scholarly journals Four Distances for Circular Intuitionistic Fuzzy Sets

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1121
Author(s):  
Krassimir Atanassov ◽  
Evgeniy Marinov
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Intuitionistic Fuzzy ◽  
The Moment ◽  
Sets Theory ◽  
First Time

In the paper, for the first time, four distances for Circular Intuitionistic Fuzzy Sets (C-IFSs) are defined. These sets are extensions of the standard IFS that are extensions of Zadeh’s fuzzy sets. As it is shown, the distances for the C-IFS are different than those for the standard IFSs. At the moment, they do not have analogues in fuzzy sets theory. Examples, comparing the proposed distances, are given and some ideas for further research are formulated.

scholarly journals Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1

2021 ◽  
Vol 27 (1) ◽  
pp. 53-59
Author(s):  
Mladen V. Vassilev-Missana
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Membership Functions ◽  
Real Numbers ◽  
Intuitionistic Fuzzy ◽  
Sets Theory

The inequality \mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1 is introduced and proved, where \mu and \nu are real numbers, for which \mu, \nu \in [0, 1] and \mu + \nu \leq 1. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E. Also, a generalization of the above inequality for arbitrary n \geq 2 is proposed and proved.

scholarly journals A Generalized Interval Valued Intuitionistic Fuzzy Sets theory

2011 ◽  
Vol 15 ◽  
pp. 2037-2041 ◽  
Author(s):  
Zhang Zhenhua ◽  
Yang Jingyu ◽  
Ye Youpei ◽  
Zhang Qian Sheng
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Intuitionistic Fuzzy ◽  
Sets Theory ◽  
Interval Valued

scholarly journals Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2

2021 ◽  
Vol 27 (4) ◽  
pp. 78-81
Author(s):  
Mladen Vassilev-Missana
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Membership Functions ◽  
Intuitionistic Fuzzy ◽  
Sets Theory

In the paper, the inequality \frac{\mu^{\frac{1}{\nu}}}{\nu} + \frac{\nu^{\frac{1}{\mu}}}{\mu} \leq \frac{1}{2\mu\nu} - 1 is introduced and proved. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E.

Target Threat Assessment Based on Intuitionistic Fuzzy Sets Choquet Integral

2013 ◽  
Vol 433-435 ◽  
pp. 736-743 ◽  
Author(s):  
Jie Huang ◽  
Bi Cheng Li ◽  
Yong Jun Zhao
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Information Fusion ◽  
Choquet Integral ◽  
Threat Assessment ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Fuzzy Measures ◽  
Intuitionistic Fuzzy ◽  
Sets Theory

For the problem that threat assessment often has some uncertainty and the correlation exist among threat factors, a technique based on intuitionistic fuzzy sets Choquet integral is proposed with intuitionistic fuzzy sets and fuzzy integral being introduced into information fusion area. First, threat estimators based on different factors are constructed with intuitionistic fuzzy sets theory. The uncertainty of each estimator is represented with membership function and non-membership function. Then, the significances of the estimators are modeled with fuzzy measures. Subsequently, threat assessment results are obtained using Choquet integral. Finally, the proposed method is validated through the air combat threat assessment of 20 typical targets.

Image enhancement based on intuitionistic fuzzy sets theory

2016 ◽  
Vol 10 (10) ◽  
pp. 701-709 ◽  
Author(s):  
He Deng ◽  
Xianping Sun ◽  
Maili Liu ◽  
Chaohui Ye ◽  
Xin Zhou
Keyword(s):  
Fuzzy Sets ◽  
Image Enhancement ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Intuitionistic Fuzzy ◽  
Sets Theory
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