scholarly journals Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 215 ◽  
Author(s):  
Xiaoyan Liu ◽  
Hee Kim ◽  
Feng Feng ◽  
José Alcantud
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Averaging Operators ◽  
Intuitionistic Fuzzy ◽  
New Concepts ◽  
Practical Progress ◽  
Atanassov’S Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy Value

Atanassov’s intuitionistic fuzzy sets extend the notion of fuzzy sets. In addition to Zadeh’s membership function, a non-membership function is also considered. Intuitionistic fuzzy values play a crucial role in both theoretical and practical progress of intuitionistic fuzzy sets. This study introduces and explores various types of centroid transformations of intuitionistic fuzzy values. First, we present some new concepts for intuitionistic fuzzy values, including upper determinations, lower determinations, spectrum triangles, simple intuitionistic fuzzy averaging operators and simply weighted intuitionistic fuzzy averaging operators. With the aid of these notions, we construct centroid transformations, weighted centroid transformations, simple centroid transformations and simply weighted centroid transformations. We provide some basic characterizations regarding various types of centroid transformations, and show their difference using an illustrating example. Finally, we focus on simple centroid transformations and investigate the limit properties of simple centroid transformation sequences. Among other facts, we show that a simple centroid transformation sequence converges to the simple intuitionistic fuzzy average of the lower and upper determinations of the first intuitionistic fuzzy value in the sequence.

On averaging operators for Atanassov’s intuitionistic fuzzy sets

2011 ◽  
Vol 181 (6) ◽  
pp. 1116-1124 ◽  
Author(s):  
G. Beliakov ◽  
H. Bustince ◽  
D.P. Goswami ◽  
U.K. Mukherjee ◽  
N.R. Pal
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Averaging Operators ◽  
Intuitionistic Fuzzy ◽  
Atanassov’S Intuitionistic Fuzzy Sets

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

Introduction to Intuitionistic Fuzzy Multisets and Its Applications

2016 ◽  
pp. 43-52
Author(s):  
T. K. Shinoj ◽  
Sunil Jacob John
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Linguistic Variable ◽  
Human Reasoning ◽  
Collaborative Robots ◽  
Intuitionistic Fuzzy

In this chapter a new concept named Intuitionistic Fuzzy Multiset is introduced, which is an attempt to combine the two concepts: Intuitionistic Fuzzy sets and Fuzzy Multisets. The basic operations and their various properties are discussed. The authors discussed two significant applications of Intuitionistic Fuzzy Multisets. Most of human reasoning involves the use of variables whose values are fuzzy sets. This is the basis for the concept of a linguistic variable. But in some situations like decision making problems, the description by a linguistic variable in terms of membership function only is not adequate. There is chance of existing a non-null complement. There are situations that each element has different membership values. In such situations Intuitionistic Fuzzy Multisets is more adequate. Here the authors present Intuitionistic Fuzzy Multisets as a tool for reasoning such a situation through a medical diagnosis problem. As the second application, accuracy of Collaborative Robots using the concept of Intuitionistic Fuzzy Multiset is discussed.

Grey Intuitionistic Fuzzy Sets and its Application in Performance Evaluation of Image Fusion

2013 ◽  
Vol 753-755 ◽  
pp. 3033-3038
Author(s):  
Yong Bin You ◽  
Ting Ting Li
Keyword(s):  
Performance Evaluation ◽  
Image Fusion ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Subjective Evaluations ◽  
Correlation Degree ◽  
Objective Performance ◽  
Grey Correlation Degree

As an important branch of multi-sensor information fusion, image fusion has been applied in many areas. During the past years, many algorithms have been proposed to solve the fusion issue. However, research on the objective performance evaluation of image fusion is relatively less. Basic methods for image fusion evaluation usually include subjective evaluations and objective evaluations. The evaluation of fused images is regarded as multi-attribute decision-make problem, thus a novel synthesis approach using grey intuitionistic fuzzy sets is proposed. The proposed approach constructs the membership function and non-membership function by the grey correlation degree, thus the intuitionistic fuzzy sets are established. The results show that the proposed approach has better performance.

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