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.

Max-min Fuzzy and soft sets approach in constructing fuzzy soft matrix for medical decision-making during epidemics

In the realm of healthcare decision-making amid outbreaks, the application of vague and pliable collections has garnered noteworthy consideration owing to their capacity to manage unpredictability and vagueness. In this study, an exclusive methodology termed Maximum-Minimum-Fuzzy and Soft-Ensembles-Based Fuzzy Pliable Array (MMFSS-FPA) is proposed for healthcare decision-making during outbreaks. The recommended approach amalgamates the notions linked with both imprecise collections and pliable collections, and maximum-minimum operations to formulate a fuzzy pliable array that encapsulates the uncertainties linked with medical data. By taking into account the association values and resolution thresholds, the MMFSS-FPA eases the identification of optimum decisions in epidemic scenarios. The effectiveness of the proposed strategy is depicted through experimental assessment on genuine medical datasets. The findings reveal that the MMFSS-FPA approach attains precise and dependable decision-making with a triumph rate surpassing 90%, establishing it as a promising instrument for healthcare professionals in addressing outbreaks.

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.

Selection of best cipher system using fuzzy soft decision methodology

Selection of a most suitable cipher system among several such systems is an important problem of the customers which help to acquire a right cipher system for meeting the requirements of information security to safeguard the vital data. Any mistake in the selection of a right cipher system is very harmful as it may lead to compromise the security of vital information. In the paper, we propose a multi-criterion fuzzy soft decision making methodology to select one of the most suitable cipher system. Proposed methodology uses fuzzy soft set, fuzzy soft matrix, dominancy matrix and S-fuzzy set to compute score values and take a right decision. It exhibits out performance over existing methods as shown by explaining some examples. We apply proposed methodology in selecting a most suitable cipher system from a set of systems with respect to the choice of desired security attributes required by the customers.

Dimensionality reduction technique under picture fuzzy environment and its application in decision making

The notion of soft matrix plays a vital role in many engineering applications and socio-economic and financial problems. A picture fuzzy set has been used to handle uncertainty data in modeling human opinion. In this work, we recall the picture fuzzy soft matrix concept and its different subsequent classes. Also, different kinds of binary operations over the proposed matrices have been provided. The main contribution of this paper is that using the concept of choice matrix and its weighted form and the score matrix, a new algorithm for decision-making has been outlined by considering the picture of fuzzy soft matrices. The current challenge In the decision-making problems is that many qualitative and quantitative criteria are involved. Hence, the dimensionality reduction technique plays an essential role in simplicity and broader applicability in the decision-making processes. We present an algorithm for the reduction process using the proposed definitions of the object and parameter-oriented picture fuzzy soft matrix and the technique to find the threshold value for the provided information. Then, illustrative numerical examples have also been provided for each proposed algorithm. A detailed comparative study of the proposed techniques has also been carried out in contrast with other existing techniques.

Computational bipolar fuzzy soft matrices with applications in decision making problems

A fuzzy soft matrix is a type of mathematical matrix that combines the principles of fuzzy set theory and soft set theory. It is used to handle uncertainty and vagueness in decision-making problems. Fuzzy soft matrix theory cannot handle negative information. To overcome this difficulty, we define the notion of bipolar fuzzy soft (BFS) matrices and study their fundamental properties. We define products of BFS matrices and investigate some useful properties and results. We also give an application of bipolar fuzzy soft matrices to decision-making problems. We propose a decision-making algorithm based on computer programs under the environment of the bipolar fuzzy soft sets.

Estimating the Efficiency of Building Stones in Complex Fuzzy Environment

Rocks are importantly used as building materials. Here chemical, biochemical, clastic and organic sedimentary rocks are chosen for building stones. These rocks are tested for their efficiency in structure strength, toughness, weathering resistances and quality. Using complex picture fuzzy soft VIKOR method it is concluded that clastic sedimentary rocks is the best building stone. First a score function is defined and is used for the construction of complex picture fuzzy soft score matrix the proficiency of CPFS score function over the existing score function is established. Next entropy measure is determined from which weight values are calculated. Complex picture fuzzy soft positive and negative ideal solutions are found and hence the group utility and individual regret values are obtained. By making use of these values the compromising ranking solution is found.

