Intuitionistic Fuzzy Entropy Research Articles

Proposed Intuitionistic Fuzzy Entropy Measure Along With Novel Multicriteria Sorting Techniques

Recently, the major environmental change and a pandemic called COVID-19 have heavily impacted the economy, business, and health of each country. Moreover, the climatic changes and COVID-19 are calamities to human life. In other words, these two aspects threaten the existence of humans and the sustenance of the overall development of a country. These two factors particularly influence the tourism sector, so a strategy balancing environmental quality and dealing with the ill effects of COVID-19 is formulated to uplift the economic sectors. Atannasov’s intuitionistic fuzzy domain is used to model the environmental quality and COVID-19 due to the involvement of hesitancy and uncertainty. The precise measurement of the imprecision in the information is obtained with the help of entropy measure. The paper analyzes the two aspects using a novel entropy measure based on multiple criteria sorting (MCS). Here, the two MCS problems are solved with the help of two proposed techniques: TOPSIS-GREY-sort and ENTROPY-TOPSIS-GREY-sort. A case study showing the impact of COVID-19 in the Philippines and the environmental quality of Tehran (the capital city of Iran) are considered to validate the functioning of the proposed techniques. We use “A novel sorting method TOPSIS-SORT: an application for Tehran environmental quality evaluation (2016), Ekonomica a management,” and “Current Issues in Tourism 25.2(2022): 168–178, Taylor and Francis” for the comparative analysis.

Threat assessment of aerial targets based on improved GRA-TOPSIS method and three-way decisions.

Target threat assessment is a critical aspect of information warfare and can offer valuable auxiliary support to combat command decision-making. Aiming to address the shortcomings of three decision-making methods in air combat target assessment, such as the inability to effectively handle uncertain situation information and quantitatively rank the decision-making targets according to their importance, a dynamic intuitionistic fuzzy decision model based on the improved GRA-TOPSIS method and three-way decisions is proposed. First, the target attribute weight is obtained by cosine intuitionistic fuzzy entropy algorithm; then, a novel intuitionistic fuzzy distance measure is introduced, and grey incidence analysis and TOPSIS are used to build the conditional probability for three-way decisions that fully utilize the existing information and reflect the consistency of dynamic change trend; finally, the comprehensive loss function matrix is constructed and the threat classification results are obtained using the decision rules. The example analysis shows that the proposed method can not only effectively handle complex battlefield situations and dynamic uncertain information, but it can also classify targets, improving the effectiveness and rationality of decision-making and providing a reference basis for scientific command decision-making.

A New Model of Interval-Valued Intuitionistic Fuzzy Weighted Operators and Their Application in Dynamic Fusion Target Threat Assessment.

Existing missile defense target threat assessment methods ignore the target timing and battlefield changes, leading to low assessment accuracy. In order to overcome this problem, a dynamic multi-time fusion target threat assessment method is proposed. In this method, a new interval valued intuitionistic fuzzy weighted averaging operator is proposed to effectively aggregate multi-source uncertain information; an interval-valued intuitionistic fuzzy entropy based on a cosine function (IVIFECF) is designed to determine the target attribute weight; an improved interval-valued intuitionistic fuzzy number distance measurement model is constructed to improve the discrimination of assessment results. Specifically, first of all, we define new interval-valued intuitionistic fuzzy operation rules based on algebraic operations. We use these rules to provide a new model of interval-valued intuitionistic fuzzy weighted arithmetic averaging (IVIFWAA) and geometric averaging (IVIFWGA) operators, and prove a number of algebraic properties of these operators. Then, considering the subjective and objective weights of the incoming target, a comprehensive weight model of target attributes based on IVIFECF is proposed, and the Poisson distribution method is used to solve the time series weights to process multi-time situation information. On this basis, the IVIFWAA and IVIFWGA operators are used to aggregate the decision information from multiple times and multiple decision makers. Finally, based on the improved TOPSIS method, the interval-valued intuitionistic fuzzy numbers are ordered, and the weighted multi-time fusion target threat assessment result is obtained. Simulation results of comparison show that the proposed method can effectively improve the reliability and accuracy of target threat assessment in missile defense.

