Intuitionistic Fuzzy Soft Matrices Research Articles

Distance and Similarity Measures of Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Matrices and Their Applications to Data Classification in Supervised Learning

Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices), proposed by Enginoğlu and Arslan in 2020, are worth utilizing in data classification in supervised learning due to coming into prominence with their ability to model decision-making problems. This study aims to define the concepts metrics, quasi-, semi-, and pseudo-metrics and similarities, quasi-, semi-, and pseudo-similarities over ifpifs-matrices; develop a new classifier by using them; and apply it to data classification. To this end, it develops a new classifier, i.e., Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Classifier (IFPIFSC), based on six pseudo-similarities proposed herein. Moreover, this study performs IFPIFSC’s simulations using 20 datasets provided in the UCI Machine Learning Repository and obtains its performance results via five performance metrics, accuracy (Acc), precision (Pre), recall (Rec), macro F-score (MacF), and micro F-score (MicF). It also compares the aforementioned results with those of 10 well-known fuzzy-based classifiers and 5 non-fuzzy-based classifiers. As a result, the mean Acc, Pre, Rec, MacF, and MicF results of IFPIFSC, in comparison with fuzzy-based classifiers, are 94.45%, 88.21%, 86.11%, 87.98%, and 89.62%, the best scores, respectively, and with non-fuzzy-based classifiers, are 94.34%, 88.02%, 85.86%, 87.65%, and 89.44%, the best scores, respectively. Later, this study conducts the statistical evaluations of the performance results using a non-parametric test (Friedman) and a post hoc test (Nemenyi). The critical diagrams of the Nemenyi test manifest the performance differences between the average rankings of IFPIFSC and 10 of the 15 are greater than the critical distance (4.0798). Consequently, IFPIFSC is a convenient method for data classification. Finally, to present opportunities for further research, this study discusses the applications of ifpifs-matrices for machine learning and how to improve IFPIFSC.

Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft matrices and their application to performance-based value assignment to noise-removal filters

Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft matrices and their application to performance-based value assignment to noise-removal filters

Generalisations of SDM Methods in fpfs-Matrices Space to Render Them Operable in ifpifs-Matrices Space and Their Application to Performance Ranking of the Noise-Removal Filters

Recently, the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) has allowed to mathematically model some problems in which the parameters and alternatives exhibit intuitionistic fuzzy uncertainties. To this end, the present study aims to generalise 24 soft decision-making (SDM) methods operating in the fuzzy parameterized fuzzy soft matrices space with a single fpfs-matrix to the ifpifs-matrices spaces. Afterwards, we propose five test scenarios to analyse whether the SDM methods constructed by ifpifs-matrices consistently work. Moreover, we make performance comparisons of the generalised SDM methods successful in the five test scenarios by applying them to the performance-based value assignment (PVA) problem of the well-known noise-removal filters. Finally, we discuss the need for further research.

Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making

This study aims to propose the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) and to present several of its basic properties. Therefore, it would be possible to improve the problem-modelling capabilities of the available intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets in the occurrence of a large number of data. Moreover, by using ifpifs-matrices, we suggest a new soft decision-making method, denoted by EA20, and apply it to a multi-criteria group decision-making (MCGDM) problem. We then compare the ranking performance of EA20 for five noise-removal filters with those of ten state-of-the-art soft decision-making methods. The results show that EA20 successfully models performance-based value assignment problems. Finally, we discuss ifpifs-matrices and EA20 for further research.

Application of Multi Intuitionistic Fuzzy Soft Matrices in Medical Diagnosis

Application of Multi Intuitionistic Fuzzy Soft Matrices in Medical Diagnosis

A Comprehensive Study of Intuitionistic Fuzzy Soft Matrices and its Applications in Selection of Laptop by using Score Function

A Comprehensive Study of Intuitionistic Fuzzy Soft Matrices and its Applications in Selection of Laptop by using Score Function

Application of Intuitionistic Fuzzy Soft Matrices for Disease Diagnosis

Decision Making is the best procedure to choose a superlative alternative from all feasible alternatives. Almost in all other issues, the overall number of criteria because decision making the general alternatives is pervasive. Nowadays decision making is a critical problem in every field of life. In some cases, we must deliberate membership unbiassed as the non- membership values for the suitable representation of an object in uncertain and indeterminate conditions that could not be handled by fuzzy sets nor by interval-valued fuzzy sets. To overcome these difficulties the notion of Intuitionistic fuzzy sets has been presented. In this paper, we study some basic concepts of fuzzy sets, soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic soft sets, intuitionistic fuzzy soft sets (IFSS), and intuitionistic fuzzy soft matrices (IFSM). Finally, in this research, we use the IFSM for disease diagnoses in patients who suffer from different diseases such as stomach ulcer and typhoid by using hypothetical data we conclude that patient p₂ suffering stomach ulcer p₂ and p₃ patients suffering from typhoid.

Generalized intuitionistic fuzzy soft matrices and their application

The purpose of this article is to define the generalized intuitionistic fuzzy soft matrices and to study their operations. Then we obtain some relevant properties of generalized intuitionistic fuzzy soft matrices. To apply the generalized intuitionistic fuzzy soft matrices for decision making problems solving, we define the Rate matrix, the Resultant matrix and the Goal matrix. Then by developing an algorithm, finally the decision is obtained based on the maximum score in the Goal matrix. This study is a generalization the concept of intuitionistic fuzzy soft matrices.

A Study on Matrices Using Interval Valued Intuitionistic Fuzzy Soft Set and Its Application in Predicting Election Results in India

Nowadays the concept of matrix is used widely in different fields such as engineering, medical, economics, game theory, geology, computer science etc. Matrices are also used in representing the real world data like the population of people, infant mortality rate etc. In economics very large matrices are used for optimization of problems. Matrices play an important role to represent different types of soft set in concise form by which we can easily perform algebraic operations on them. Classical matrices can’t represent all types of uncertainties present in daily life problems. To tackle those problems related to uncertainties fuzzy matrix is introduced in which every member belongs to the unit interval [0, 1]. By combining soft set and fuzzy matrix a new concept fuzzy soft matrix is introduced. Later it has been extended to intuitionistic fuzzy soft matrix, interval-valued fuzzy soft matrix, interval-valued intuitionistic fuzzy soft matrix etc. In this paper we give a brief discussion on different types of interval valued intuitionistic fuzzy soft matrices and apply some new matrix operations on them. Moreover a new methodology has been developed to solve interval valued intuitionistic fuzzy soft set based real life decision making problems which may contain more than one decision maker and put an effort to apply it to a more relevant way in predicting election results in India by using the concept of choice matrix.

Some Results of Intuitionistic Fuzzy Soft Matrix

The purpose of this article is to consider the notions of intuitionistic fuzzy soft matrices and some basic results. This work deals particularly with the definit ion of transpose of intuitionistic fu zzy soft matrices and then some properties of transpose of intuit ionistic fuzzy soft matrices are studied. After that symmet ric intuitionistic fu zzy matrices are also defined and some properties are discussed. Nu merical examp les are provided to make the concept clear. Index Terms—Fu zzy sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft matrices .

Study of Some Properties of Intuitionistic Fuzzy Soft Matrix

The purpose of this article is to consider the notions of intuitionistic fuzzy soft matrices(IFSM) and to study some basic results associated with such matrices. This work deals particularly with the definition and some properties of transpose of intuitionistic fuzzy soft matrices. In the process, symmetric intuitionistic fuzzy matrix is also defined and some properties are discussed. Numerical examples are provided to make the concept clear.

Intuitionistic Fuzzy Soft Matrix Theory and Multi Criteria in Decision Making Based on T-Norm Operators

The aim of this paper is to find multi criteria decision making problems to a selected project using intuitionistic fuzzy soft matrix based on generalized operators of t-norm and t-conorm. We use the concept of level operators of intuitionistic fuzzy sets ( K.T.Atanassov, On intuitionistic fuzzy sets theory , Springer - Verlag 2012 ) to define intuitionistic fuzzy soft level matrix. Finally, we give an application of decision making problem by using the operators of t-norm and t-conorm . intuitionistic fuzzy parameterized soft sets. They have also applied to the problems that contain uncertainties based on intuitionistic fuzzy parameterized soft sets. Chetia and Das (5) defined five types of products of intuitionistic fuzzy soft matrices . Babitha and John(11) described generalized intuitionistic fuzzy soft sets and solved multi criteria decision making problem in generalized intuitionistic fuzzy soft sets . Rajarajeswari and Dhanalakshmi(10) described intuitionistic fuzzy soft matrix with some traditional operations. In this paper , we will propose definition of intuitionistic fuzzy soft level matrix . We will also discuss their properties . Finally we will give an application of multi criteria decision making based on t- norm and t-conorm operators.

Application of Intuitionist Fuzzy Soft Matrices in Decision Making Problem by Using Medical Diagnosis

Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. In this paper, we proposed the definition of T-product of intuitionistic fuzzy soft matrices with examples. Finally, We extend our approach in application of these matrices in decision making problem, by using medical diagnosis. Keywords: Soft set, Fuzzy soft set(FSS), Fuzzy soft matrix, T-product of fuzzy soft matrix, Intuitionistic fuzzy soft set(IFSS), Intuitionistic fuzzy soft matrix.

Revised Max-Min Average Composition Method for Decision Making Using Intuitionistic Fuzzy Soft Matrix Theory

In this paper a revised Intuitionistic Fuzzy Max-Min Average Composition Method is proposed to construct the decision method for the selection of the professional students based on their skills by the recruiters using the operations of Intuitionistic Fuzzy Soft Matrices. In Shanmugasundaram et al. (2014), Intuitionistic Fuzzy Max-Min Average Composition Method was introduced and applied in Medical diagnosis problem. Sanchez’s approach (Sanchez (1979)) for decision making is studied and the concept is modified for the application of Intuitionistic fuzzy soft set theory. Through a survey, the opportunities and selection of the students with the help of Intuitionistic fuzzy soft matrix operations along with Intuitionistic fuzzy max-min average composition method is discussed.

Intuitionistic Fuzzy Soft Matrix Theory

The purpose of this paper is to put forward the notion of intuitionistic fuzzy soft matrix theory and some basic results. In this paper, we define intuitionistic fuzzy soft matrices and have introduced some new operators with weights, some properties and their proofs and examples which make theoretical studies in intuitionistic fuzzy soft matrix theory more functional. Moreover, we have given one example on weighted arithmetic mean for decision making problem.

Group decision making methods based on intuitionistic fuzzy soft matrices

Soft set theory was originally proposed by Molodtsov as a general mathematical tool for dealing with uncertainty in 1999. Recently, researches of decision making based on soft sets have got some progress, but few people consider multi-experts situation. As such, this paper discusses multi-experts group decision making problems. Firstly, we give a concept of intuitionistic fuzzy soft matrix (IFSM) and prove some relevant properties of IFSM. Then, an adjustable approach is presented by means of median level soft set and p-quantile level soft set for dealing with decision making problems based on IFSM. Thirdly, we study aggregation methods of IFSM, give two kinds of aggregation operators and methods that how to determine experts’ weights under different situation with programming models, four corresponding algorithms have been proposed, too. Finally, a practical example has been demonstrated the reasonability and efficiency of these new algorithms.