Fuzzy Soft Expert Matrix Theory and Its Application in Decision-Making

Fuzzy Soft Expert Matrix Theory and Its Application in Decision-Making

Fuzzy Quadripartitioned Neutrosophic Soft Matrix Theory and Its Decision-Making Approach

Earlier several fuzzy oriented matrix theories have been proposed by the researchers to model uncertainty for real-world decision-making (DM). Among them, fuzzy neutrosophic soft matrix (FNSM) theory has been developed recently by combining the fuzzy neutrosophic set and soft set to handle the indeterminate information parametrically. The main purpose to represent this paper is to introduce the notion of fuzzy quadripartitioned neutrosophic soft matrix (FQNSM) theory to generalize the FNSM concept. Moreover, several properties and matrix operations on fuzzy quadripartitioned neutrosophic soft sets are investigated with appropriate examples. Finally, a DM model based on FQNSMs has been developed and thus validated by showing an application to real problems.

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.

MCDM method on complex picture fuzzy soft environment

In this paper the concept of complex picture fuzzy soft set is defined. The MCDM problem considered consists of two methods. In the first method called CPFS CRITIC method complex picture fuzzy soft matrix is constructed. Normalized CPFS decision function is defined and using this function the normalized CPFS decision matrix is constructed and the weights of the parameters are determined. In the second method the weights of CPFS CRITIC method are taken to find CPFS decision matrix using selected parameters and their alternatives. The utility function depending on the beneficial and non-beneficial alternatives are defined and the integrated utility of each parameter is determined. This method is illustrated by taking four types of chillies as the alternatives and five nutrients as parameters and the best yielding variety of chilli is found. The proposed method is compared with CPFS-TOPSIS method. It is found that the best variety of chilli is the same in both the methods. However, the ranking of the other types of chilli differ.

T-spherical Fuzzy Soft Matrices with Applications in Decision Making and Selection Process

In the present communication, we have introduced the notion of T-spherical fuzzy soft matrix (TSFSM) and studied various types of associated binary operations and properties. In literature, it has been observed that the concept of soft matrix plays a vital role in many engineering applications as well as to cater different socio-economic and financial sector problems. As per the definition of T-spherical fuzzy set, the proposed notion would have an additional capability to address the impreciseness of the information close enough to human opinion mathematically.Further, on the basis of the structure of proposed TSFSM and using the concept of choice matrix along with its weighted form, a new algorithm for the decision-making process has been outlined. Next, utilizing the score/utility matrix, we present another algorithm for the selection process. For the sake of understanding of the proposed methodologies, illustrative examples have also been presented. Some comparative remarks for the proposed techniques in contrast with existing techniques have been listed for a better readability and understanding.

Decision-Making with Fuzzy Soft Matrix Using a Revised Method: A Case of Medical Diagnosis of Diseases

In this paper, we study the matrix representation of fuzzy soft sets, complement of fuzzy soft sets, product of fuzzy soft matrices and the application of fuzzy soft matrices in medical diagnosis presented by Lavanya and Akila. Additionally, a new method (max-min average) based on fuzzy reference function is introduced instead of the max-product method by Lavanya and Akila to extend Sanchez’s technique for decision making problems in medical diagnosis. Using the same data by Lavanya and Akila, the result shows that the new method gives more information about the medical status of the patients being considered in relation to a set of diseases.

Fuzzy Neutrosophic Soft Matrices of Type I and Type II

In this paper, two types of fuzzy neutrosophic soft matrix have been introduced and it is shown that the set of all fuzzy neutrosophic soft matrices form a semiring. Further it is explored that the set of all fuzzy neutrosophic soft matrices of both types form a vector space.

