Neutrosophic statistical analysis of resistance depending on the temperature variance of conducting material

In this work, we have proposed a neutrosophic statistical approach for the analysis of resistance of conducting material depending on the temperature variance. We have developed a neutrosophic formula and applied it to the resistance data. We also use the classical statistical approach for making a comparison between both approaches. As a result, it is observed that the neutrosophic statistical approach is more flexible and informative. Also, this work suggests that the neutrosophic statistical approach analyzes the resistance of conducting material for big data.

www.nature.com/scientificreports/ and temperature. By exploring the literature and according to the best of our knowledge, there is no work on studying these variables using neutrosophic statistics. In this paper, we will introduce neutrosophic statistics to analyze the resistance with respect to change in temperature data. We will compare the performance of the proposed method with the existing method under classical statistics. We expect that the proposed method will be efficient, effective and adequate to be applied for resistance with respect to change in temperature data.

Methodology
Let X iN is the neutrosophic numbers having X iL lower values and X iU higher values, so the neutrosophic formula for the ith interval: Here, The variable X iN ∈ [X iL , X iU ] has two parts: lower value X iL a classical part, and upper-value X iU I N an indeterminate part having indeterminacy interval Similarly, neutrosophic mean X N ∈ [ X L , X U ] is defined as follows: Here, X U = nL i=1 (X iL /n L ) and X L = nU i=1 (X iU /n U ) As we are studying the change in resistance of a conducting material w.r.t. variation in temperature, so we can write the resistance as the function of the temperature i.e. R(T). Now, let R(T) N is measured interval value of the resistance i.e. R(T) N ∈ [R(T) L , R(T) U ], here, R(T) L and R(T) L are the lower and upper values of the interval, respectively. The neutrosophic formula for resistance of the conducting material is written as follows: Experiment. The main purpose of this research work is to express the advantages of neutrosophic a statistical approach for the analysis of measured resistance data with respect to (w.r.t) temperature variation of the conducting material. For this purpose, we have used a sample 200 nm thin film of a conducting material whose resistance values are measured at 100 Hz w.r.t. to change temperature through the LCR meter in intervals. The characterization setup is as shown in Fig. 1.
The measurement of the values has been performed in intervals i.e. at specific temperature value the maximum and minimum value change of resistance [min; max]. As we measured values in the interval, so for classical analysis, we convert these values into fix point. For using the neutrosophic approach, we first make a neutrosophic formula for resistance and then use this interval data for analysis.

Results and discussion
The measured resistance values of the sample w.r.t change in temperature from 0 to 350 K (these values are not measured from experiment but by concerning the previous work on the resistance w.r.t temperature as in references 28,29 ) as shown in Table 1. Comparison between classical statistical approach and neutrosophic statistical approach. In this section, we will compare the efficiency of the proposed method over the existing classical method in terms of a measure of indeterminacy, information and flexibility. The neutrosophic data and data using the classical method are shown in Table 2. The analysis using the resistance changing with respect to temperature variance data are shown in Table 2.
From Table 2, it can be seen that in the classical method a fixed value is calculated on the basis of the average of each interval. Therefore, the classical analysis provides only one value at the time against a specific temperature for the conducting material. The classical method may mislead the decision-makers when extreme values are present in the intervals. On the other hand, the neutrosophic analysis used imprecise values and give information about the measure of indeterminacy. For example, when the temperature is 0 K, the classical analysis gives the value R(0) = 0.132. On the other hand, the proposed method provides the neutrosophic form R(0) = 0.120 + 0.143I N . According to the proposed method, the values of R(0) will be between 0.12 to 0.143 with measure of indeterminacy that is 0.023. By comparing both methods, it can be concluded that the existing method in Physics gives only information about the average value of the interval. On the other hand, the proposed method is quite flexible and adequate to be applied for the interval data. Now, we compare the proposed method with the classical method graphically. Let us draw the graphs for classical and neutrosophic analysis as shown in Fig. 2. From these graphs, it can be seen that graph of classical analysis is not much flexible because this graph is drawn at fix point values i.e. there is no indeterminacy. The graph using the proposed method is also shown in Fig. 2 which shows more flexibility. This means that the proposed method is more effective to analyze the resistance of the conducting material. From the graph, the information about the resistance at a specific value can be obtained with additional information about the measure of indeterminacy. Also, Fig. 2 shows that the neutrosophic approach is a generalization of the classical method as the curve using the classical method lies between the curves of the proposed method. As a result, it is found that neutrosophic statistics is informative, flexible and adequate than classical statistics.

Conclusions
In this paper, the electrical property of the conducting material through resistance containing indeterminacy i.e. interval values have been analyzed. The neutrosophic statistical approach is used to analyze the interval values and the classical statistical approach is used to analyze the fix point values. From this study, it can be concluded that the analysis of resistance with respect to temperature of conducting material through the neutrosophic  www.nature.com/scientificreports/ statistics approach is more informative, flexible and adequate than the analysis through classical statistics. Moreover, the proposed analysis suggests the use of a neutrosophic statistical approach for big data analysis as part of future research.

Data availability
The data is given in the paper.