Improved Correlation Coefficients of Quadripartitioned Single-Valued Neutrosophic Sets and Interval-Quadripartitioned Neutrosophic Sets

A correlation coefficient is one of the statistical measures that helps to find the degree of changes to the value of one variable predict change to the value of another. Quadripartitioned single valued neutrosophic sets is an improvization of Wang's single valued neutrosophic sets. This chapter deals the improved correlation coefficients of quadripartitioned single valued neutrosophic sets, interval quadripartitioned neutrosophic sets, and investigates its properties. And this concept is also applied in multiple-attribute decision-making methods with quadripartitioned single valued neutrosophic environment and interval quadripartitioned neutrosophic environment. Finally an illustrated example is given in the proposed method to the multiple-attribute decision-making problems.

A Novel Python Toolbox for Single and Interval-Valued Neutrosophic Matrices

Recently, single valued neutrosophic sets and interval valued neutrosophic sets have received great attention among the scholars and have been applied in many applications. These two concepts handle the indeterminacy and consistent information existing in real-life problems. In this chapter, a new Python toolbox is proposed under neutrosophic environment, which consists of some Python code for single valued neutrosophic matrices and interval valued neutrosophic matrices. Some definitions of interval neutrosophic vague set such as union, complement, and intersection are presented. Furthermore, the related examples are included.

A New LCS-Neutrosophic Similarity Measure for Text Information Retrieval

The reality of human existence and their interactions with various things that surround them reveal that the world is imprecise, incomplete, vague, and even sometimes indeterminate. Neutrosophic logic is the only theory that attempts to unify all previous logics in the same global theoretical framework. Extracting data from a similar environment is becoming a problem as the volume of data keeps growing day-in and day-out. This chapter proposes a new neutrosophic string similarity measure based on the longest common subsequence (LCS) to address uncertainty in string information search. This new method has been compared with four other existing classical string similarity measure using wordlist as data set. The analyses show the performance of proposed neutrosophic similarity measure to be better than the existing in information retrieval task as the evaluation is based on precision, recall, highest false match, lowest true match, and separation.

An Improved PID Tuning Method by Applying Single-Valued Neutrosophic Cosine, Tangent, and Exponential Measures and a Simulated Annealing Algorithm

This chapter introduces an improved proportional-integral-derivative (PID) adjusting method by applying a simulated annealing algorithm (SAA) and the cosine, tangent, exponential measures of single-valued neutrosophic sets (SvNSs). For the approach, characteristic values of the unit step response (rise time, peak time, settling time, undershoot ratio, overshoot ratio, and steady-state error) in the control system should be neutrosophicated by the neutrosophic membership functions. Next, one of cosine, tangent, and exponential measures is used to obtain the similarity measure of the ideal SvNS and the response SvNS to assess the control performance of the PID controller by the optimization values of the PID parameters Kp, Ki, and Kd searched by SAA. The results of the illustrative example obtained by these measures and SAA are better than the existing ones and indicate better PID controller performance. Comparative results can demonstrate the rationality and superiority of the improved PID adjusting method.

Generalised Single-Valued Neutrosophic Number and Its Application to Neutrosophic Linear Programming

In this chapter, the concept of single valued neutrosophic number (SVN-Number) is presented in a generalized way. Using this notion, a crisp linear programming problem (LP-problem) is extended to a neutrosophic linear programming problem (NLP-problem). The coefficients of the objective function of a crisp LP-problem are considered as generalized single valued neutrosophic number (GSVN-Number). This modified form of LP-problem is here called an NLP-problem. An algorithm is developed to solve NLP-problem by simplex method. Finally, this simplex algorithm is applied to a real-life problem. The problem is illustrated and solved numerically.

Extended GRA-Based MADM Strategy With Single-Valued Trapezoidal Neutrosophic Numbers

Multi-attribute decision-making(MADM) strategy has been proposed to handle uncertain decision-making problems. The most extensively used models of grey system theory is grey relational analysis (GRA). This strategy was flourished by Chinese Professor J. Deng. This strategy also known as Deng's grey incidence analysis model. GRA uses a generic concept of intelligence. It describes any circumstance as no information as black and perfect information as white. Nevertheless, these idealized situations appear in real-world problems. In this chapter, the authors extend GRA strategy for multi-attribute decision making in trapezoidal neutrosophic number (TrNN) environment. To develop a GRA strategy in trapezoidal neutrosophic number (TrNN) environment, the authors use score function and accuracy function. Then Hamming distance for two trapezoidal neutrosophic number (TrNN) are also described. The authors solve a numerical problem to explain the pertinence of the proposed strategy. Lastly, they provide a comparison between VIKOR strategy with existing strategy.

Interval Rough Neutrosophic TOPSIS Strategy for Multi-Attribute Decision Making

In this chapter, the authors present a new strategy for multi-attribute decision making in interval rough neutrosophic environment. They define Hamming distance and Euclidean distance between interval rough neutrosophic numbers. They also define interval rough neutrosophic relative positive ideal solution (IRNRPIS) and interval rough neutrosophic relative negative ideal solution (IRNRNIS). Then the ranking order of the alternatives is obtained by the technique for order preference by similarity to ideal solution (TOPSIS) strategy. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the proposed interval rough neutrosophic TOPSIS strategy.

Geometric Programming Dealing With Neutrosophic Relational Equations Under the (Max-Min) Operation

The neutrosophic relation equations are important elements of neutrosophic mathematics, and it can be widely applied in power systems, neutrosophic comprehensive evaluation. The aim of this chapter is to find the minimal solutions for the neutrosophic relation geometric programming having (V, Λ) operator. In this chapter, a max-min method has been built for finding an optimal solution in the neutrosophic relation equations, and a new characteristic matrix has been defined which is an important step to test the consistency of the system Aοx=b and for finding all effective paths that lead to the set of all quasi-minimum solutions. The gained results are reasonable and harmonized with those results in Khalid's work. The method overcomes the problems of poor convergence efficiency inherited from the stochastic hill-climbing method or genetic algorithms. The suggested algorithm has the intersection column method which was proposed to find the effective paths that neglect the fallacious paths, and two new theorems were presented to deal with the optimal solution for (NREGP).

A New Multi-Attribute Decision-Making Method Based on Similarity Measures of SVTN-Numbers

In this study, the authors develop a new decision-making method on single-valued trapezoidal neutrosophic numbers (SVTN-Numbers) where all the decision information take the form of SVTN-Numbers. To construct the method, some new similarity measures between two SVTN-Numbers are presented. Then, concept of impact value on SVTN-Numbers by using the cut sets of SVTN-Numbers is proposed, and the corresponding properties are discussed. Finally, a real example is introduced and compared with different methods to show the applicability and feasibility of the proposed multi-attribute decision-making method.

A TOPSIS Method Under SVTN-Numbers Based on Multi-Attribute Decision-Making Problems

Ranking of single valued trapezoidal neutrosophic numbers (SVTN-Numbers) plays a vital role in decision making and other single valued trapezoidal neutrosophic applications. In this chapter, the authors propose a new ranking method of SVTN-Numbers based on distance measure. Firstly, a new distance measure based on cut sets of SVTN-Numbers is developed. Secondly, some desired proportions and results of the distance measure are examined. Finally, the SVTN-Number method based on distance measure is given, and the effectiveness of our algorithm through a numerical example is illustrated.