Neutrosophic Similarity Measure Research Articles

A Novel PI-PD Controller Tuning Method based on Neutrosophic Similarity Measure for Unstable and Integrating Processes with Time Delay

Integrating systems and unstable systems are two types of systems that are widely used in various industries, including control engineering and electrical engineering. However, controlling these systems can be a daunting task due to their inherent complexity. To address this challenge, the PI-PD controller structure has been widely adopted in the industry, as it has proven to be very successful in controlling integrating and unstable systems. In this paper, a new design method is proposed to determine the optimal controller parameters in the control of integrating and unstable systems with time delay. The design method utilizes a Genetic Algorithm-based optimization technique, which incorporates a new objective function that is based on the neutrosophic similarity measure. Two different types of plants have been chosen as examples in this study. The first plant is a time-delayed integrating system. The second plant is an unstable system, which means that the output signal is very sensitive to any changes or disturbances in the input signal. This study examines the parameter uncertainties of systems by comparing them with some design methods from the literature. The results are presented comparatively in figures and tables to show the superiority of the proposed method.

Cotangent Similarity Measure of Consistent Neutrosophic Sets and Application to Multiple Attribute Decision-Making Problems in Neutrosophic Multi-Valued Setting

A neutrosophic multi-valued set (NMVS) is a crucial representation for true, false, and indeterminate multi-valued information. Then, a consistent single-valued neutrosophic set (CSVNS) can effectively reflect the mean and consistency degree of true, false, and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS. However, there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature. This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting. The cosine similarity measures show the cosine of the angle between two vectors projected into a multidimensional space, rather than their distance. The cotangent similarity measures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent. Then, a decision-making approach is presented in view of the established cotangent similarity measures in the case of NMVSs. Finally, the developed decision-making approach is applied to selection problems of potential cars. The proposed approach has obtained two different results, which have the same sort sequence as the compared literature. The decision results prove its validity and effectiveness. Meantime, it also provides a new manner for neutrosophic multi-valued decision-making issues.

Application of Neutrosophic Similarity Measures in Covid-19.

The contemporary situation of the world is very pathetic due to the spread of COVID-19. In this article, we have prepared a decision making model on COVID-19 pandemic patients with the help of the neutrosophic similarity measures. The model is to predict the COVID-19 patents for testing positive and testing negative. The decision making is based on the testing result of the COVID-19 cases. We have used the neutrosophic similarity measure theory and the distance function. We have used the C-programming for finding the result of the suspected patients.

H-Max Single-Valued Neutrosophic Distance Measure in Medical Diagnosis

As an instance of a neutrosophic set, a single-valued neutrosophic set (SVNS) can be used to handle uncertainty, inaccuracy, indeterminacy, and inconsistency. In this paper, a new not-so-sophisticated distance measure between two SVNSs is defined by considering the cross-assessment between characteristic functions for the forward and backward differences. Furthermore, a single-valued neutrosophic similarity measure, a single-valued neutrosophic entropy measure, and their basic properties are presented and proven. In addition, an application to medical diagnosis is shown to illustrate the effective applicability of the proposals.

Refined Simplified Neutrosophic Similarity Measures Based on Trigonometric Function and Their Application in Construction Project Decision Making

Refined simplified neutrosophic sets (RSNSs) are appropriately used in decision-making problems with sub-attributes considering their truth components, indeterminacy components and falsity components independently.

Refined Simplified Neutrosophic Similarity Measures Based on Trigonometric Function and Their Application in Construction Project Decision-Making

Refined Simplified Neutrosophic Similarity Measures Based on Trigonometric Function and Their Application in Construction Project Decision-Making

Vector Similarity Measures between Refined Simplified Neutrosophic Sets and Their Multiple Attribute Decision-Making Method

A refined single-valued/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees. However, existing refined single-valued/interval neutrosophic similarity measures and their decision-making methods are scarcely studied in existing literature and cannot deal with this decision-making problem with the weights of both attributes and sub-attributes in a refined interval and/or single-valued neutrosophic setting. To solve the issue, this paper firstly introduces a refined simplified neutrosophic set (RSNS), which contains the refined single-valued neutrosophic set (RSVNS) and refined interval neutrosophic set (RINS), and then proposes vector similarity measures of RSNSs based on the Jaccard, Dice, and cosine measures of simplified neutrosophic sets in vector space, and the weighted Jaccard, Dice, and cosine measures of RSNSs by considering weights of both basic elements and sub-elements in RSNS. Further, a decision-making method with the weights of both attributes and sub-attributes is developed based on the weighted Jaccard, Dice, and cosine measures of RSNSs under RSNS (RINS and/or RSVNS) environments. The ranking order of all the alternatives and the best one can be determined by one of weighted vector similarity measures between each alternative and the ideal solution (ideal alternative). Finally, an actual example on the selecting problem of construction projects illustrates the application and effectiveness of the proposed method.

