A Different Approach for Solving the Shortest Path Problem Under Mixed Fuzzy Environment

Abstract

The authors present a new algorithm for solving the shortest path problem (SPP) in a mixed fuzzy environment. With this algorithm, the authors can solve the problems with different sets of fuzzy numbers e.g., normal, trapezoidal, triangular, and LR-flat fuzzy membership functions. Moreover, the authors can solve the fuzzy shortest path problem (FSPP) with two different membership functions such as normal and a fuzzy membership function under real-life situations. The transformation of the fuzzy linear programming (FLP) model into a crisp linear programming model by using a score function is also investigated. Furthermore, the shortcomings of some existing methods are discussed and compared with the algorithm. The objective of the proposed method is to find the fuzzy shortest path (FSP) for the given network; however, this is also capable of predicting the fuzzy shortest path length (FSPL) and crisp shortest path length (CSPL). Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical results show that this method is superior to the existing methods.

A Pythagorean fuzzy approach to the transportation problem

“…After maximum allotting in the cell (2, 3) we get a new table. Table 5 shows the first allotment with penalties ( Tables 6,7,8). Table 9 shows the initial basic feasible solution of Example 5.1.…”

“…However, in most of the cases, the data to be handled are uncertain, imprecise and inconsistence, the obtained results are not consistent, and, therefore, uncertainty theory came into existence. During the last few decades, the topic of fuzzy optimization has achieved substantial popularity among researchers because of its widespread applications in different branches of network flow problem [2], production [3], shortest path problem [4][5][6][7][8], pick up delivery problem [9], travel salesman problem [10], traffic assignment problem [11].…”

Anti-Forensics: Countering Sensor Noise Camera Identification

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“…This is when the concept of file carving comes in handy, it allows you to recover deleted files based on the content that was present in the before deletion. The used for file carving are Autopsy, Foremost [29].  Header Analysis: This technique is used for email related crime investigations.…”

On Direct Product of a Fuzzy Subgroup with an Anti-fuzzy Subgroup

“…Fuzzy set theory [1] is more reliable in tackling such scenarios. Since the very beginning of fuzzy set theory, many researchers have carried out that perception on various realistic problems like in optimization technique [2], game theory [3], statistical analysis [4], uncertainty theory [5,6,7,8], database [9], etc. Presently, neutrosophic set theory [10] has been developed which is nothing but generalization of fuzzy set theory.…”