scholarly journals Using Interval Operations in the Hungarian Method to Solve the Fuzzy Assignment Problem and Its Application in the Rehabilitation Problem of Valuable Buildings in Egypt

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
M. A. Elsisy ◽  
A. S. Elsaadany ◽  
M. A. El Sayed
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Original Function ◽  
Fuzzy Environment ◽  
Order Relations ◽  
Hungarian Method ◽  
The Social ◽  
Optimum Solution ◽  
Methods Numerical

Assignment problem (AP) is an entrenched tool for solving engineering and management problems. The Hungarian method is always used to fathom the AP in crisp cases. This paper presents an algorithm of finding the optimum solution of the fuzzy AP by using the modified Hungarian method. This method is utilized to get a minimum assignment cost in the fuzzy environment for a fuzzy AP. Firstly, we use the fuzzy numbers without any transformation. Secondly, the fuzzy AP is transformed into an interval AP based on the α-cut methodology. Then, the interval arithmetic operations and the order relations are applied to get the optimal solution by utilizing the modified Hungarian method. The proposed algorithm requires less efforts and time to reach optimality, compared to the existing methods. Numerical examples are given to ensure the efficiency and the validity of the proposed algorithm. A study on the reuse of many valuable buildings is presented after using different government and service buildings in a manner that does not fit with its original function and heritage value. We offer a solution based on the scientific and realistic basis for requalification according to the variables and requirements of the social, cultural, and economic environments in the environment surrounding the valuable buildings.

A Study on Cooperative Continuous Static Games without Differentiability under Fuzzy Environment

2022 ◽  
Vol 11 (1) ◽  
pp. 0-0
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Concept ◽  
Proper Understanding ◽  
Fuzzy Environment ◽  
The Stability ◽  
The Right ◽  
The Cost ◽  
Stability Sets ◽  
Fuzzy Parameters

In this study, a fuzzy cooperative continuous static game (PQFCCSG) with n players having fuzzy parameters in all of the cost functions and the right- hand-side of constraints is characterized. Their fuzzy parameters are represented by piecewise quadratic fuzzy numbers. The α-pareto optimal solution concept is specified. In addition, the stability sets of the first and second kind without differentiability are conceptualized and established. An illustrated numerical example is discussed for proper understanding and interpretation of the proposed concept.

A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

2018 ◽  
Vol 15 (01) ◽  
pp. 95-112 ◽  
Author(s):  
Abhishekh ◽  
A. K. Nishad
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Ranking Functions ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

scholarly journals Group Replacement Strategy under Fuzzy Methods

2019 ◽  
Vol 9 (1S5) ◽  
pp. 250-254
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Active Role ◽  
Replacement Policy ◽  
Replacement Strategy ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Methods ◽  
Fuzzy Environment

Intuitionistic Fuzzy Numbers play an active role in finding an optimal solution for replacement problems under vague and uncertain situations. This paper gives a group replacement policy under fuzzy environment. Here all the costs and the number of units are taken as Triangular Intuitionistic Fuzzy Numbers (TIFNs). An example is used for illustration of the policy

Trapezoidal fuzzy model to optimize transportation problem

2016 ◽  
Vol 07 (03) ◽  
pp. 1650028 ◽  
Author(s):  
Nirbhay Mathur ◽  
Pankaj Kumar Srivastava ◽  
Ajit Paul
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Model ◽  
Optimal Solution ◽  
Transportation Cost ◽  
New Method ◽  
Trapezoidal Fuzzy Numbers ◽  
North West ◽  
Fuzzy Environment ◽  
Practical Usefulness

The main aim of this paper is to develop an approach based on trapezoidal fuzzy numbers to optimize transportation problem in fuzzy environment. The present algorithm has representation of availability, demand and transportation cost as trapezoidal fuzzy numbers. This algorithm is found quicker in terms of runtime as comparison to fuzzy VAM discussed in [Kaur A., Kumar A., A new method for solving fuzzy transportation problem using ranking function, Appl. Math. Model. 35:5652–5661, 2011; Ismail Mohideen S., Senthil Kumar P., A comparative study on transportation problem in fuzzy environment, Int. J. Math. Res. 2:151–158, 2010]. On the other hand this technique gives much better results than some classical methods like north-west corner and least cost method. Another benefit of this algorithm is that for certain transportation problems it directly gives optimal solution. It is one of the simplest methods to apply and perceive. Practical usefulness of the new method over other existing methods is demonstrated with two numerical examples.

scholarly journals Optimization of Inventory Model-Cost Parameters, Inventory and Lot Size as Fuzzy Numbers

2020 ◽  
Vol 10 (1) ◽  
pp. 365-368
Keyword(s):  
Fuzzy Numbers ◽  
Analytic Solution ◽  
Unit Cost ◽  
Optimal Solution ◽  
Inventory Model ◽  
Lot Size ◽  
Fuzzy Environment ◽  
Demand Rate ◽  
Cost Parameters ◽  
Fuzzy Parameters