Selection of Third-Party Reverse Logistics Service Provider Based on Intuitionistic Fuzzy Multi-Criteria Decision Making

The scientific selection of a third-party reverse logistics service provider (3PRLP) is helpful for enterprises to obtain the expected ecological and economic benefits. Different enterprises have different requirements for 3PRLP selection and, thus, should adopt personalized and simplified evaluation criteria. However, there is a lack of research on criteria screening. Therefore, this paper proposes a criteria screening method based on a rough set for the first time. The 3PRLP selection is a multi-criteria decision making (MCDM) problem in essence, and different criteria can be expressed in different forms. The existing research mostly uses one method for 3PRLP selection, lacking the comprehensive application of various methods. In this paper, various criteria values are transformed into intuitionistic fuzzy numbers (IFNs) for the comparison and combination of various intuitionistic fuzzy MCDM methods. In terms of criteria weighting, a subjective weighting method based on an analytical network process (ANP) is proposed due to the possible correlation between the criteria at the same level. Meanwhile, an objective weighting method based on intuitionistic fuzzy entropy is proposed. The subjective and objective weights are integrated to form the more scientific combination weights. Combining the modeling principles of different intuitionistic fuzzy MCDM methods, the representative methods under each principle are chosen to build a combination evaluation idea that integrates multiple single evaluation models, and the specific evaluation steps are given, including the single evaluation, Kendall compatibility test, combination evaluation, and Spearman consistency test. An illustrative example of 3PRLP selection is provided to verify the feasibility of the methods of criteria screening and weighting and the combination evaluation idea.

Interval-Valued Intuitionistic Fuzzy Decision With Graph Pattern in Big Graph

Graph pattern matching (GPM) in big graph has been widely used in decision making, such as expert finding, social group discovery, etc. However, these existing works consider neither the preference of the decision maker (DM), nor the subjectivity of constraints during the process of GPM. Therefore, this paper proposes an interval-valued intuitionistic fuzzy decision (IVIFD) with graph pattern in big graph. As traditionally IVIFD can maximally reduce the uncertainty of decision making and it is only valid for small datasets, which makes it impossible to be applied in big graph. In this paper, GPM is adopted to prune the searching space, which makes it possible to process IVIFD under the preference of the DM later. Technically, firstly, each DM selects the preferred vertices and/or edges in big graph, and the interval-valued intuitionistic fuzzy preference (IVIFP) is calculated and used to form the contextual constraints to conduct GPM. Secondly, a probability-certainty density function is introduced to capture the subjective probability of the contextual preference of subgraphs via the bijection from rating space of the context to preference space of the context, which leads to an interval-valued intuitionistic fuzzy set (IVIFS). In addition to the IVIFS, the IVIFD is made through interval-valued intuitionistic fuzzy cross entropy and grey relation degree. Moreover, the weight problem between different contexts is taken into account and handled respectively as three cases. Finally, numerical experiments and perturbation analysis validate the effectiveness and stability of our proposed method, and verify its necessity and efficiency through ablation experiments.

Mechanical equipment health management method based on improved intuitionistic fuzzy entropy and case reasoning technology

Management becomes more challenging as machinery becomes more widely used. From the health management history case records of mechanical devices, we can find that there are many health problems of the same type occurring repeatedly, but when similar problems occur again, solutions are not found in a short period. Case-based reasoning technology aimed at solving the above problems are widely used in equipment health management, but there are problems such as inadequate data utilization and failure to achieve the required accuracy and reliability. To uncover important information from historical failure case data and help reduce equipment downtime due to failure, this paper proposes a machinery equipment health management method based on improved intuitionistic fuzzy entropy and case reasoning technology. Firstly, the axiomatic definition of traditional intuitionistic fuzzy entropy is optimized and a new intuitionistic fuzzy entropy formula in the framework of case-based reasoning decision matrix is proposed. Secondly, the weight value of each attribute is obtained by combining the formula of the entropy weight method. Finally, the feature attribute weight values are fused into the case-based reasoning, and the historical cases that are most similar to the target cases are obtained by combining the existing case base. The effectiveness of the method was verified by comparing and analyzing the example calculation results with the traditional method. The method improves the management of machinery equipment operation and maintenance data. Furthermore, it helps enterprises to carry out the management and analysis of machinery equipment health problems.

Grading Nursing Care Study in Integrated Medical and Nursing Care Institution Based on Two-Stage Gray Synthetic Clustering Model under Social Network Context.

Establishing a scientific and sustainable grading nursing care evaluation system is the key to realizing the rational distribution of medical and nursing resources in the combined medical and nursing care services. This study establishes a grading nursing care index system for medical and nursing institutions from both medical and nursing aspects, and proposes a grading nursing care evaluation model based on a combination of interval-valued intuitionistic fuzzy entropy and a two- stage gray synthetic clustering model for interval gray number under a social network context. Through case analysis, the proposed method can directly classify the elderly into corresponding grading nursing care grades and realize the precise allocation of medical and nursing resources, which proves the feasibility of the method.

