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

2020 ◽  
Vol 9 (2) ◽  
pp. 132-161 ◽  
Author(s):  
Ranjan Kumar ◽  
Sripati Jha ◽  
Ramayan Singh
Keyword(s):  
Linear Programming ◽  
Shortest Path ◽  
Path Length ◽  
Real Life ◽  
Shortest Path Problem ◽  
Fuzzy Linear Programming ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Membership Functions ◽  
Fuzzy Environment

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.

SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH MODIFIED S-CURVE MEMBERSHIP FUNCTION

2005 ◽  
Vol 13 (01) ◽  
pp. 97-109 ◽  
Author(s):  
PANDIAN M. VASANT
Keyword(s):  
Linear Programming ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Numerical Solutions ◽  
Real Life ◽  
Optimization Method ◽  
Fuzzy Linear Programming ◽  
Membership Functions ◽  
Linear Programming Problems ◽  
S Curve

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy resource variables and linear programming problems in which both the resource variables and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with modified s-curve membership functions. We propose here the modified s-curve membership function as a methodology for fuzzy linear programming and use it for solving these problems. We also compare the new proposed method with non-fuzzy linear programming optimization method. Finally, we provide real life application examples in production planning and their numerical solutions.

Type 2 Fully Fuzzy Linear Programming

2021 ◽  
Vol 10 (4) ◽  
pp. 37-56
Author(s):  
Mohamed El Alaoui
Keyword(s):  
Linear Programming ◽  
Real Life ◽  
Inequality Constraints ◽  
Fuzzy Linear Programming ◽  
Fuzzy Membership Function ◽  
Programming Approach ◽  
Life Problems ◽  
Comparative Results ◽  
Interval Type

Since its inception, fuzzy linear programming (FLP) has proved to be a more powerful tool than classical linear programming to optimize real-life problems dealing with uncertainty. However, the proposed models are partially fuzzy; in other words, they suppose that only some aspects can be uncertain, while others have to be crisp. Furthermore, the few methods that deal with fully fuzzy problems use Type 1 fuzzy membership function, while Type 2 fuzzy logic captures the uncertainty in a more suitable way. This work presents a fully fuzzy linear programming approach in which all parameters are represented by unrestricted Interval Type 2 fuzzy numbers (IT2FN) and variables by positive IT2FN. The treated comparative results show that the proposed achieves a better optimized function while permitting consideration of both equality and inequality constraints.

scholarly journals The Knowledge of Expert Opinion in Intuitionistic Fuzzy Linear Programming Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
A. Nagoorgani ◽  
J. Kavikumar ◽  
K. Ponnalagu
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Real Life ◽  
Fuzzy Linear Programming ◽  
Limited Resources ◽  
Fuzzy Data ◽  
Intuitionistic Fuzzy ◽  
Competing Demands ◽  
Intuitionistic Fuzzy Data

In real life, information available for certain situations is vague and such uncertainty is unavoidable. One possible solution is to consider the knowledge of experts on the parameters involved as intuitionistic fuzzy data. We examine a linear programming problem in which all the coefficients are intuitionistic in nature. An approach is presented to solve an intuitionistic fuzzy linear programming problem. In this proposed approach, a procedure for allocating limited resources effectively among competing demands is developed. An example is given to highlight the illustrated study.

Note on “Optimal path selection approach for fuzzy reliable shortest path problem”

2020 ◽  
Vol 39 (5) ◽  
pp. 7653-7656
Author(s):  
Ranjan Kumar ◽  
SA Edalatpanah ◽  
Hitesh Mohapatra
Keyword(s):  
Shortest Path ◽  
Fuzzy Systems ◽  
Optimal Path ◽  
Vital Role ◽  
Path Selection ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Fuzzy Environment ◽  
Selection Approach ◽  
Arc Lengths

