Interval-valued Intuitionistic Fuzzy Entropy Research Articles

Green knowledge management capability assessment based on interval-valued intuitionistic Fuzzy EWM-TOPSIS-Sort-B

As an emerging concept in knowledge management (KM), green knowledge management plays a crucial role in the sustainable development of enterprises. A reasonable assessment of an enterprise’s green knowledge management capabilities can help the company effectively manage the embedded green knowledge within its operational processes, thereby achieving self-reinforcement of competitive advantages for the enterprise. Therefore, this paper proposes a multi-criteria classification method based on interval-valued intuitionistic fuzzy entropy weight method-TOPSIS-Sort-B (EWM-TOPSIS-Sort-B) to assess the green knowledge management capabilities of enterprises. In this method, expert assessments are expressed using interval-valued intuitionistic fuzzy sets. A new entropy weight method is introduced into TOPSIS-Sort-B to determine the weights of various evaluation indicators, and TOPSIS-Sort-B is employed to classify and rate each evaluation scheme. It is worth noting that this paper has improved the TOPSIS-Sort-B method by not converting interval-valued intuitionistic fuzzy sets into precise values throughout the entire evaluation process, thus avoiding information loss. Finally, we applied a case of knowledge management capability assessment to validate the proposed method, and conducted sensitivity analysis and comparative analysis on this approach. The analysis results indicate that variations in the parameter ϑ of the interval-valued intuitionistic fuzzy aggregation operator lead to changes in criterion weights and the comprehensive evaluation matrix, resulting in unordered changes in the final classification results. Due to the absence of transformation of interval values in this study, compared to the four classification methods of TOPSISort-L, the classification results are more detailed, and the evaluation levels are more pronounced.

Green Supplier Selection Based on Sequential Group Three-Way Decision Making

Environmental protection and sustainable development have become the consensus of all countries in the world. Enterprises must pay attention to the impact on the environment in their operations. Therefore, the selection of green suppliers has become a crucial issue for companies. Supplier selection is a dynamic and complex multi-attribute group decision-making process. The decision results have the tripartite characteristics of “accepted”, “rejected” and “pending further investigation”, and experts need to constantly negotiate in the decision-making process to achieve consensus. In view of the above characteristics, this study constructs a sequential group three-way decision making (TWDM) method to support green supplier selection. Firstly, we review the existing literature on the evaluation criteria and selection methods of green suppliers. In this process, we construct an evaluation attribution system including the following four aspects: product formation, service level, development capability, and green level. Secondly, combining with the sequential and group characteristics of decision making, we propose a multiple-attribute sequential group TWDM method based on a multi-level granularity structure. The weight of each decision maker is determined by his influence weight and interval-valued intuitionistic fuzzy entropy weight. The attribute weight is determined by entropy weight and subjective weight. By using the VIsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method improved by grey relation analysis (GRA), we calculate conditional probabilities. Since the cumulative prospect theory can reflect the risk attitude of decision makers, we apply it to calculate the decision thresholds. Finally, we apply a case of Q automobile manufacturer to verify the effectiveness, applicability and feasibility of the method. The innovation of this study is to construct social networks at each granularity level and introduce an expert information exchange model to promote group consensus. The sequential group TWDM method provides a new reference and idea for the selection of green suppliers.

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.

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.

Research on Interval-Valued Intuitionistic Fuzzy Multi-Attribute Decision Making Based on Projection Model

Background: Regarding the multi-attribute decision making where the decision information is the interval-valued intuitionistic fuzzy number and the attribute weight information is not completely determined. Methods: Intuitionistic fuzzy set theory introduces non-membership function, as an extension of the fuzzy set theory, it has certain advantages in solving complex decision-making problems. A projection model based interval-valued intuitionistic fuzzy multi-attribute decision-making scheme was proposed in this study. The objective weight of the attribute was obtained using improved intervalvalued intuitionistic fuzzy entropy, and thus the comprehensive weight of the attribute was obtained according to the preference information. Results: In the aspect of the decision-making matrix processing, the concept of interval-valued intuitionistic fuzzy ideal point and its related concepts were defined, the score vector of each scheme was calculated, the projection model was constructed to measure the similarity between each scheme and the interval-valued intuitionistic fuzzy ideal point, and the scheme was sorted according to the projection value. Conclusion: The efficiency and usability of the proposed approach are considered in the case study.

Humanitarian Rescue Scheme Selection under the Covid-19 Crisis in China: Based on Group Decision-Making Method

Humanitarian rescue has become an important part of government emergency management in China. In order to select the optimal humanitarian rescue scheme accurately and in a timely manner in an emergency, reduce the harm of disasters to human life and health, and improve the government’s emergency management ability, a multi-attribute emergency group decision-making method is proposed. First, interval-valued intuitionistic fuzzy sets are used to express the preferences of decision-makers, and interval-valued intuitionistic fuzzy entropy is used to calculate attribute weights. Then, based on the technique for order preference by similarity to an ideal solution (TOPSIS) method, the weight of the decision-maker is calculated. Then, the relevant interval intuitionistic fuzzy operators are used to summarize the preferences of decision-makers in group decision-making. Finally, we will use the closeness ranking method to choose the optimal scheme, and the feasibility and practicability of the proposed method are demonstrated by an example. The example shows that the model is more scientific, objective, and comprehensive in solving the problem of multi-attribute group decision-making than the traditional scheme selection, which only depends on the subjective discussion of decision-makers.

An Intelligent Group Decision Evaluation Model with Interval-Valued Intuitionistic Fuzzy Entropy Technology for Microblog User Influence

Aiming at the shortcomings of some existing interval-valued intuitionistic fuzzy entropy, this paper proposes an interval-valued intuitionistic fuzzy entropy, which contains not only the interval distance between membership and nonmembership but also the average hesitancy information. On this basis, the impact evaluation of microblog users is studied. Through the multilevel decomposition of user influence, the coverage of microblog, user interaction, and user activity are constructed as the first level indicators, and nine secondary indicators are selected as the comprehensive evaluation index system of microblog influence. Considering the highly dynamic and unstructured characteristics of social network data, the idea of interval-valued intuitionistic fuzzy is introduced to transform the evaluation of social network users’ influence into interval-valued intuitionistic fuzzy multiattribute group decision-making problem. Finally, the model is applied to dynamic evaluation of Sina Weibo users’ influence to verify the effectiveness of the model.

Extended CPT-TODIM method for interval-valued intuitionistic fuzzy MAGDM and its application to urban ecological risk assessment

The urban ecological risk assessment is a new research field, which has been rising and developing with the change of environment management objectives and environment conception. The urban ecological risk assessment could be regarded as a classical multi-attribute group decision making (MAGDM) issue. The interval-valued intuitionistic fuzzy set (IVIFS) can fully describe the uncertain information for the urban ecological risk assessment. Furthermore, the classical TODIM (an acronym in Portuguese for Interactive Multi-Criteria Decision Making) is built on cumulative prospect theory (CPT), which is a selectable method in reflecting the DMs’ psychological behavior. Thus, in this paper, the TODIM method based on the CPT is proposed for MAGDM issue under IVIFS. At the same time, it is enhancing rationality to get the weight information of attributes by using the interval-valued intuitionistic fuzzy entropy weight method. And focusing on hot issues in contemporary society, this article applies the discussed method to urban ecological risk assessment, and demonstrates urban ecological risk assessment model based on the proposed method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable.