Research on Hybrid Multi-Attribute Three-Way Group Decision Making Based on Improved VIKOR Model

In the era of internet connection and IOT, data-driven decision-making has become a new trend of decision-making and shows the characteristics of multi-granularity. Because three-way decision-making considers the uncertainty of decision-making for complex problems and the cost sensitivity of classification, it is becoming an important branch of modern decision-making. In practice, decision-making problems usually have the characteristics of hybrid multi-attributes, which can be expressed in the forms of real numbers, interval numbers, fuzzy numbers, intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy numbers (IVIFNs). Since other forms can be regarded as special forms of IVIFNs, transforming all forms into IVIFNs can minimize information distortion and effectively set expert weights and attribute weights. We propose a hybrid multi-attribute three-way group decision-making method and give detailed steps. Firstly, we transform all attribute values of each expert into IVIFNs. Secondly, we determine expert weights based on interval-valued intuitionistic fuzzy entropy and cross-entropy and use interval-valued intuitionistic fuzzy weighted average operator to obtain a group comprehensive evaluation matrix. Thirdly, we determine the weights of each attribute based on interval-valued intuitionistic fuzzy entropy and use the VIKOR method improved by grey correlation analysis to determine the conditional probability. Fourthly, based on the risk loss matrix expressed by IVIFNs, we use the optimization method to determine the decision threshold and give the classification rules of the three-way decisions. Finally, an example verifies the feasibility of the hybrid multi-attribute three-way group decision-making method, which provides a systematic and standard solution for this kind of decision-making problem.

Interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering risk preference of decision-makers and its application

An improved interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering the risk preference of decision-makers is proposed to solve the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy numbers and the condition that the attribute weight information is completely unknown. Firstly, the decision-maker weight of each attribute is determined by combining similarity and proximity. In order to consider the influence of the decision-maker's risk preference on the decision result and avoid the asymptotic behavior of interval-valued intuitionistic fuzzy matrix, the risk aversion coefficient of the decision-maker is introduced and combined with the determined decision-maker's weight aggregation to form a group decision matrix. Then, the information of group decision matrix is mined, and the interval-valued intuitionistic fuzzy entropy is used to determine the attribute weight and relative weight. Based on the interval-valued intuitionistic fuzzy distance measure formula and the TODIM method, the overall superiority of each scheme relative to other schemes is obtained by calculating the superiority between schemes, and the optimal scheme is determined by comparing and sequencing. Finally, the rationality and effectiveness of the proposed method are verified by an example of mechanical assembly supplier selection decision.

Evaluation on the Risk of Water Inrush Due to Roof Bed Separation Based on Improved Set Pair Analysis-Variable Fuzzy Sets.

To study and prevent bed separation water inrush accidents in coal mines, it is necessary to evaluate the risk according to the limited geological data correctly. In this work, based on hydrogeological and mining conditions, we established a risk evaluation model and selected seven important factors, including the aquifer thickness, aquifer water abundance, hydraulic pressure of the aquifer, effective aquifuge thickness, mining failure ratio, mining height of the working face, and advancing distance as evaluation indexes. The intuitionistic fuzzy analytic hierarchy process (IFAHP) and entropy weight method (EWM) were used to analyze the weights of the original data, and the minimum information entropy principle was used to further integrate the abovementioned calculation results. With the weight results, set pair analysis–variable fuzzy set (SPA-VFS) theory was applied to determine the risk grade of each working face, which provided scientific guidance for the safe mining of coal mines. For the working face where water inrush may occur, the risk of bed separation water inrush can be reduced by optimizing the parameters or changing the mining conditions through the model analysis.

Improved Intuitionistic Fuzzy Entropy and Its Application in the Evaluation of Regional Collaborative Innovation Capability

Intuitionistic fuzzy entropy is an important concept to describe the uncertainty of intuitionistic fuzzy sets (IFSs). To fully measure the fuzziness of IFSs, this paper comprehensively considers the deviation between membership and non-membership and the influence of hesitation, constructs the general expression of intuitionistic fuzzy entropy based on special functions, and proves some of its major properties. Then, it is verified that some existing intuitionistic fuzzy entropies can be constructed by specific functions. Finally, based on a specific parametric intuitionistic fuzzy entropy, this paper applies it to evaluate the regional collaborative innovation capability, to verify the feasibility and practicability of the entropy. In addition, the effectiveness and practicability of this entropy in decision making are further illustrated by comparing it with other entropy measures.

Contingency response decision of network public opinion emergencies based on intuitionistic fuzzy entropy and preference information of decision makers

A multi-attribute group decision-making (MAGDM) method based on intuitionistic fuzzy preference information is proposed for the multi-attribute intuitionistic fuzzy group decision-making problem where the decision-makers weight and attribute weight are completely unknown and the decision-maker has preference information for the scheme. Firstly, an intuitionistic fuzzy interval judgment matrix is established to describe the original data of the key decision indicators for multiple network public opinion emergencies that erupt simultaneously. Secondly, the attribute weights are determined based on the improved intuitionistic fuzzy entropy construction method, and the expert weights are determined by using objective decision information, taking into account the intuitionistic fuzzy entropy of decision matrix. MAGDM can not only synthesize experts' professional experience in different aspects, but also avoid experts' decision-making errors caused by insufficient domain knowledge. It is necessary to continuously adjust the expert weight based on decision-making information to make the comprehensive decision-making information more accurate. Thirdly, a scheme preference model and an attribute weight optimization model are established to determine the ranking method of intuitionistic fuzzy interval values. Then, a modified distance measure of intuitionistic fuzzy sets (IFSs) is introduced to make the evaluation result more accurate and reasonable when it comes to solving the deviation between the evaluation value and ideal solution of each scheme. Finally, the effectiveness and practicability of the proposed decision-making method are verified by an example of emergency crisis severity, It assists decision makers in selecting and implementing the optimal emergency response plan in a timely and efficient manner, which improves the emergency treatment efficiency of network public opinion crisis, helps emergency departments to better deal with the network public opinion crisis, improves the ability of public opinion guidance and control, and provides a new method and idea for multi-attribute intuitionistic fuzzy group decision-making problem.

An Intelligent Expert Combination Weighting Scheme for Group Decision Making in Railway Reconstruction

The intuitionistic fuzzy entropy has been widely used in measuring the uncertainty of intuitionistic fuzzy sets. In view of some counterintuitive phenomena of the existing intuitionistic fuzzy entropies, this article proposes an improved intuitionistic fuzzy entropy based on the cotangent function, which not only considers the deviation between membership and non-membership, but also expresses the hesitancy degree of decision makers. The analyses and comparison of the data show that the improved entropy is reasonable. Then, a new IF similarity measure whose value is an IF number is proposed. The intuitionistic fuzzy entropy and similarity measure are applied to the study of the expert weight in group decision making. Based on the research of the existing expert clustering and weighting methods, we summarize an intelligent expert combination weighting scheme. Through the new intuitionistic fuzzy similarity, the decision matrix is transformed into a similarity matrix, and through the analysis of threshold change rate and the design of risk parameters, reasonable expert clustering results are obtained. On this basis, each category is weighted; the experts in the category are weighted by entropy weight theory, and the total weight of experts is determined by synthesizing the two weights. This scheme provides a new method in determining the weight of experts objectively and reasonably. Finally, the method is applied to the evaluation of railway reconstruction scheme, and an example shows the feasibility of the method.

Entropy on Intuitionistic Fuzzy Sets and Hesitant Fuzzy Sets

Since the sufficient conditions for the maximum value of the intuitionistic fuzzy entropy are not unified and the hesitant fuzzy entropy cannot be compared when the lengths of the hesitation fuzzy elements are not equal, improved axiomatic definitions of intuitionistic fuzzy entropy and hesitant fuzzy entropy are proposed, and new intuitionistic fuzzy entropy and hesitant fuzzy entropy based on the improved axiomatic definitions are established. This paper defines the fuzzy entropy that satisfies the properties based on the axiomatized definition of fuzzy entropy and, based on the fuzzy entropy, defines new intuitionistic fuzzy entropy and hesitant fuzzy entropy, so that the three are unified in form. The validity and rationality of the proposed intuitionistic fuzzy entropy and hesitant fuzzy entropy are verified by analysis.

INTERVAL-VALUED INTUITIONISTIC FUZZY TOPSIS-BASED MODEL FOR TROUBLESHOOTING MARINE DIESEL ENGINE AUXILIARY SYSTEM

In this paper, we present an interval-valued Intuitionistic Fuzzy TOPSIS model, which is based on an improved score function for detecting failure in a marine diesel engine auxiliary system, using groups of experts’ opinions to detect the root cause of failure in the engine system and the area most affected by failures in the diesel engine. The improved score function has been used for the computation of the separation measures from the intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) of alternatives while the criteria weight have been determined using an intuitionistic fuzzy entropy. The study is aimed at providing an alternative method for the identification and analysis of failure modes in engine systems. The results from the study show that although detection of failures in Engines is quite difficult to identify due to the dependency of the engine systems on each other, however using intuitionistic fuzzy multi-criteria decision-making method the faults/failure can easily be diagnosed.

