scholarly journals Mehar Approach for Finding Shortest Path in Supply Chain Network

2021 ◽  
Vol 13 (7) ◽  
pp. 4016
Author(s):  
Tanveen Kaur Bhatia ◽  
Amit Kumar ◽  
Srimantoorao S. Appadoo ◽  
Yuvraj Gajpal ◽  
Mahesh Kumar Sharma
Keyword(s):  
Shortest Path ◽  
Fuzzy Numbers ◽  
New Approach ◽  
Shortest Path Problems ◽  
Shortest Distance ◽  
Lexicographic Method ◽  
Different Types ◽  
The Cost ◽  
Pythagorean Fuzzy Numbers ◽  
Interval Valued

The aim of each company/industry is to provide a final product to customers at the minimum possible cost, as well as to protect the environment from degradation. Ensuring the shortest travel distance between involved locations plays an important role in achieving the company’s/industry’s objective as (i) the cost of a final product can be minimized by minimizing the total distance travelled (ii) finding the shortest distance between involved locations will require less fuel than the longest distance between involved locations. This will eventually result in lesser degradation of the environment. Hence, in the last few years, various algorithms have been proposed to solve different types of shortest path problems. A recently proposed algorithm for solving interval-valued Pythagorean fuzzy shortest path problems requires excessive computational efforts. Hence, to reduce the computational efforts, in this paper, firstly, an alternative lexicographic method is proposed for comparing interval-valued Pythagorean fuzzy numbers. Then, using the proposed lexicographic comparing method, a new approach (named as Mehar approach) is proposed to solve interval-valued Pythagorean fuzzy shortest path problems. Furthermore, the superiority of the proposed lexicographic comparing method, as well as the proposed Mehar approach, is discussed.

scholarly journals Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm

2020 ◽  
pp. 53-61
Author(s):  
admin admin ◽  
◽  
◽  
◽  
Said Broumi ◽  
...  
Keyword(s):  
Shortest Path ◽  
Score Function ◽  
Shortest Path Problem ◽  
Destination Node ◽  
A Algorithm ◽  
Shortest Path Problems ◽  
Different Types ◽  
The Cost ◽  
Arc Lengths ◽  
Interval Valued

Many researchers have been proposing various algorithms to unravel different types of fuzzy shortest path problems. There are many algorithms like Dijkstra’s, Bellman-Ford,Floyd-Warshall and kruskal’s etc are existing for solving the shortest path problems. In this work a shortest path problem with interval valued neutrosophic numbers is investigated using the proposed algorithm. A* algorithm is extensively applied in pathfinding and graph traversal.Unlike the other algorithms mentioned above, A* algorithm entails heuristic function to uncover the cost of path that traverses through the particular state. In the structured work A* algorithm is applied to unravel the length of the shortest path by utilizing ranking function from the source node to the destination node. A* algorithm is executed by applying best first search with the help of this search, it greedily decides which vertex to investigate subsequently. A* is equally complete and optimal if an acceptable heuristic is concerned. The arc lengths in interval valued neutrosophic numbers are defuzzified using the score function. A numerical example is used to illustrate the proposed approach.

scholarly journals Modified artificial bee colony algorithm for solving mixed interval-valued fuzzy shortest path problem

2021 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Mohammad Enayattabr ◽  
Homayun Motameni ◽  
Harish Garg
Keyword(s):  
Shortest Path ◽  
Artificial Bee Colony ◽  
Fuzzy Numbers ◽  
Pso Algorithm ◽  
Convergence Time ◽  
Bee Colony ◽  
Different Types ◽  
Implementation Time ◽  
Fuzzy Network ◽  
Interval Valued

AbstractIn recent years, numerous researchers examined and analyzed several different types of uncertainty in shortest path (SP) problems. However, those SP problems in which the costs of arcs are expressed in terms of mixed interval-valued fuzzy numbers are less addressed. Here, for solving such uncertain SP problems, first a new procedure is extended to approximate the summation of mixed interval-valued fuzzy numbers using alpha cuts. Then, an extended distance function is introduced for comparing the path weights. Finally, we intend to use a modified artificial bee colony (MABC) algorithm to find the interval-valued membership function of SP in such mixed interval-valued fuzzy network. The proposed algorithm is illustrated via two applications of SP problems in wireless sensor networks and then the results are compared with those derived from genetic and particle swarm optimization (PSO) algorithms, based on three indexes convergence iteration, convergence time and run time. The obtained results confirm that the MABC algorithm has less convergence iteration, convergence time and implementation time compared to GA and PSO algorithm.