The Novel Generalized Exponential Entropy for Intuitionistic Fuzzy Sets and Interval Valued Intuitionistic Fuzzy Sets

The purpose of this paper is to propose the novel generalized exponential intuitionistic fuzzy entropy (GIFE) and generalized exponential interval valued intuitionistic fuzzy entropy (GIVIFE) with interval area. First, we propose a novel GIFE. Then we compare the new GIFE with the existing intuitionistic fuzzy entropy (IFE) measures. Second, we define the interval area and the new axioms for the interval valued intuitionistic fuzzy entropy (IVIFE). Third, according to the newly defined axioms for the IVIFE, we use the interval area to construct the new GIVIFE. Finally, the advantages of the new generalized entropy measures are compared with the existing IVIFE measures by some examples. The two novel generalized exponential entropy measures can distinguish the special cases well. We have the conclusion that the two novel generalized entropy measures are reasonable and more flexible than the existing entropy.

Multi-perspective collaborative scheduling using extended genetic algorithm with interval-valued intuitionistic fuzzy entropy weight method

Scheduling multiple heterogeneous tasks in a manufacturing system to satisfy customized requirements becomes challenging, especially in uncertain manufacturing environment. In cloud manufacturing, a serious problem is to schedule multiple heterogeneous tasks to balance the benefit conflicts among customers, manufacturing enterprises, and manufacturing platform comprehensively. Therefore, this study formulates the multi-task scheduling problem mathematically as a new fuzzy mixed-integer linear programming (FMILP) model based on multi-perspective collaborative optimization and fuzzy set theory. To solve the FMILP model, an extended genetic algorithm (EGA) with the interval-valued intuitionistic fuzzy entropy weight (IVIFEW) method is proposed. The IVIFEW method is adapted to obtain the preference of QoS attributes and task priority. In addition, the basic genetic algorithm is improved by integrating a migration operator, local search, and restart strategy to maintain the diversity of population and enhance the exploitation ability. A suitable parameter combination of EGA is found in a series of experiments based on the Taguchi method. The experimental results demonstrate that the proposed EGA solves the FMILP model effectively, providing better optimal solutions compared with the baseline algorithms.

Generalised interval-valued intuitionistic fuzzy entropy with some similarity measures

Interval-valued intuitionistic fuzzy environment is appropriate for the most of the practical scenarios involving uncertainty, vagueness and insufficient information such as pattern recognition, medical diagnoses and decision making, etc. Entropy, similarity, distance, inclusion and cross entropy measures are few methods used for the measuring uncertainty and classifying interval-valued intuitionistic fuzzy sets. This paper presents the generalised entropy measure for the interval-valued intuitionistic fuzzy sets and relation is established that is used to define the generalised similarity measures using the proposed entropy measure. Further, the proposed entropy measure is compared with some existing measure of entropy with the help of an illustrative example and lastly we have demonstrated how the proposed measure can be used in decision making.

A threat assessment method of group targets based on interval-valued intuitionistic fuzzy multi-attribute group decision-making

Group target (GT) is consisted of multi-class weapons that can collaboratively work and it is a basic application unit in the information warfare. Assessing the threat of GT is required for the optimal decision of troop deployment. However, it is difficult to obtain a reasonable and effective threat assessment result of GT due to the uncertain battlefield information and different judgments from various decision makers (DMs). The study aims to investigate the multi-attribute group decision-making (MAGDM) method for solving the interval-valued intuitionistic fuzzy threat assessment problem of GTs without known attribute weights and DM’s preference weights. Based on the assessment information of DMs, attribute weights are determined with the interval-valued intuitionistic fuzzy entropy. To derive the DM’s preference weights objectively, we construct a nonlinear optimization model to minimize decision makers’ overall decision-making conflict. Moreover, the artificial bee colony algorithm is introduced to solve the nonlinear constrained optimization problem in the optimization model. The decision information of multi-DM is aggregated by the interval-valued intuitionistic fuzzy weighted averaging operator (IVIFWA) with the DMs’ preference weights. In order to describe the attribute closeness degree to the ideal solution, the decision-making judgment matrix is constructed according to the ideal solution closeness degree of each GT’s attribute calculated with the cross-entropy distance. Subsequently, based on the decision-making judgment matrix, the threat degree is calculated according to the weighted average method with the attribute weights. Finally, a case of the threat assessment of group targets is provided to illustrate the implementation process and applicability of the method proposed in this paper.

