Intuitionistic Fuzzy Multiset Research Articles

A New Approach towards Intuitionistic Fuzzy Multisets

In this paper a new definition of Intuitionistic fuzzy multisets (IFMS) has been introduced. Algebraic operations on these intuitionistic fuzzy multisets are defined and their properties under these algebraic operations are studied. The author has also introduced a new notion of complement for an IFMS in which the complement of the original set is also an IFMS. The notion of distance and similarity between two IFMS’s has been defined and their properties have also been studied here. An application of IFMS in solving a medical diagnosis problem has been provided at the end.

A New Approach Towards Intuitionistic Fuzzy Multisets

In this paper a new definition of Intuitionistic fuzzy multisets (IFMS) has been introduced. Algebraic operations on these intuitionistic fuzzy multisets are defined and their properties under these algebraic operations are studied. The author has also introduced a new notion of complement for an IFMS in which the complement of the original set is also an IFMS. The notion of distance and similarity between two IFMS’s has been defined and their properties have also been studied here. An application of IFMS in solving a medical diagnosis problem has been provided at the end.

Pattern recognition based on multiple attribute decision making in intuitionistic fuzzy environment

In this paper we adapt an algorithm from the multiple attribute decision making field in order to be used in pattern recognition, working with intuitionistic fuzzy sets and intuitionistic fuzzy multi sets. Our method is implemented in two versions: using the score matrix (that is characteristic of decision making problems) and using a similarity measure (that is characteristic of pattern recognition problems). Firstly, the method is built to work with intuitionistic fuzzy sets and after it is extended for intuitionistic fuzzy multi sets. Experimental results demonstrate the superiority of the second versions in pattern recognition problems. For each example we compare our results with those given by other measures whose accuracy has been validated by the respective examples and we conclude that our method can be successfully used in pattern recognition instead of some specific methods in this area.

New Similarity Measure between Intuitionistic Fuzzy Multisets based on Tangent Function and its Application in Medical Diagnosis

In recent years, Intuitionistic fuzzy set is very useful in decision making problems such as medical diagnosis, pattern recognition, clustering etc., which deals with vagueness and uncertainty. Similarity measure is a tool used to find the closeness of the intuitionistic fuzzy sets by considering the membership, nonmembership and hesitation function. In this paper, we propose an effective similarity measure based on tangent function for intuitionistic fuzzy multi sets in which membership, nonmembership, hesitation function occurs more than once and also we apply this measure in medical diagnosis and pattern recognition.

Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems

Intuitionistic trapezoidal fuzzy multi-numbers (ITFM-numbers) are a special intuitionistic fuzzy multiset on a real number set, which are very useful for decision makers to depict their intuitionistic fuzzy multi-preference information. In the ITFM-numbers, the occurrences are more than one with the possibility of the same or the different membership and non-membership functions. In this paper, we define ITFM-numbers based on multiple criteria decision-making problems in which the ratings of alternatives are expressed with ITFM-numbers. Firstly, some operational laws using t-norm and t-conorm are proposed. Then, some aggregation operators on ITFM-numbers are developed. Also, the ranking order of alternative is given according to the similarity of the alternative with respect to the positive ideal solution. Finally, a numerical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Intuitionistic Fuzzy Multisets in Medical Diagnosis

In this paper, sine inverse distance among intuitionistic fuzzy multi sets is proposed and some of its properties are discussed herein. The concept of the above method is an essential tool for dealing with uncertainties and shortcomings that affect the existing methods. Implementation of medical diagnosis is presented to find out the disease impacting the patient.

A New Similarity Measure between Intuitionistic Fuzzy Multisets based on their Cardinality with Applications to Pattern Recognition and Medical Diagnosis

In this paper, a new similarity measure between Intuitionistic Fuzzy Multisets (IFMSs) based on their cardinality is proposed. Some properties of the proposed similarity measure between IFMSs are proved. The unique feature of the proposed measure is that the similarity measure can be applied for both intuitionistic fuzzy sets (IFS) and intuitionistic fuzzy multisets (IFMSs). Illustrative examples are taken to discuss that the proposed similarity measure can overcome the drawback of the existing similarity measure. Further the proposed similarity measure is also applied to pattern recognition and medical diagnosis problems.

Application of Intuitionistic Fuzzy Multisets in Appointment Process

In this paper, a precise note on intuitionistic fuzzy multisets is given and the concept is applied to appointment process. This process was carried out assuming three sets of 10-man committees screened five candidates vying for positions in an organization independently to obtain intuitionistic fuzzy multi-data. The obtained data are compared with the organization requirements of appointments via a new distance measure.

Medical Diagnosis Using Distance-Based Similarity Measures of Single Valued Neutrosophic Multisets

This paper proposes a generalized distance measure and its similarity measures between single val- ued neutrosophic multisets (SVNMs). Then, the similari- ty measures are applied to a medical diagnosis problem with incomplete, indeterminate and inconsistent infor- mation. This diagnosis method can deal with the diagno- sis problem with indeterminate and inconsistent infor- mation which cannot be handled by the diagnosis method based on intuitionistic fuzzy multisets (IFMs).

Dice Similarity Measure between Single Valued Neutrosophic Multisets and Its Application in Medical Diagnosis

This paper introduces the concept of a single valued neutrosophic multiset (SVNM) as a generalization of an intuitionistic fuzzy multiset (IFM) and some basic operational relations of SVNMs, and then proposes the Dice similarity measure and the weighted Dice similarity measure for SVNMs and investigates their properties. Finally, the Dice similarity measure is applied to a medical diagnosis problem with SVNM information. This diagnosis method can deal with the medical diagnosis problem with indeterminate and inconsistent information which cannot be handled by the diagnosis method based on IFMs.

CORRELATION MEASURE FOR INTUITIONISTIC FUZZY MULTI SETS

In this paper, the Correlation measure of Intuitionistic Fuzzy Multi sets (IFMS) is proposed. The concept of this Correlation measure of IFMS is the extension of Correlation measure of IFS. Using the Correlation of IFMS measure, the application of medical diagnosis and pattern recognition are presented. The new method also shows that the correlation measure of any two IFMS equals one if and only if the two IFMS are the same.

English

As Similarity measure for fuzzy sets is one of the important research topics of fuzzy set theory, there are several methods to measure similarity between two fuzzy sets (FS), Intuitionistic fuzzy sets (IFS) and Intuitionistic fuzzy multi sets (IFMS). In this paper, the Normalized Hamming Similarity measure of Intuitionistic Fuzzy Multi sets (IFMS) is introduced. This new measure for IFMS is based on the geometrical interpretation of IFS which involves both similarity and dissimilarity. Using this measure, the application of medical diagnosis and pattern recognition are shown.

On Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set

On Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set