Application of fuzzy soft and interval valued fuzzy soft matrices in dimension reduction and medical diagnosis by geometric mean approach

In decision making problems several techniques have been used by the researchers. They focused on the use of fuzzy matrices and fuzzy soft matrices in decision making problems. The use of fuzzy set, soft set and fuzzy soft set have been made in handling imprecise information. However,, matrices are also the important tools to handle such problems.In the present communication, we study the application of fuzzy soft matrix in data dimension reduction by geometric mean approach. Geometric mean method for interval valued fuzzy soft matrix is also described. An alternative method to study Sanchez’s approach for medical diagnosis through geometric mean of interval valued fuzzy soft matrix is proposed and studied.

Unknown Values Estimation in Incomplete Fuzzy Soft and Interval Valued Soft Matrices

In day-to-day problems, incomplete information due to unknown values in data is the cause of the loss of information which leads to uncertainly, ambiguity and vagueness. There are many reasons for unknown values in data, like errors in data collection, lack of data information, inappropriate technique, and illegibility of data which cause incompleteness in data. Thus, estimating the unknown values in data of various information systems is an important area of research. In this communication, the definitions of incomplete Fuzzy soft and interval-valued fuzzy soft matrices are given with application in numerical problems. An algorithm is proposed for unknown values estimation in an incomplete fuzzy soft matrix and applied in solving a numerical problem. An application of an incomplete fuzzy soft matrix after inserting the unknown values in dimension reduction is studied. The unknown values in the incomplete interval-valued fuzzy soft matrix are also estimated and applied in the multi-criteria decision-making method.

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.

Fuzzy logic decision support system for hospital employee performance evaluation with maple implementation

In any organization, the capability, knowledge and skills play a significant role in success of an employee. For instant, in hospital management, the performance evaluation of an employee is mainly based on qualitative in nature. Evaluation of certain factors such as uncertainty, vagueness and imprecision is based on the decision making ability of the evaluator. The performance evaluation for promotion, incentives, bonuses, growth and development of any employee should be recognized in effective and efficiency manner with appropriate ratings. Therefore, this paper aims to design and implement a multi criteria performance evaluation for hospital employees to get promotion, incentives, bonus, growth and development. In this paper, we propose an Interval Valued Fuzzy Weighted Distance Algorithm (IVFWDA) for performance evaluation. The expected interval and the actual interval of the work achievement, management skill, personal quality, care, safety and risk management features are extracted by Interval Valued Fuzzy Soft Matrix (IVFSM) and it is effectively done using the proposed algorithm. An example is presented as a case study to illustrate the proposed algorithm. Implementation of the proposed algorithm in Maple is also discussed with sample computations.

Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

Dimensionality Reduction Technique in Decision Making Using Pythagorean Fuzzy Soft Matrices

Background:Dimensionality reduction plays an effective role in downsizing the data having irregular factors and acquires an arrangement of important factors in the information. Sometimes, most of the attributes in the information are found to be correlated and hence redundant. The process of dimensionality reduction has a wider applicability in dealing with the decision making problems where a large number of factors are involved.Objective:To take care of the impreciseness in the decision making factors in terms of the Pythagorean fuzzy information which is in the form of soft matrix. The perception of the information has the parameters - degree of membership, degree of indeterminacy (neutral) and degree of nonmembership, for a broader coverage of the information.Methods:We first provided a technique for finding a threshold element and value for the information provided in the form of Pythagorean fuzzy soft matrix. Further, the proposed definitions of the object-oriented Pythagorean fuzzy soft matrix and the parameter-oriented Pythagorean fuzzy soft matrix have been utilized to outline an algorithm for the dimensionality reduction in the process of decision making.Results:The proposed algorithm has been applied in a decision making problem with the help of a numerical example. A comparative analysis in contrast with the existing methodologies has also been presented with comparative remarks and additional advantages.Conclusion:The example clearly validates the contribution and demonstrates that the proposed algorithm efficiently encounters the dimension reduction. The proposed dimensionality reduction technique may further be applied in enhancing the performance of large scale image retrieval.