Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application

The FFS is an influential extension of the available IFS and PFS, whose benefit is to better exhaustively characterize ambiguous information. For FFSs, the correlation between them is usually evaluated by the correlation coefficient. To reflect the perspective of professionals, in this paper, a new correlation coefficient of FFSs is proposed and investigated. The correlation coefficient is very important and frequently used in every field from engineering to economics, from technology to science. In this paper, we propose a new correlation coefficient and weighted correlation coefficient formularization to evaluate the affair between two FFSs. A numerical example of diagnosis has been gotten to represent the efficiency of the presented approximation. Outcomes calculated by the presented approximation are compared with the available indices

Fuzzy models in regional statistics

Many regional data are not provided as precise numbers, but they are frequently non-precise (fuzzy). In order to provide realistic statistical information, the imprecision must be described quantitatively. This is possible using special fuzzy subsets of the set of real numbers ℝ, called fuzzy numbers, together with their characterising functions. In this study, the uncertainty of measured data is highlighted through an example of environmental data from a regional study. The generalised statistical methods, through the characterising function and the δ-cut, that are suitable for the situations of fuzzy uni- and multivariate data are described. In addition, useful generalised descriptive statistics and predictive models frequently applicable for analysis of fuzzy data in regional studies as well as the concept of fuzzy data in databases are presented

Fuzzy models in regional statistics

Many regional data are not provided as precise numbers, but they are frequently non-precise (fuzzy). In order to provide realistic statistical information, the imprecision must be described quantitatively. This is possible using special fuzzy subsets of the set of real numbers ℝ, called fuzzy numbers, together with their characterising functions. In this study, the uncertainty of measured data is highlighted through an example of environmental data from a regional study. The generalised statistical methods, through the characterising function and the δ-cut, that are suitable for the situations of fuzzy uni- and multivariate data are described. In addition, useful generalised descriptive statistics and predictive models frequently applicable for analysis of fuzzy data in regional studies as well as the concept of fuzzy data in databases are presented

Fuzzy correlation and regression analysis.

The first half of the dissertation focuses on the motivation and concept of fuzzy correlation. Fuzzy data will be formulated in a mathematical way, and then we will build models of two types of fuzzy correlations, their computation methods are also presented in this dissertation. For the first type of fuzzy correlation problem we proposed an approximate bound as well as a number of computationally efficient algorithms. Monte Carlo sampling method is used to compute the second type of fuzzy correlation problem. The results provided by the second type of fuzzy correlation are more informative than the result of the classical correlation.Some application examples are given at the end. Fuzzy regression models could be applied in short term stock price prediction. Intel Corp. 2003 stock price data are used in this demo. The Dosage-film response is estimated with a fuzzy regression model, this procedure is presented in detail in the last section. It is found that fuzzy regression gives more consistent results than the conventional regression model since it successfully models the inherent vagueness which exists in the application by formulated form.In the second part of the dissertation, eight fuzzy regression models are discussed. In order to enhance the central tendency and remove outliers which have important impact on the regression result, different techniques are used to improve the original model. The fuzzy regression method presented in this dissertation also applies to crisp data regression cases. Numerical examples are given for all the fuzzy correlation and fuzzy regression models we explored in this dissertation for illustration and verification purpose.Correlation and regression analysis are widely used in all kinds of data mining applications. However many real world data have the characteristic of vagueness; the classical data analysis techniques have limitation in managing this vagueness systematically. Fuzzy sets theory can be applied to model this kind of data. New concepts and methods of correlation and regression analysis for data with uncertainty are presented in this dissertation. Recently, fuzzy correlation and regression have been applied to many applications. Successful examples include quality control, marketing, image processing, robot control, medical diagnosis, etc. The purpose of this dissertation is to revisit the ongoing research work that people have already done on this issue and to develop some new models related to fuzzy data correlation and regression. In this dissertation, we define and conceptualize the correlation and regression concepts within the fuzzy context. Then the presently available methods are explored in light of their limitations. Then new concepts and new models are presented. Throughout this dissertation, a number of test data sets are used to verify how our ideas are implemented. Suggestions for further research will be provided

Fuzzy Sets in Business Management, Finance, and Economics

This book collects fifteen papers published in s Special Issue of Mathematics titled “Fuzzy Sets in Business Management, Finance, and Economics”, which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling. We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences