MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

The concept of complex fuzzy set (CFS) and complex intuitionistic fuzzy set (CIFS) is two recent developments in the field of fuzzy set (FS) theory. The significance of these concepts lies in the fact that these concepts assigned membership grades from unit circle in plane, i.e., in the form of a complex number instead from [0, 1] interval. CFS cannot deal with information of yes and no type, while CIFS works only for a limited range of values. To deal with these kinds of problems, in this article, the concept of complex Pythagorean fuzzy set (CPFS) is developed. The novelty of CPFS lies in its larger range comparative to CFS and CIFS which is demonstrated numerically. It is discussed how a CFS and CIFS could be CPFS but not conversely. We investigated the very basic concepts of CPFSs and studied their properties. Furthermore, some distance measures for CPFSs are developed and their characteristics are studied. The viability of the proposed new distance measures in a building material recognition problem is also discussed. Finally, a comparative study of the proposed new work is established with pre-existing study and some advantages of CPFS are discussed over CFS and CIFS.

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On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems

As the extension of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, and picture fuzzy set, the spherical fuzzy set is characterized by three functions expressing the positive-membership degree, the neutral-membership degree and the negative-membership degree which the sum squares of them is equal or less than 1. In this work, we shall present some novel Dice similarity measures of spherical fuzzy sets and the generalized Dice similarity measures of spherical fuzzy sets and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision making models with spherical fuzzy information. Then, we apply the generalized Dice similarity measures between spherical fuzzy sets to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

https://informatica.vu.lt/journal/INFORMATICA/article/875/file/pdf

The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications

The principle of a complex interval-valued Pythagorean fuzzy set (CIVPFS) is a valuable procedure to manage inconsistent and awkward information genuine life troubles. The principle of CIVPFS is a mixture of the two separated theories such as complex fuzzy set and interval-valued Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real and unreal parts are the sub-interval of the unit interval. The superiority of the CIVPFS is that the sum of the square of the upper grade of the real part (also for an unreal part) of the duplet is restricted to the unit interval. The goal of this article is to explore the new principle of CIVPFS and its algebraic operational laws. By using the CIVPFSs, certain Einstein operational laws by using the t-norm and t-conorm are also developed. Additionally, we explore the complex interval-valued Pythagorean fuzzy Einstein weighted geometric (CIVPFEWG), complex interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (CIVPFEOWG) operators and utilized their special cases. Moreover, a multicriteria decision-making (MCDM) technique is explored based on the elaborated operators by using the complex interval-valued Pythagorean fuzzy (CIVPF) information. To determine the consistency and reliability of the elaborated operators, we illustrated certain examples by using the explored principles. Finally, to determine the supremacy and dominance of the explored theories, the comparative analysis and graphical expressions of the developed principles are also discussed.

/pdf/einstein-geometric-aggregation-operators-using-a-novel-1kha3pa9xr.pdf

Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management

Human opinion cannot be restricted to yes or no as depicted by conventional fuzzy set (FS) and intuitionistic fuzzy set (IFS) but it can be yes, abstain, no and refusal as explained by picture fuzzy set (PFS). In this article, the concept of spherical fuzzy set (SFS) and T-spherical fuzzy set (T-SFS) is introduced as a generalization of FS, IFS and PFS. The novelty of SFS and T-SFS is shown by examples and graphical comparison with early established concepts. Some operations of SFSs and T-SFSs along with spherical fuzzy relations are defined, and related results are conferred. Medical diagnostics and decision-making problem are discussed in the environment of SFSs and T-SFSs as practical applications.

An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets

The framework of T-spherical fuzzy set is a generalization of fuzzy set, intuitionistic fuzzy set and picture fuzzy set having a great potential of dealing with uncertain events with no limitation. A T-spherical fuzzy framework can deal with phenomena of more than yes or no type; for example, consider the scenario of voting where one’s voting interest is not limited to “in favor’’ or “against’’ rather there could be some sort of abstinence or refusal degree also. The objective of this paper is to develop some correlation coefficients for T-spherical fuzzy sets due to the non-applicability of correlations of intuitionistic fuzzy sets and picture fuzzy sets in some certain circumstances. The fitness of new correlation coefficients has been discussed, and their generalization is studied with the help of some results. Clustering and multi-attribute decision-making algorithms have been proposed in the environment of T-spherical fuzzy sets. To demonstrate the viability of proposed algorithms and correlation coefficients, two real-life problems including a clustering problem and a multi-attribute decision-making problem have been solved. A comparative study of the newly presented and pre-existing literature is established showing the superiority of proposed work over the existing theory. Some advantages of new correlation coefficients and drawbacks of the pre-existing work are demonstrated with the help of numerical examples.

Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making

In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed.

Kifayat Ullah

Papers

An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets

On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management

Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making

Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition