Intuitionistic Fuzzy Soft Matrix Research Articles

Group Decision-Making Method with Incomplete Intuitionistic Fuzzy Soft Information for Medical Diagnosis Model

The medical diagnosis of many critical diseases is difficult as it usually requires the combined effort of several doctors. At this time, the process of medical diagnosis is actually a group decision-making (GDM) problem. In group medical diagnosis, considering doctors’ weight information and fusing the interaction relation of symptoms remain open issues. To address this problem, a group decision-making method for intuitionistic fuzzy soft environments is proposed for medical diagnosis because the intuitionistic fuzzy soft set (IFSS) integrates the advantages of the soft set and intuitionistic fuzzy set (IFS). Intuitionistic fuzzy soft weighted Muirhead mean operators are constructed by combining Einstein operations with the Muirhead mean (MM) operator, and some properties and results are revealed. A group medical diagnosis model with unknown doctor weight information and incomplete intuitionistic fuzzy soft information is proposed. Similarity measures of the intuitionistic fuzzy soft matrix (IFSM) given by the doctors are used to estimate the incomplete information. To take into account the advantages of objective weight and subjective weight, the combined weights of doctors are calculated based on the IFSMs’ similarity measure and doctors’ grades. The developed operators are then used to combine the evaluation information and handle the correlation of input arguments in the group medical diagnosis process. Finally, a numerical problem is selected to illustrate the superiority of the proposed approach compared to related methods. The combined weights are determined to overcome the shortcomings of the single-weight method to some extent. Meanwhile, the proposed method is more comprehensive, and can provide more flexible and reasonable choices for group medical diagnosis problems.

Estimation of missing data in intuitionistic fuzzy soft matrix (IFSM) with application in MCDM

The theory of fuzzy soft as well as intuitionistic soft set generally depends on complete information. But there are situations in which the complete information is not available due to various different reasons like data erroneous, in sufficiency of data, lacking of evidence and illegibility of data. Missing data restrict fuzzy soft matrix and intuitionistic fuzzy soft matrix and that causes more ambiguous uncertainty in the process of decision making. Thus, estimation of incomplete information data plays an important role in multi criteria decision making process which has been developed recently. Here, a novel method of missing data estimation in intuitionistic fuzzy soft matrix is described. Firstly, we estimate the missing values using the information given in data. After estimation the missing values in IFSM thus obtained is applied in a multi-criteria decision-making problem with illustration by an example.

SIFAT-SIFAT MATRIKS LUNAK FUZZY INTUISIONISTIK

Fuzzy soft sets is one of the mathematical tools that are used to deal with the problem of uncertainty, such as problems in the field of economic, health, and others. The concept of fuzzy soft sets is extended into intuitiononistic fuzzy soft sets to intuitiononistic fuzzy soft matrices. This article examines the intuitionistic fuzzy soft matrix and defines the various types and operations of the intuitionistic fuzzy soft matrix. In addition, the application of an intuitionistic fuzzy soft matrix is ​​given to decision-making problems such as the selection of swimming athletes who have the best swimming techniques.

A novel intuitionistic fuzzy soft set based colonogram enhancement for polyps localization

AbstractThis article represents a colonogram enhancement approach using intuitionistic fuzzy set (IFS) and fuzzy soft set (FSS) to improve the visual quality and highlight the local details in enhanced images without artifacts. The proposed method has the advantages of IFSs and fuzzy soft sets (FSSs) which can deal with gray‐level ambiguity in colonoscopy images. The combination of IFS and FSS works on intricate color variations with an adaptive parametric maps. First, the S‐membership function has been applied on the images to map into intuitionistic fuzzy space. We obtain intuitionistic fuzzy image from source image followed by decomposition of several blocks. Thereafter, the FSS is employed to get subsequent intuitionistic fuzzy soft matrix from individual image block. The FSS utilizes a class of parametric coefficients to obtain the hesitant score of individual pixels in each block through the soft‐score measure (SSM). Finally, the proposed method intensifies each membership degree in all blocks in the fuzzy plane using SSM and achieves an enhanced colonogram via defuzzification. Extensive experiment involving large data sets shows that the designed method exhibits better performance in contrast enhancement and visual quality improvement of colonograms for malformation detection (such as a polyps, malignant precancerous cells) in comparison with the state‐of‐art methods.

Colonoscopy contrast-enhanced by intuitionistic fuzzy soft sets for polyp cancer localization

Medical images often suffer from low contrast, irregular gray-level spacing and contain a lot of uncertainties due to constraints of imaging devices and environment (various lighting conditions) when capturing images. In order to achieve any clinical-diagnosis method for medical imaging with better comprehensibility, image contrast enhancement algorithms would be appropriate to improve the visual quality of medical images. In this paper, an automated image enhancement method is presented for colonoscopy images based on the intuitionistic fuzzy soft set. The fuzzy soft set is used to model the intuitionistic fuzzy soft image matrix based on a set of soft features of the colonoscopy images. The technique decomposes the fuzzy image into multiple blocks and estimates a soft-score based on an adaptive soft parametric hesitancy map by using the hesitant entropy for each block to quantify the uncertainties. In the processing stage, an adaptive intensity modification process is done for each block according to its soft-score. These scores are accurately addressed the gray-level ambiguities in colonoscopy images that lead to better results. Finally, the enhanced image achieved by performing a defuzzification together with all unprocessed blocks. Qualitative and quantitative assessments demonstrate that the proposed method improves image contrast and region-of-interest of polyps in colonogram. Experimental results on enhancing a large CVC-Clinic-DB and ASU-Mayo clinic colonoscopy benchmark datasets show that the proposed method outperforms the state-of-the-art medical image enhancement methods.

A Minimum Trust Discount Coefficient Model for Incomplete Information in Group Decision Making with Intuitionistic Fuzzy Soft Set

This article proposes a framework to deal with incomplete information in multiple criteria group decision making with intuitionistic fuzzy soft set. To do that, the weighted sum method for choice values and simple mathematical expectation method are extended to the case of obtained fuzzy soft set, and they are proved to have the same result in estimating the incomplete information. In order to reduce the system error in the estimating process cause by multiple decision information, a minimum trust discount coefficient model is established according to the relevant methods of evidence theory. Then, a new definition of entropy for intuitionistic fuzzy sets is introduced to determine the weights of group experts. Therefore, individual decision-making matrices are integrated into a comprehensive decision-making matrix by the integration operation formula of intuitionistic fuzzy soft matrix. The decision making is realized according to the difference of the score values of objects. Finally, the steps of this method are concluded, and one example is given to explain the application of this method.

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.

An Application of Intuitionistic Fuzzy Soft Matrix in Medical Diagnosis

An Application of Intuitionistic Fuzzy Soft Matrix in Medical Diagnosis

English

English

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 its Application in Human Life

Intuitionistic Fuzzy Soft Matrix Theory and its Application in Human Life

Group decision making in medical system: An intuitionistic fuzzy soft set approach

In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.

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.

Group Decision Making using Interval-Valued Intuitionistic Fuzzy Soft Matrix and Confident Weight of Experts

Abstract This article proposes an algorithmic approach for multiple attribute group decision making (MAGDM) problems using interval-valued intuitionistic fuzzy soft matrix (IVIFSM) and confident weight of experts. We propose a novel concept for assigning confident weights to the experts based on cardinals of interval-valued intuitionistic fuzzy soft sets (IVIFSSs). The confident weight is assigned to each of the experts based on their preferred attributes and opinions, which reduces the chances of biasness. Instead of using medical knowledgebase, the proposed algorithm mainly relies on the set of attributes preferred by the group of experts. To make the set of preferred attributes more important, we use combined choice matrix, which is combined with the individual IVIFSM to produce the corresponding product IVIFSM. This article uses IVIFSMs for representing the experts’ opinions. IVIFSM is the matrix representation of IVIFSS and IVIFSS is a natural combination of interval-valued intuitionistic fuzzy set (IVIFS) and soft set. Finally, the performance of the proposed algorithm is validated using a case study from real life

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.