Fermatean fuzzy sets and their variants
Vishnu Narayan Mishra; Tarun Kumar; Mukesh Kumar Sharma; Laxmi Rathour
Abstract
This paper aims to study Pythagorean and Fermatean Fuzzy Subgroups (FFSG) in the context of -norm and -conorm functions. The paper examines the extensions of fuzzy subgroups, specifically "Pythagorean Fuzzy Subgroups (PFSG)" and "FFSG", along with their properties. In the existing literature ...
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This paper aims to study Pythagorean and Fermatean Fuzzy Subgroups (FFSG) in the context of -norm and -conorm functions. The paper examines the extensions of fuzzy subgroups, specifically "Pythagorean Fuzzy Subgroups (PFSG)" and "FFSG", along with their properties. In the existing literature on Pythagorean and FFSG, the standard properties for membership and non-membership functions are based on the "min" and "max" operations, respectively. However, in this work, we develop a theory that utilizes the -norm for "min" and the -conorm for "max", providing definitions of Pythagorean and FFSG with these functions, along with relevant examples. By incorporating this approach, we introduce multiple options for selecting the minimum and maximum values. Additionally, we prove several results related to Pythagorean and FFSG using the -norm and -conorm, and discuss important properties associated with them.
Type-2 fuzzy sets and their variants
Mahmut Dirik
Abstract
In this study, a hybrid model for prediction issues based on IT2FLS and Particle Swarm Optimization (PSO) is proposed. The main contribution of this work is to discover the ideal strategy for creating an optimal value vector to optimize the membership function of the fuzzy controller. It should be emphasized ...
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In this study, a hybrid model for prediction issues based on IT2FLS and Particle Swarm Optimization (PSO) is proposed. The main contribution of this work is to discover the ideal strategy for creating an optimal value vector to optimize the membership function of the fuzzy controller. It should be emphasized that the optimized fuzzy controller is a type-2 interval fuzzy controller, which is better than a type-1 fuzzy controller in handling uncertainty. The limiting membership functions of the type-2 fuzzy set domain is type-1 fuzzy sets, which explains the trace of uncertainty in this situation. The proposed optimization strategy was tested using ECG signal data. The accuracy of the proposed IT2FLS_PSO estimation technique was evaluated using a number of performance metrics (MSE, RMSE, error mean, error STD). RMSE and MSE with IT2FI were calculated as 0.1183 and 0.0535, respectively. With IT2FISPSO, these values were calculated as 0.0140 and 0.0029, respectively. The proposed PSO-optimized IT2FIS controller significantly improved its performance under various operating conditions. The simulation results show that PSO is effective in designing optimal type 2 fuzzy controllers. The experimental results show that the proposed optimization strategy significantly improves the prediction accuracy.
Intuitionistic fuzzy sets and their variants
Jaydip Bhattacharya
Abstract
An operator is a special symbol for performing a specific function. Several operators like modal operators, topological operators, level operators, etc. have been defined over intuitionistic fuzzy sets. At the same time, so many operations were introduced and studied. The key objective of this paper ...
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An operator is a special symbol for performing a specific function. Several operators like modal operators, topological operators, level operators, etc. have been defined over intuitionistic fuzzy sets. At the same time, so many operations were introduced and studied. The key objective of this paper is to study those operations over intuitionistic fuzzy sets and to investigate their properties. Some new results are obtained and proved.
Neutrosophic sets and their variants
Mamoni Dhar
Abstract
In real life situations, there are many issues in which we face uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant ...
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In real life situations, there are many issues in which we face uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets and neutrosophic soft matrices theory which are very useful and applicable in various situations involving uncertainties and imprecisions. Thereafter our intention is to find a new method for constructing a decision matrix using neutrosophic soft matrices as an application of the theory. A neutrosophic soft matrix based algorithm is considered to solve some problems in the diagnosis of a disease from the occurrence of various symptoms in patients. This article deals with patient-symptoms and symptoms-disease neutrosophic soft matrices. To come to a decision, a score matrix is defined where multiplication based on max-min operation and complementation of neutrosophic soft matrices are taken into considerations.
Fuzzy sets and their variants
Mehrdad Rasoulzadeh; Mohammad Fallah
Abstract
A combination of projects, assets, programs, and other components put together in a set is called a portfolio. Arranging these components helps to facilitate the efficient management of the set and subsequently leads to achieving the strategic goals. Generally, the components of the portfolio are quantifiable ...
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A combination of projects, assets, programs, and other components put together in a set is called a portfolio. Arranging these components helps to facilitate the efficient management of the set and subsequently leads to achieving the strategic goals. Generally, the components of the portfolio are quantifiable and measurable which makes it possible for management to manage, prioritize, and measure different portfolios. In recent years, the portfolio in various sectors of economics, management, industry, and especially project management has been widely applied and numerous researches have been done based on mathematical models to choose the best portfolio. Among the various mathematical models, the application of data envelopment analysis models due to the unique features as well as the capability of ranking and evaluating performances has been taken by some researchers into account. In this regard, several articles have been written on selecting the best portfolio in various fields, including selecting the best stocks portfolio, selecting the best projects, portfolio of manufactured products, portfolio of patents, selecting the portfolio of assets and liabilities, etc. After presenting the Markowitz mean-variance model for portfolio optimization, these pieces of research have witnessed significant changes. Moreover, after the presentation of the fuzzy set theory by Professor Lotfizadeh, despite the ambiguities in the selection of multiple portfolios, a wide range of applications in portfolio optimization was created by combining mathematical models of portfolio optimization.