A novel approach for solving all-pairs shortest path problem in an interval-valued fuzzy network: Suggested modifications

2021 ◽  
pp. 1-18
Author(s):  
Tanveen Kaur Bhatia ◽  
Amit Kumar ◽  
S.S. Appadoo
Keyword(s):  
Shortest Path ◽  
Fuzzy Number ◽  
Fuzzy Systems ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Novel Approach ◽  
Shortest Distance ◽  
All Pairs Shortest Path ◽  
Fuzzy Network ◽  
Interval Valued

Enayattabr et al. (Journal of Intelligent and Fuzzy Systems 37 (2019) 6865– 6877) claimed that till now no one has proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems (all-pairs shortest path problems in which distance between every two nodes is represented by an interval-valued trapezoidal fuzzy number). Also, to fill this gap, Enayattabr et al. proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems. In this paper, an interval-valued trapezoidal fuzzy shortest path problem is considered to point out that Enayattabr et al.’s approach fails to find correct shortest distance between two fixed nodes. Hence, it is inappropriate to use Enayattabr et al.’s approach in its present from. Also, the required modifications are suggested to resolve this inappropriateness of Enayattabr et al.’s approach.

scholarly journals A MODIFIED GENETIC ALGORITHM FOR FINDING FUZZY SHORTEST PATHS IN UNCERTAIN NETWORKS

2016 ◽  
Vol XLI-B2 ◽  
pp. 299-304 ◽  
Author(s):  
A. A. Heidari ◽  
M. R. Delavar
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Shortest Paths ◽  
The Body ◽  
Shortest Path Problems ◽  
Conventional Procedure ◽  
Path Lengths ◽  
The Cost ◽  
Uncertain Networks ◽  
Exploration Exploitation

In realistic network analysis, there are several uncertainties in the measurements and computation of the arcs and vertices. These uncertainties should also be considered in realizing the shortest path problem (SPP) due to the inherent fuzziness in the body of expert's knowledge. In this paper, we investigated the SPP under uncertainty to evaluate our modified genetic strategy. We improved the performance of genetic algorithm (GA) to investigate a class of shortest path problems on networks with vague arc weights. The solutions of the uncertain SPP with considering fuzzy path lengths are examined and compared in detail. As a robust metaheuristic, GA algorithm is modified and evaluated to tackle the fuzzy SPP (FSPP) with uncertain arcs. For this purpose, first, a dynamic operation is implemented to enrich the exploration/exploitation patterns of the conventional procedure and mitigate the premature convergence of GA technique. Then, the modified GA (MGA) strategy is used to resolve the FSPP. The attained results of the proposed strategy are compared to those of GA with regard to the cost, quality of paths and CPU times. Numerical instances are provided to demonstrate the success of the proposed MGA-FSPP strategy in comparison with GA. The simulations affirm that not only the proposed technique can outperform GA, but also the qualities of the paths are effectively improved. The results clarify that the competence of the proposed GA is preferred in view of quality quantities. The results also demonstrate that the proposed method can efficiently be utilized to handle FSPP in uncertain networks.

A Lexicographic Approach to Fuzzy Linear Assignment Problems with Different Types of Fuzzy Numbers

2020 ◽  
Vol 28 (03) ◽  
pp. 421-441 ◽  
Author(s):  
Boris Pérez-Cañedo ◽  
Eduardo R. Concepción-Morales
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Multiple Criteria Decision Analysis ◽  
Assignment Problems ◽  
Solution Approach ◽  
Linear Assignment Problem ◽  
Different Types ◽  
Standard Solution ◽  
The Cost ◽  
Linear Assignment

The fuzzy linear assignment problem (FLAP) is an extension of the classical linear assignment problem (LAP) to situations in which uncertainty in the cost coefficients is represented by fuzzy numbers. FLAP applications range from the assignment of workers to tasks to multiple-criteria decision analysis in fuzzy environments and many other engineering applications. Most FLAP formulations assume that all cost coefficients are fuzzy numbers of the same type (e.g. triangular, trapezoidal). The standard solution approach is the defuzzification of the cost coefficients, thus transforming the FLAP into a crisp LAP that can be solved by classical assignment algorithms such as the Hungarian method. It is known that defuzzification methods suffer from lack of discrimination when comparing fuzzy numbers which may lead to suboptimal assignments. The solution approach proposed in this paper is based on the theory of algebraic assignment problems and total orderings in the set of all fuzzy numbers, and it allows to solve FLAPs with different types of fuzzy numbers. More specifically, the FLAP is transformed into a lexicographic linear assignment problem (LLAP) which is solved in its place. We show, both theoretically and numerically, how this transformation overcomes the limitations present in existing approaches.

A chance-constraint programming model with interval-valued pythagorean fuzzy constraints

2021 ◽  
pp. 1-17
Author(s):  
Muhammad Touqeer ◽  
Rimsha Umer ◽  
Muhammad Irfan Ali
Keyword(s):  
Fuzzy Sets ◽  
Constraint Programming ◽  
Fuzzy Numbers ◽  
Chance Constraint ◽  
Pythagorean Fuzzy Sets ◽  
Fuzzy Constraints ◽  
Network Problems ◽  
Chance Constraint Programming ◽  
Pythagorean Fuzzy Numbers ◽  
Interval Valued

Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets are more proficient in handling uncertain and imprecise information than intuitionistic fuzzy sets and fuzzy sets. In this article, we put forward a chance-constraint programming method to solve linear programming network problems with interval-valued Pythagorean fuzzy constraints. This practice is developed using score function and upper and lower membership functions of interval-valued Pythagorean fuzzy numbers. The feasibility of the anticipated approach is illustrated by solving an airway network application and shown to be used to solve different types of network problems with objective function having interval-valued Pythagorean fuzzy numbers by employing it on shortest path problem and minimum spanning tree problem. Furthermore, a comparative examination was performed to validate the effectiveness and usefulness of the projected methodology.

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