed approach could be of great help to those who are required to make decisions in uncertain settings. The paper took into consideration a sustainable biomass crop selection problem to exemplify the effectiveness of the presented approach in handling real MCDA problems. Moreover, a sensitivity analysis with respect to the diverse values of the attributes is presented in order to assess the stability of the introduced model. This study reveals that the combination of the objective and subjective weights enhances the stability of the introduced approach with diverse attribute weights. Finally, the results of the introduced model are compared to some existing intuitionistic fuzzy information-based methods. The findings of the comparison confirm the efficiency of the present approach in performing the defined tasks under uncertain environments.

A Monotonous Intuitionistic Fuzzy TOPSIS Method Under General Linear Orders via Admissible Distance Measures

All intuitionistic fuzzy TOPSIS methods contain two key elements: (1) the order structure, which can affect the choices of positive ideal-points and negative ideal-points, and construction of admissible distance/similarity measures; (2) the distance/similarity measure, which is closely related to the values of the relative closeness degrees and determines the accuracy and rationality of decision-making. For the order structure, many efforts are devoted to constructing some score functions, which can strictly distinguish different intuitionistic fuzzy values (IFVs) and preserve the natural partial order for IFVs.This paper proves that such a score function does not exist, namely the application of a single monotonous and continuous function does not distinguish all IFVs. For the distance or similarity measure, some examples are given to show that classical similarity measures based on the normalized Euclidean distance and normalized Minkowski distance do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. Moreover,some illustrative examples are given to show that classical intuitionistic fuzzy TOPSIS methods do not ensure the monotonicity with the natural partial order or linear orders, which may yield some counter-intuitive results. To overcome the limitation of non-monotonicity, we propose a novel intuitionistic fuzzy TOPSIS method,using three new admissible distances with the linear orders measured by a score degree/similarity function and accuracy degree, or two aggregation functions, and prove that the proposed TOPSIS method is monotonous under these three linear orders.} This is the first result with a strict mathematical proof on the monotonicity with the linear orders for the intuitionistic fuzzy TOPSIS method.

Selecting features by utilizing intuitionistic fuzzy Entropy method

Feature selection is the most significant pre-processing activity, which intends to reduce the data dimensionality for enhancing the machine learning process. The evaluation of feature selection must consider classification, performance, efficiency, stability, and many factors. Nowadays, uncertainty is commonly occurred in the feature selection process due to time limitations, imprecise information, and the subjectivity of human minds. Moreover, the theory of intuitionistic fuzzy set has been proven as an extremely valuable tool to tackle the uncertainty and ambiguity that arises in many practical situations. Thus, this study introduces a novel feature selection framework using intuitionistic fuzzy entropy. In this regard, new entropy for IFS is proposed first and then compared with some of the previously developed entropy measures. As entropy is a measure of uncertainty present in data (features), features with higher entropy values are filtered out, and the remaining features having lower entropy values have been used to classify the data. To verify the effectiveness of the proposed entropy-based feature selection, some experiments are done with ten standard benchmark datasets by employing a support vector machine, K-nearest neighbor, and Naïve Bias classifiers. The outcomes of the study validate that the proposed entropy-based filter feature selection is more feasible and impressive than existing filter-based feature selection methods.