scholarly journals Intuitionistic Fuzzy Three-Way Decision Model Based on the Three-Way Granular Computing Method

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1068
Author(s):  
Xianwei Xin ◽  
Jihua Song ◽  
Weiming Peng
Keyword(s):  
Probability Distribution ◽  
Granular Computing ◽  
Coarse Grained ◽  
Uncertain Information ◽  
Advantages And Disadvantages ◽  
Model Based ◽  
Intuitionistic Fuzzy ◽  
Compatibility Relation ◽  
Computing Method ◽  
Decision Cost

Three-way decisions, as a general model for uncertain information processing and decisions, mainly utilize the threshold generated by the decision cost matrix to determine the decision category of the object. However, the determination of the threshold is usually accompanied by varying degrees of subjectivity. In addition, the potential symmetrical relationship between the advantages and disadvantages of the decision cost is also a problem worthy of attention. In this study, we propose a novel intuitionistic fuzzy three-way decision (IFTWD) model based on a three-way granular computing method. First, we present the calculation methods for the possibility of membership state and non-membership state, as well as prove the related properties. Furthermore, we investigate the object information granules, i.e., the fine-grained, medium-grained, and coarse-grained objects, by combining the state probability distribution and probability distribution. Then, for decision and evaluation issues, we define the superiority-compatibility relation and inferiority-compatibility relation for IFTWD model construction. In addition, we use the superiority degree and inferiority degree instead of the original thresholds and design a new method for evaluating decision cost. Finally, we focus on the algorithm research of the proposed model and present an empirical study of agricultural ecological investment in Hubei Province to demonstrate the effectiveness of our model.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

2020 ◽  
Vol 39 (3) ◽  
pp. 4427-4441
Author(s):  
Bin Xu
Keyword(s):  
Network Security ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computer Network ◽  
Information Aggregation ◽  
Security Evaluation ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Computer Network Security

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

An Optimized Logistic Regression Model Based on the Maximum Entropy Estimation Under the Hesitant Fuzzy Environment

2021 ◽  
pp. 1-25
Author(s):  
Chenyang Song ◽  
Liguo Wang ◽  
Zeshui Xu
Keyword(s):  
Logistic Regression ◽  
Regression Model ◽  
Maximum Entropy ◽  
Logistic Regression Model ◽  
Uncertain Information ◽  
Entropy Estimation ◽  
Model Based ◽  
Fuzzy Environment ◽  
Maximum Entropy Estimation ◽  
Specific Implementation

The logistic regression model is one of the most widely used classification models. In some practical situations, few samples and massive uncertain information bring more challenges to the application of the traditional logistic regression. This paper takes advantages of the hesitant fuzzy set (HFS) in depicting uncertain information and develops the logistic regression model under hesitant fuzzy environment. Considering the complexity and uncertainty in the application of this logistic regression, the concept of hesitant fuzzy information flow (HFIF) and the correlation coefficient between HFSs are introduced to determine the main factors. In order to better manage situations with small samples, a new optimized method based on the maximum entropy estimation is also proposed to determine the parameters. Then the Levenberg–Marquardt Algorithm (LMA) under hesitant fuzzy environment is developed to solve the parameter estimation problem with fewer samples and uncertain information in the logistic regression model. A specific implementation process for the optimized logistic regression model based on the maximum entropy estimation under the hesitant fuzzy environment is also provided. Moreover, we apply the proposed model to the prediction problem of Emergency Extreme Air Pollution Event (EEAPE). A comparative analysis and a sensitivity analysis are further conducted to illustrate the advantages of the optimized logistic regression model under hesitant fuzzy environment.

Novel Similarity Measures, Entropy of Intuitionistic Fuzzy Sets and their Application in Software Quality Evaluation

2021 ◽  
Author(s):  
Xuan Thao Nguyen ◽  
Shuo Yan Chou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Uncertain Information ◽  
Membership Functions ◽  
Software Projects ◽  
Intuitionistic Fuzzy ◽  
Software Quality Evaluation

Abstract Intuitionistic fuzzy sets (IFSs), including member and nonmember functions, have many applications in managing uncertain information. The similarity measures of IFSs proposed to represent the similarity between different types of sensitive fuzzy information. However, some existing similarity measures do not meet the axioms of similarity. Moreover, in some cases, they could not be applied appropriately. In this study, we proposed some novel similarity measures of IFSs constructed by combining the exponential function of membership functions and the negative function of non-membership functions. In this paper, we also proposed a new entropy measure as a stepping stone to calculate the weights of the criteria in the proposed multi-criteria decision making (MCDM) model. The similarity measures used to rank alternatives in the model. Finally, we used this MCDM model to evaluate the quality of software projects.

A Multi-Criteria Intuitionistic Fuzzy Group Decision Making Method for Supplier Selection with VIKOR Method

2012 ◽  
pp. 967-983
Author(s):  
Razieh Roostaee ◽  
Mohammad Izadikhah ◽  
Farhad Hosseinzadeh Lotfi ◽  
Mohsen Rostamy-Malkhalifeh
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Supplier Selection ◽  
Group Decision ◽  
Decision Makers ◽  
Uncertain Information ◽  
Vikor Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Right

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain, and is typically a multi-criteria group decision problem. In many practical situations, there usually exists incomplete and uncertain information, and the decision makers cannot easily express their judgments on the candidates with exact and crisp values. Therefore, in this paper an extended VIKOR method for group decision making with intuitionistic fuzzy numbers is proposed to solve the supplier selection problem under incomplete and uncertain information environment. In other researches in this area, the weights of each decision makers and in many of them the weights of criteria are pre-determined, but these weights have been calculated in this paper by using the decision matrix of each decision maker. Also, normalized Hamming distance is proposed to calculate the distance between intuitionistic fuzzy numbers. Finally, a numerical example for supplier selection is given to clarify the main results developed in this paper.

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