ENTROPY FOR INTUITIONISTIC FUZZY SETS BASED ON DISTANCE AND INTUITIONISTIC INDEX

2013 ◽  
Vol 21 (01) ◽  
pp. 139-155 ◽  
Author(s):  
HUIMIN ZHANG
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Future Research ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Basic Concepts

Many researchers have put forward lots of entropy and distance measures for intuitionistic fuzzy sets (IFSs). This paper firstly reviews some basic concepts for IFSs and several widely used distance measures between IFSs. And then a series of distance measures are presented on the basis of above widely used distance measures. Based on such distance measures and intuitionistic index, a set of entropies for IFSs are proposed and proved to meet the axiomatic requirements given by Szmidt and Kacprzyk in 2001. Besides, two numerical examples are demonstrated to verify the efficiency of the proposed entropies for IFSs. Finally, the paper concludes with suggestions for future research.

scholarly journals A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Debashree Guha ◽  
Debjani Chakraborty
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

scholarly journals A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Zhenhua Zhang ◽  
Min Wang ◽  
Yong Hu ◽  
Jingyu Yang ◽  
Youpei Ye ◽  
...  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Recognition Accuracy ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Simulation Results ◽  
Interval Valued

We present dynamic interval-valued intuitionistic fuzzy sets (DIVIFS), which can improve the recognition accuracy when they are applied to pattern recognition. By analyzing the degree of hesitancy, we propose some DIVIFS models from intuitionistic fuzzy sets (IFS) and interval-valued IFS (IVIFS). And then we present a novel ranking condition on the distance of IFS and IVIFS and introduce some distance measures of DIVIFS satisfying the ranking condition. Finally, a pattern recognition example applied to medical diagnosis decision making is given to demonstrate the application of DIVIFS and its distances. The simulation results show that the DIVIFS method is more comprehensive and flexible than the IFS method and the IVIFS method.

Extension of TOPSIS for Multiple Attribute Decision Making Using Intuitionistic Fuzzy Sets

2012 ◽  
Vol 433-440 ◽  
pp. 4053-4058 ◽  
Author(s):  
Yuan Yuan ◽  
Li Yang He
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quantitative Estimation ◽  
Ideal Point ◽  
Real Life ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

This electronic document is a “live” template. The various components of your paper [title, text, heads, etc.] are already defined on the style sheet, as illustrated by the portions given in this document. Due to the nature of vagueness inherent to real-life situations, some fuzzy data are deemed to suitable enough to describe the qualitative and/or quantitative estimation for decision making problems. Therefore, a new method for multiple attribute decision making under fuzzy environment is discussed, in which the attribute values take the form of intuitionistic fuzzy numbers. To overcome some disadvantages of existing distance measures like indiscrimination, counterintuitive results and difficulty of interpretation, we introduce a new class of distance for describing the deviation degrees between intuitionistic fuzzy sets. Furthermore, the measure of similarity degree for each alternative to ideal point is calculated through using the new proposed fuzzy distance. A model of TOPSIS is designed with the introduction of the particular closeness coefficient composed of similarity degrees. Then, we extend the TOPSIS method to aggregate the fuzzy information corresponding to each alternative, and rank the alternatives according to their closeness coefficients. Finally, an illustrative example is given to demonstrate the proposed approach practicality and effectiveness.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1147-1160
Author(s):  
Yali Cheng ◽  
Yonghong Li ◽  
Jie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Linguistic Intuitionistic Fuzzy Sets ◽  
Linguistic Scale Function ◽  
Different Response

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

scholarly journals On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Tanuj Kumar ◽  
Rakesh Kumar Bajaj
Keyword(s):  
Fuzzy Sets ◽  
Real Life ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

We introduce the concept of complex intuitionistic fuzzy soft sets which is parametric in nature. However, the theory of complex fuzzy sets and complex intuitionistic fuzzy sets are independent of the parametrization tools. Some real life problems, for example, multicriteria decision making problems, involve the parametrization tools. In order to get their new entropies, some important properties and operations on the complex intuitionistic fuzzy soft sets have also been discussed. On the basis of some well-known distance measures, some new distance measures for the complex intuitionistic fuzzy soft sets have also been obtained. Further, we have established correspondence between the proposed entropies and the distance measures of complex intuitionistic fuzzy soft sets.

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