Algorithms for neutrosophic soft decision making based on EDAS, new similarity measure and level soft set

This paper presents three novel single-valued neutrosophic soft set (SVNSS) methods. First, we initiate a new axiomatic definition of single-valued neutrosophic similarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via grey system theory.

ALGORITHMS FOR INTERVAL NEUTROSOPHIC MULTIPLE ATTRIBUTE DECISION-MAKING BASED ON MABAC, SIMILARITY MEASURE, AND EDAS

In this paper, we define a new axiomatic definition of interval neutrosophic similarity measure, which is presented by interval neutrosophic number (INN). Later, the objective weights of various attributes are determined via Shannon entropy theory; meanwhile, we develop the combined weights, which can show both subjective information and objective information.

A Neutrosophic Graph Similarity Measures

This paper is devoted for presenting new neutrosophic similarity measures between neutrosophic graphs. We proposetwo ways to determine the neutrosophic distance between neutrosophic vertex graphs. The two neutrosophic distances are based on the Haussdorff distance,and a robust modified variant of the Haussdorff distance, moreover we show that they both satisfy the metric distance measure axioms. Furthermore, a similarity measure between neutrosophic edge graphs that is based on a probabilistic variant of Haussdorff distance is introduced. The aim is to use those measures for the purpose of matching neutrosophic graphs whose structure can be described in the neutrosophic domain.

PID Tuning with Neutrosophic Similarity Measure

In this paper, a method for adjusting the proportional-integral-derivative (PID) coefficients based on the neutrosophic similarity measure is proposed. First, rough PID coefficients were determined by the Ziegler–Nichols method, and the upper and lower limit values for the search range of the PID coefficients were determined. At each step of the search range, we applied a unit step function to the system and obtained the transient response characteristics. The obtained values were converted into a neutrosophic set (real set) by using defined membership functions. Then, the optimal PID coefficients were obtained using the similarity ratio between the real and ideal (target) neutrosophic sets. In calculating the similarity ratio, the Hamming, Euclidean, Set-theoretic, Jaccard, and Dice approaches were applied, and the results were compared. Finally, the proposed method was tested on two transfer functions, and it was demonstrated that the proposed method can be used to adjust PID coefficients.

PID Tuning with Neutrosophic Similarity Measure

PID Tuning with Neutrosophic Similarity Measure

Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function

Similarity measures play an important role in pattern recognition and medical diagnosis, and then existing medical diagnosis methods deal scarcely with the multi-period medical diagnosis problems with neutrosophic information. Hence, this paper proposed similarity measures between single-valued neutrosophic sets (SVNSs) based on tangent function and weighted similarity measures of SVNSs considering the importance of each element.

Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function

Because of the increased volume of information available to physicians from advanced medical technology, the obtained information of each symptom with respect to a disease may contain truth, falsity and indeterminacy information. Since a single-valued neutrosophic set (SVNS) consists of the three terms like the truth-membership, indeterminacy-membership and falsity-membership functions, it is very suitable for representing indeterminate and inconsistent information. Then, similarity measure plays an important role in pattern recognition and medical diagnosis. However, existing medical diagnosis methods can only handle the single period medical diagnosis problem, but cannot deal with the multi-period medical diagnosis problems with neutrosophic information. Hence, the purpose of this paper was to propose similarity measures between SVNSs based on tangent function and a multi-period medical diagnosis method based on the similarity measure and the weighted aggregation of multi-period information to solve multi-period medical diagnosis problems with single-valued neutrosophic information. Then, we compared the tangent similarity measures of SVNSs with existing similarity measures of SVNSs by a numerical example about pattern recognitions to indicate the effectiveness and rationality of the proposed similarity measures. In the multi-period medical diagnosis method, we can find a proper diagnosis for a patient by the proposed similarity measure between the symptoms and the considered diseases represented by SVNSs and the weighted aggregation of multi-period information. Then, a multi-period medical diagnosis example was presented to demonstrate the application of the proposed diagnosis method and to indicate the effectiveness of the proposed diagnosis method by the comparative analysis. The diagnosis results showed that the developed multi-period medical diagnosis method can help doctors make a proper diagnosis by the comprehensive information of multi-periods.

Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine

Similarity measure is an important tool in pattern recognition and fault diagnosis. This paper proposes two cotangent similarity measures for single-valued neutrosophic sets (SVNSs) based on cotangent function. Then, the weighted cotangent similarity measures are introduced by considering the importance of each element. Moreover, by the comparison between the cotangent similarity measures of SVNSs and existing cosine similarity measure of SVNSs, the developed cotangent similarity measures demonstrate their advantages and rationality and in some cases can overcome some disadvantages of the cosine similarity measure defined in vector space. Finally, the cotangent similarity measures are applied to the fault diagnosis of steam turbine. The proposed fault diagnosis method demonstrates its effectiveness and rationality by the comparative analysis with the cosine similarity measure in the fault diagnosis of steam turbine.