There are different conditions where SPP play a vital role. However, there are various conditions, where we have to face with uncertain parameters such as variation of cost, time and so on. So to remove this uncertainty, Yang et al. [1] “[Journal of Intelligent & Fuzzy Systems, 32(1), 197-205”] have proposed the fuzzy reliable shortest path problem under mixed fuzzy environment and claimed that it is better to use their proposed method as compared to the existing method i.e., “[Hassanzadeh et al.; A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modeling, 57(2013) 84-99” [2]]. The aim of this note is, to highlight the shortcoming that is carried out in Yang et al. [1] article. They have used some mathematical incorrect assumptions under the mixed fuzzy domain, which is not true in a fuzzy environment.

scholarly journals Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 569
Author(s):  
Wu
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Optimal Solutions ◽  
Membership Functions ◽  
Fuzzy Decision ◽  
Existence Of Optimal Solutions ◽  
Decision Variables ◽  
Linear Programming Problems

The numerical method for solving the fuzzy linear programming problems with fuzzydecision variables is proposed in this paper. The difficulty for solving this kind of problem is thatthe decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative realnumbers. In other words, the decision variables are assumed to be membership functions. One of thepurposes of this paper is to derive the analytic formula of error estimation regarding the approximateoptimal solution. On the other hand, the existence of optimal solutions is also studied in this paper.Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

scholarly journals Routing Optimization Algorithms Based on Node Compression in Big Data Environment

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Lifeng Yang ◽  
Liangming Chen ◽  
Ningwei Wang ◽  
Zhifang Liao
Keyword(s):  
Big Data ◽  
Shortest Path ◽  
Optimization Algorithms ◽  
Real Life ◽  
Large Data ◽  
Path Selection ◽  
Shortest Path Problem ◽  
Limited Time ◽  
Starting Point ◽  
Data Environment

Shortest path problem has been a classic issue. Even more so difficulties remain involving large data environment. Current research on shortest path problem mainly focuses on seeking the shortest path from a starting point to the destination, with both vertices already given; but the researches of shortest path on a limited time and limited nodes passing through are few, yet such problem could not be more common in real life. In this paper we propose several time-dependent optimization algorithms for this problem. In regard to traditional backtracking and different node compression methods, we first propose an improved backtracking algorithm for one condition in big data environment and three types of optimization algorithms based on node compression involving large data, in order to realize the path selection from the starting point through a given set of nodes to reach the end within a limited time. Consequently, problems involving different data volume and complexity of network structure can be solved with the appropriate algorithm adopted.

CLASSIFICATIONS OF CREDIT CARDHOLDER BEHAVIOR BY USING FUZZY LINEAR PROGRAMMING

2004 ◽  
Vol 03 (04) ◽  
pp. 633-650 ◽  
Author(s):  
JING HE ◽  
XIANTAO LIU ◽  
YONG SHI ◽  
WEIXUAN XU ◽  
NIAN YAN
Keyword(s):  
Linear Programming ◽  
Portfolio Management ◽  
Credit Card ◽  
Real Life ◽  
Research Direction ◽  
Fuzzy Linear Programming ◽  
Research Topics ◽  
Score System ◽  
Main Research ◽  
Heuristic Classification

Behavior analysis of credit cardholders is one of the main research topics in credit card portfolio management. Usually, the cardholder's behavior, especially bankruptcy, is measured by a score of aggregate attributes that describe cardholder's spending history. In real-life practice, statistics and neural networks are the major players to calculate such a score system for prediction. Recently, various multiple linear programming-based classification methods have been promoted for analyzing credit cardholders' behaviors. As a continuation of this research direction, this paper proposes a heuristic classification method by using the fuzzy linear programming (FLP) to discover the bankruptcy patterns of credit cardholders. Instead of identifying a compromise solution for the separation of credit cardholder behaviors, this approach classifies the credit cardholder behaviors by seeking a fuzzy (satisfying) solution obtained from a fuzzy linear program. In this paper, a real-life credit database from a major US bank is used for empirical study which is compared with the results of known multiple linear programming approaches.

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