Compromise Ratio Method of MADM Problem Based on a New Interval-valued Intuitionistic Fuzzy Entropy

Compromise Ratio Method of MADM Problem Based on a New Interval-valued Intuitionistic Fuzzy Entropy

A New Type of Compositive Information Entropy for IvIFS and Its Applications

We first show the interval-valued intuitionistic fuzzy entropy which reflects intuitionism and fuzziness of interval-valued intuitionistic fuzzy set (IvIFS) based on interval-valued intuitionistic fuzzy cross-entropy. As for intuitionism and fuzziness of IvIFS, we propose interval-valued intuitionistic entropy and interval-valued fuzzy entropy, respectively. Furthermore, we establish the interval-valued span entropy describing the uncertainty of membership degree and nonmembership degree and show some concrete measure formulas. Combining intuitionistic factor, fuzzy factor, and span factor, we ultimately put forward the axiomatic definition of the compositive entropy and give a measure formula of compositive entropy. In addition, the effectiveness of the compositive entropy measure is illuminated by comparison with other entropy measures. Furthermore, the compositive entropy is applied to multiple attributes’ decision-making by using the weighted correlation coefficient between IvIFSs and pattern recognition by a similarity measure transformed from the compositive entropy.

An Improved Axiomatic Definition and Structural Formula of Interval-Valued Intuitionistic Fuzzy Entropy

In view of the defects of existing axiomatic definitions of interval-valued intuitionistic fuzzy entropy, an improved axiomatic definition of the interval-valued intuitionistic fuzzy entropy is presented and the corresponding formula is structured in the paper. Firstly, defects in three kinds of the axiomatic system of entropy of IVIFS are analyzed in detail respectively. New axiomatic entropy definition is proposed for the sake of more reasonable depiction of the fuzziness of IVIFS. Based on the new axiomatic entropy definition, a new computational formula is mentioned. Finally, an example is showed to illustrate the effectiveness of this new formula. Overall, the results indicate that the improved axiomatic definition and the new proposed formula are reasonable and effective.

An Effective Interval-Valued Intuitionistic Fuzzy Entropy to Evaluate Entrepreneurship Orientation of Online P2P Lending Platforms

This paper describes an approach to measure the entrepreneurship orientation of online P2P lending platforms. The limitations of existing methods for calculating entropy of interval-valued intuitionistic fuzzy sets (IVIFSs) are significantly improved by a new entropy measure of IVIFS considered in this paper, and then the essential properties of the proposed entropy are introduced. Moreover, an evaluation procedure is proposed to measure entrepreneurship orientation of online P2P lending platforms. Finally, a case is used to demonstrate the effectiveness of this method.

Interval-valued Intuitionistic Fuzzy Weighted Entropy in Evaluation of Service Quality

The importance of measuring service quality perceived by customers is an issue since the service quality is a key to success in service oriented industry. The estimation of service quality should be carried out with suitable measurement scales according to the types of service provided. To the best of authors’ knowledge, there have been little discussion about the applications of interval-valued intuitionistic fuzzy sets- based evaluation in measuring service quality. This paper proposes an evaluation for service quality of five vehicle insurance companies using interval-valued intuitionistic fuzzy entropy measure. Linguistic data were collected from customers using a questionnaire. An averaged interval-valued intuitionistic fuzzy number is used to construct decision matrix. Interval-valued intuitionistic fuzzy weighted averaging operator is used to aggregate the interval-valued intuitionistic fuzzy numbers for alternatives. It is found that PCF Insurance was evaluated as the best vehicle insurance company in providing service quality to customers DOI: http://dx.doi.org/10.11591/ij-ict.v2i1.1525