Total Difference Method Research Articles

Improved Segregated Advancement (I-SA): a new method for solving full triangular fuzzy transportation problems

ABSTRACT In this paper, triangular fuzzy numbers (TFN) are used to represent the uncertainty of data in the transportation problems (TP), which are referred to as fuzzy transportation problems (FTP). The main issues in the FTP are the lack of information, error of the basic trading rules, incomplete fuzzy data, and the limitations of the existing fuzzy-ranking functions which is failed to compare two TFN. Segregated advancement (SA) is a separation approach where the TFN represented by low, middle, and upper are solved part by part. The flaw of SA is that it uses the classical algorithms which are NWC, LCM, and VAM. Therefore, we proposed the improvement based on the combination of total ratio cost matrix and total difference method by column without using classical ranking functions. The first and second examples illustrate the existing methods without using the SA approach. The results show that the proposed method obtained the optimal solution of FTP, whereas the existing methods produced infeasible solution. The third example presents the limitation of existing methods along with the SA approach. The results show that the proposed method is capable in solving the third example whereas the existing approach failed to solve the said example.

Technical Modifications for the Application of the Total Difference Method for Frontal Sinus Comparison.

Simple SummaryThe individuality observed in the frontal sinus cavity (located in the skull) can be used to corroborate an identification of an unknown skeleton, with a success rate that is comparable to that obtained by using dentition or DNA. For admissibility in court, however, forensic methods should be continually tested to assess their repeatability and accuracy. This study tests one technical method for obtaining the frontal sinus shape: the Total Difference Method, which quantifies the sinus shape from 59 linear measurements. We develop a more streamlined application by using a measurement aid (a tracing overlay) and a semi-automated macro to collect the multiple required measurements. The radiographs of 10 adults were assessed by two observers. The data were collected following the original method in addition to the use of a measurement aid with and without the semi-automated macro. The results indicate that this technique for assessing the frontal sinus is reliable and repeatable between and within observers, both for the original method and when using the newly developed applications. Further, the semi-automated macro improved the accuracy and efficiency over the original method. Importantly, the measurement aid will allow researchers to conduct the Total Difference Method on a larger scale, creating comparative databases that can be utilized for future forensic research and practice.Despite being used in personal identification since the 1920s, frontal sinus-based methods are rarely validated. This study is a validation test of the Total Difference Method (TDM). The posterior-anterior radiographs of 10 adults were assessed by two observers using three modes: the Freehand Mode largely followed the original protocols; the Overlay Mode utilized a tracing overlay; and the Semi-Auto Mode used the overlay and macro, walking the user through multiple steps. The modes were evaluated for the time taken to complete each image and the accuracy and repeatability of the line lengths, midline assessment, and angle placement. The repeated measures analysis of variance results for the intra-observer error revealed differences in bias in the angle placement and line length mean error between the rounds and modes. The differences between the rounds were approximately consistent for each mode, suggesting observer error. Significant differences in the inaccuracy of the angle placement and the line lengths between observers by mode were evident; in post hoc testing, the Freehand Mode and Overlay Mode had the greatest error in both variables (p.adj < 0.0001). The Semi-Auto Mode retained no significant error for angle inaccuracy and had the fewest errors for line length inaccuracy (p.adj < 0.01). When using the Semi-Auto Mode, the time was 46.1% faster than that of the Freehand Mode and 34% faster than that of the Overlay Mode (F2,18 = 52.71, p < 0.0001); time slightly improved with method familiarity. The results suggest that the technique required for the TDM can reliably be repeated, and the semi-automated macro improves accuracy and efficiency, but only after the users are familiar with the method and macro procedures. All resources needed to repeat this study are freely available on GitHub.

A combination of TDM and KSAM to determine initial feasible solution of transportation problems

In case of the Transportation Problem (TP), it was found that TP had equal the smallest &nbsp;so that the existing methods will be generated two or more IFS values. The newly developed algorithm is generated through a combination of Total Difference Method (TDM) and Karagul-Sahin Approximation Method (KSAM) algorithm, is capable to determine the initial feasible solution of TP. Based on the numerical illustration of TP example to evaluate the performance of the new proposed algorithm. The computational performances have been compared to the existing methods (TDM1 and KSAM) and the results shown this algorithm achieved better performance than the existing methods for TP example.

Three stages algorithm for finding optimal solution of balanced triangular fuzzy transportation problems

In the literature, the fuzzy optimal solution of balanced triangular fuzzy transportation problem is negative fuzzy number. This is contrary to the constraints that must be non-negative. Therefore, the three stages algorithm is proposed to overcome this problem. The proposed algorithm consist of segregated method with segregating triangular fuzzy parameters into three crisp parameters. This method avoids the ranking technique. Next, total difference method is used to get initial basic feasible solution (IBFS) value based on segregating triangular fuzzy parameters. While, modified distribution algorithm is used to determine optimal solution based on IBFS velue. In order to illustrate the proposed algorithm is given the numerical example and based on the result comparison, the proposed algorithm equality to the two existing algorithms and better then the one existing algorithm. The proposed algorithm can solve in the fuzzy decision-making problems and can also be extended to an unbalanced fuzzy transportation problem.