Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further, we discuss some of their properties and give three numerical examples to illustrate our proposed method reasonable.

In this paper, newly de ned level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

Visual features extracted from images in content-based image retrieval systems are inherently ambiguous. Consequently, applying fuzzy sets for image indexing in image retrieval systems has improved efficiency. In this article, the intuitionistic fuzzy sets are used to enhance the performance of the Fuzzy Content-Based Image Retrieval (F-CBIR) system. To this aim, an Intuitionistic Fuzzy Content-Based Image Retrieval (IF-CBIR) is proposed by applying intuitionistic fuzzy generators on fuzzy sets. Due to the diversity of the intuitionistic fuzzy distance measure, several are assessed in IF-CBIR,in these assessments, the measure with higher performance is identified. Finally, the proposed IF-CBIR and the existing crisp CBIR and F-CBIR simulate on Corel 5K and Corel 10K databases. The results show that our proposed method has higher (10-15%) precision compared to the mentioned methods.

In this study, we present the ideas of logical entropy and logical conditional entropy for partitions in interval-valued intuitionistic fuzzy sets, and we establish their fundamental properties. First, we establish the definitions of logical entropy and logical conditional entropy, demonstrating their key characteristics and relationships. We then define logical mutual information and explore its properties, providing a comprehensive understanding of its behavior within the context of interval-valued intuitionistic fuzzy sets. Additionally, we propose the concept of logical divergence of states defined on interval-valued intuitionistic fuzzy sets and examine its properties in detail, including its application and implications for understanding state transitions within these fuzzy sets. Finally, we extend our study to dynamical systems, introducing the logical entropy of such systems when modeled with intervalvalued intuitionistic fuzzy sets. We present several results related to this extension, highlighting the applicability and relevance of logical entropy in analyzing and understanding the behavior of dynamical systems. Overall, this paper offers a thorough exploration of logical entropy, mutual information, and divergence within the framework of interval-valued intuitionistic fuzzy sets, providing new insights and potential applications in various fields.

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets. On the other hand it is a generalization of the fuzzy set pretopological operators introduced by Wenzhong and Kimfung.

The Intuitionistic Fuzzy Sets (IFSs) are generalizations of Zadeh’s fuzzy sets, in which the elements of the universe have apart from Zadeh’s membership and the degree of non-membership in [0, 1]. This paper studies applications of intuitionistic Fuzzy Sets (FS) to assessment and multi-criteria decision making, which are very useful when uncertainty characterizes the grades or parameters respectively assigned to the elements of the universal set. Applications to everyday life situations are also presented illustrating our results.

The objective of image fusion for medical images is to combine multiple images obtained from various sources into a single image suitable for better diagnosis. Most of the state-of-the-art image fusing technique is based on nonfuzzy sets, and the fused image so obtained lags with complementary information. Intuitionistic fuzzy sets (IFS) are determined to be more suitable for civilian, and medical image processing as more uncertainties are considered compared with fuzzy set theory. In this paper, an algorithm for effectively fusing multimodal medical images is presented. In the proposed method, images are initially converted into Yager’ s intuitionistic fuzzy complement images (YIFCIs), and a new objective function called intuitionistic fuzzy entropy (IFE) is employed to obtain the optimum value of the parameter in membership and non-membership functions. Next, the YIFCIs are compared using contrast visibility (CV) to construct a decision map (DM). DM is refined with consistency verification to create a fused image. Simulations on several pairs of multimodal medical images are performed and compared with the existing fusion methods, such as simple average, discrete cosine transform (DCT), redundant wavelet transform (RWT), intuitionistic fuzzy set, fuzzy transform and interval-valued intuitionistic fuzzy set (IVIFS). The superiority of the proposed method is presented and is justified. Fused image quality is also verified with various quality metrics, such as spatial frequency (SF), average gradient (AG), fusion symmetry (FS), edge information preservation (QAB=F ), entropy (E) and computation time (CoT).

Distance size, similarity size, and entropy size provide useful results for decision makers to make decisions about problems with uncertain data. The main focus of this research is to introduce a new measure for interval-valued intuitive fuzzy numbers. Many of the defined measures have shortcomings such as not being comprehensive, high volume of calculations and application in limited cases. Therefore, the main goal of this research is to introduce a measure of distance and similarity with a new and reduced approach for intuitive fuzzy numbers with a value interval. After presenting the structure and effective indicators in the proposed size, it can be seen that the amount of calculations is clearly reduced in the defined interval size. In addition, the proof that size properties hold for it is shown correctly. The presented size structure has the ability to be combined with the process related to multi-criteria decision making and medical diagnosis problems. For this purpose, while presenting hybrid algorithms, effective applications of it have been given by mentioning several prominent examples.

In this paper, the notions of single-valued intuitionistic neutrosophic sets and single-valued intuitionistic neutrosophic graphs are introduced. Also, the concepts of degree and total degree of a node in single-valued intuitionistic neutrosophic graphs are presented. Then the concepts of irregular single-valued intuitionistic neutrosophic graphs, highly irregular neutrosophic intuitionistic single-valued intuitionistic neutrosophic graphs and neighborly irregular single-valued intuitionistic neutrosophic graphs are expressed.