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making.

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

Infrared and visible image fusion method based on compound decomposition and intuitionistic fuzzy set

To overcome the shortcomings of traditional image fusion algorithms based on multiscale transform, an infrared and visible image fusion method based on compound decomposition and intuitionistic fuzzy set is proposed. Firstly, the non-subsampled contour transform is used to decompose the source image into low-frequency coefficients and high-frequency coefficients. Then the potential low-rank representation model is used to decompose low-frequency coefficients into basic sub-bands and salient sub-bands, in which the visual saliency map is taken as weighted coefficient. The weighted summation of low-frequency basic sub-bands is used as the fusion rule. The maximum absolute value of low-frequency salient sub-bands is also used as the fusion rule. The two fusion rules are superimposed to obtain low-frequency fusion coefficients. The intuitionistic fuzzy entropy is used as the fusion rule to measure the texture information and edge information of high-frequency coefficients. Finally, the infrared visible fusion image is obtained with the non-subsampled contour inverse transform. The comparison results on the objective and subjective evaluation of several sets of fusion images show that our image fusion method can effectively keep edge information and rich information on source images, thus producing better visual quality and objective evaluation than other image fusion methods.

INTUITIONISTIC FUZZY ENTROPY AND ITS APPLICATIONS TO MULTICRITERIA DECISION MAKING WITH IF-TODIM

The intuitionistic fuzzy entropy (IFE) is being used to measure the degree of uncertainty of a fuzzy set (FS) with alarming accuracy and precision more accurately than the fuzzy set theory. Entropy plays a very important role in managing the complex issues efficiently which we often face in our daily life. In this paper, we first review several existing entropy measures of intuitionistic fuzzy sets (IFSs) and then suggest two new entropies of IFSs better than the existing ones. To show the efficiency of proposed entropy measures over existing ones, we conduct a numerical comparison analysis. Our entropy methods are not only showing better performance but also handle those IFSs amicably which the existing method fails to manage. To show the practical applicability and reliability, we utilize our methods to build intuitionistic fuzzy Portuguese of interactive and multicriteria decision making (IF-TODIM) method. The numerical results show that the suggested entropies are convenient and reasonable in handling vague and ambiguous information close to daily life matters.

Cold chain vulnerability assessment through two-stage grey comprehensive measurement of intuitionistic fuzzy entropy

PurposeThis study aims to investigate the vulnerability of cold chain logistics through a comprehensive assessment and provide targeted control measures.Design/methodology/approachThe index system of the cold chain vulnerability assessment was established with knowledge obtained from three different dimensions, namely, exposure, sensitivity and adaptability. The final index weight was determined through combination of the intuitionistic fuzzy (IF) entropy and compromise ratio approaches, followed by the comprehensive vulnerability assessment through the two-stage grey comprehensive measurement model. The feasibility and effectiveness of the proposed method were verified by evaluation with SF, HNA, China Merchants and COFCO as target examples.FindingsThe results revealed that the most influential factors in the cold chain vulnerability problem were the temperature reaching the standard, as well as the storage and preservation levels; through their analysis combined with the overall cold chain vulnerability assessment, the targeted control measures were obtained.Originality/valueBased on the research perspective of cold chain vulnerability assessment, a novel assessment model of cold chain logistics vulnerability was proposed, which is based on IF entropy two-stage grey comprehensive measurement. It provides more powerful theoretical support to improve the quality management of cold chain products.

Multi-Criteria Decision-Making Model using Intuitionistic Fuzzy Entropy and Variable Weight Theory

The aim of this research is to develop a new multi-criteria decision-making method that integrates an intuitionistic fuzzy entropy measure and variable weight theory to be implemented in different fields to provide a solution for MCDM problems when the available information is incomplete. A limited number of studies have considered determining decision maker’s weights by performing objective techniques, and almost all of these researches detected a constant weights for the decision makers. In addition, most of the MCDM studies were not formulated to perform sensitivity analysis. The new method is based on the TOPSIS model with an intuitionistic fuzzy entropy measure in the exponential-related function form and the engagement of the variable weight theory to determine weights for the decision-makers that vary as per attibutes. Lastly, a mathematical model was developed in this research to be as an input for developing the mobile-aplication based method in future for virtual use of the new MCDM method.