In general, the demand rate and the unit cost of the items remains constant inspite of lot size in inventory models. But in reality, the demand rate and the unit cost of the items are connected together. In this research, demand dependent unit cost inventory model is considered where different cost parameters, maximum inventory and the lot size of the model are taken under fuzzy environment. First an analytic solution of the crisp model is obtained by the method of calculus where the inventory parameters are exact and deterministic. Later, the problem is developed with fuzzy parameters where inaccuracy has been introduced through triangular membership function.Then the defuzzification of the model is done by using the method of Graded mean integration. An optimal solution is obtained using Karush Kuhn-Tucker conditions approach. An illustrative model is done and an analysis of total cost for different measures of possibility are performed and tabulated.

scholarly journals ANALISIS SENSIVITAS MODEL PENUGASAN DENGAN METODE HUNGARIAN

2021 ◽  
Vol 10 (1) ◽  
pp. 41
Author(s):  
ELFRIDA RIANI TSANI ◽  
NI KETUT TARI TASTRAWATI ◽  
KARTIKA SARI
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Assignment Problem ◽  
Optimal Solution ◽  
Working Time ◽  
Optimal Decision ◽  
Optimal Decisions ◽  
Hungarian Method

In linear programming the assignment problem can be solved by the Hungarian method. This method produces an optimal solution for the placement of employees on their assignments. The purpose of this research is to determine the sensitivity analysis of the optimal results from the assignment that has been obtained by the Hungarian Method. Sensitivity analysis is used to determine the extent to which changes can occur without changing the optimal decisions that have been obtained. The results of this research obtain interval working time that can be tolerated without changing the optimal decision that has been obtained. So, no matter how much working time of the Employee changes, as long as the change is still within the interval, it does not interfere with the optimal solution that has been obtained previously.

Decision Making Approach to Fuzzy Linear Programming (FLP) Problems with Post Optimal Analysis

2015 ◽  
Vol 6 (4) ◽  
pp. 75-90 ◽  
Author(s):  
Monalisha Pattnaik
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Fuzzy Decision ◽  
Optimal Analysis ◽  
Fuzzy Environment ◽  
Multi Objective Programming ◽  
Decision Variables ◽  
Ranking Technique

This paper finds solutions to the fuzzy linear program where some parameters are fuzzy numbers. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi objective programming methods. Unfortunately all these methods have shortcomings. In this paper, using the concept of comparison of fuzzy numbers, the author introduces a very effective method for solving these problems. This paper extends linear programming based problem in fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the simplex based method. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. The model is illustrated with an application and a post optimal analysis approach is obtained. The proposed procedure was programmed with MATLAB (R2009a) version software, the four dimensional slice diagram is represented to the application. Finally, numerical example is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights.

scholarly journals Application of Fuzzy Optimization Problem in Fuzzy Environment

2015 ◽  
Vol 62 (2) ◽  
pp. 119-125
Author(s):  
Shapla Shirin ◽  
Kamrunnahar
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Optimization Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Daily Life ◽  
Fuzzy Optimization ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Environment ◽  
Optimum Solution

In this paper application of optimization problem has been introduced which belong to fuzzy environment. An attempt has been taken to find out a suitable option in order to obtain the optimum solutions of optimization problems in fuzzy environment. Optimum solutions of the proposed optimization problem computed by using three methods, such as Bellman-Zadeh’s method, Zimmerman’s Method, and Fuzzy Version of Simplex method, are compared to each other. In support of that the three algorithms of the above three methods have been reviewed. However, the main objective of this paper is to focus on the appropriate method and how to achieve good enough or optimum solution of linear programming using triangular fuzzy numbers with equal widths because of complex and undefined situations in our daily life. DOI: http://dx.doi.org/10.3329/dujs.v62i2.21976 Dhaka Univ. J. Sci. 62(2): 119-125, 2014 (July)

scholarly journals Implementation of Modified Best Candidate Method in Fuzzy Assignment Problem

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 196-207
Author(s):  
M Maragatham ◽  
◽  
Suzane Raj L ◽  
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
The Other ◽  
Limited Time ◽  
Assignment Problems ◽  
Trapezoidal Fuzzy Numbers ◽  
Ranking Of Fuzzy Numbers ◽  
Ranking Technique

To meet the demands of every customer by supplying the products at the limited time by maximizing the profit is a dream for many companies. By choosing the best candidate among the other candidates and effectively reaching the optimal solution with a new modified approach using Best Candidate Method in Fuzzy assignment problems. In this paper the author solve Fuzzy assignment problem in which Triangular and Trapezoidal fuzzy numbers are used. Robust Ranking Technique is used for the ranking of fuzzy numbers.

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