scholarly journals Solving Fuzzy Assignment Problems with Hexagonal Fuzzy Numbers by using Diagonal Optimal Algorithm

2019 ◽  
Vol 9 (1) ◽  
pp. 54-57
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Optimal Algorithm ◽  
Subject Classification ◽  
Assignment Problems ◽  
Optimal Method ◽  
Numerical Examples ◽  
Ranking Technique

In this article, an approach involving diagonal optimal method has been proposed to solve Hexagonal fuzzy assignment problem(HxFAP). To order the hexagonal fuzzy numbers Yager’s Ranking technique is applied. To understand the algorithm two numerical examples are illustrated.Mathematics Subject Classification: 90C08, 90C70, 90B06, 90C29, 90C90.

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.

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.

scholarly journals An Interpretation of Non-Preemptive Priority Fuzzy Queuing Model with Asymmetrical Service Rates

2021 ◽  
pp. 791-797
Author(s):  
Usha Prameela Karupothu ◽  
Richard Wurmbrand ◽  
R P S Jayakar
Keyword(s):  
Performance Measures ◽  
Fuzzy Numbers ◽  
Arrival Rate ◽  
Service Rate ◽  
Preemptive Priority ◽  
Queuing Model ◽  
Numerical Examples ◽  
Cut Method ◽  
Service Rates ◽  
Ranking Technique

This  paper presents Non-Preemptive  priority fuzzy queuing model with asymmetrical service rates. Arrival rate and  service rate are taken to be hexagonal, heptagonal, and octagonal fuzzy numbers. Here an interpretation  is given to determine the performance measures by applying a new  ranking technique through which the fuzzy values are reduced to the crisp values. This ranking technique has the benefit of being precise and relevant compared to other methods such as alpha-cut method and LR method. The main intention is to evaluate the fuzziness before the performance measures are processed by utilizing the regular queueing hypothesis. Three numerical examples are exhibited to show the validity implementation of the methodology.

scholarly journals An Approach to solve Hexagonal Fuzzy Assignment Problem using Modified Best Candidate Method and Comparative Study with Existing Methods

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 208-221
Author(s):  
M Maragatham ◽  
◽  
Suzane Raj L ◽  
Keyword(s):  
Comparative Study ◽  
Assignment Problem ◽  
Fuzzy Numbers ◽  
New Method ◽  
Optimal Solutions ◽  
Numerical Example ◽  
Systematic Procedure ◽  
Fuzzy Cost ◽  
Ranking Technique

The objective of fuzzy assignment problem is to find the least assignment fuzzy cost (maximum fuzzy profit) of workers with varying degree of skills to job. To attain the objective in this article, an approach involving modified best candidate method has been used to solve Hexagonal fuzzy assignment problem. To order the hexagonal fuzzy numbers Robust’s Ranking technique is applied. We examine a numerical example by using new method and compute by existing two methods. Also we compare the optimal solutions among this new method and two existing method .The proposed method is a systematic procedure, easy to apply for solving fuzzy assignment problem.

scholarly journals Random Assignment Problems on 2d Manifolds

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  
Keyword(s):  
Assignment Problem ◽  
Unit Area ◽  
Constant Term ◽  
Beltrami Operator ◽  
Explicit Calculation ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Random Assignment ◽  
Assignment Problems ◽  
Theoretical Formulation

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.

A Determinant Elimination Method for Bottleneck Assignment and Generalized Assignment Problems

2012 ◽  
Vol 239-240 ◽  
pp. 1522-1527
Author(s):  
Wen Bo Wu ◽  
Yu Fu Jia ◽  
Hong Xing Sun
Keyword(s):  
Computational Complexity ◽  
Optimization Algorithm ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
High Efficiency ◽  
Synthesis Method ◽  
Assignment Problems ◽  
Generalized Assignment ◽  
The Cost ◽  
Time And Space Complexity

The bottleneck assignment (BA) and the generalized assignment (GA) problems and their exact solutions are explored in this paper. Firstly, a determinant elimination (DE) method is proposed based on the discussion of the time and space complexity of the enumeration method for both BA and GA problems. The optimization algorithm to the pre-assignment problem is then discussed and the adjusting and transformation to the cost matrix is adopted to reduce the computational complexity of the DE method. Finally, a synthesis method for both BA and GA problems is presented. The numerical experiments are carried out and the results indicate that the proposed method is feasible and of high efficiency.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

Computationally Simple and Efficient Method for Solving Real-Life Mixed Intuitionistic Fuzzy 3D Assignment Problems

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Assignment Problem ◽  
Graphical Representation ◽  
Real Life ◽  
Optimal Solution ◽  
Future Research ◽  
Assignment Problems ◽  
3 Dimensional ◽  
Intuitionistic Fuzzy ◽  
Comparison Results ◽  
Future Research Directions

This article addresses the 3-dimensional mixed intuitionistic fuzzy assignment problems (3D-MIFAPs). In this article, firstly, the author formulates an assignment problem (AP) and assumes the parameters are in uncertainty with hesitation. Secondly, based on the nature of the parameter the author defines various types of solid assignment problem (SAP) in uncertain environment. Thirdly, to solve 3D-MIFAP the PSK method for finding an optimal solution of fully intuitionistic fuzzy assignment problem (FIFAP) is extended by the author. Fourthly, the author presents the proofs of the proposed theorems and corollary. Fifthly, the proposed approach is illustrated with three numerical examples and the optimal objective value of 3D-MIFAP is obtained in the form of intuitionistic fuzzy number and the solution is checked with MATLAB and their coding are also given by the author. Sixthly, the author presents the comparison results and their graphical representation, merits and demerits of the proposed and existing methods and finally the author presents conclusion and future research directions.

A Study on Optimum Design Using Fuzzy Numbers As Design Variables

1995 ◽  
Author(s):  
Masao Arakawa ◽  
Hiroshi Yamakawa
Keyword(s):  
Fuzzy Sets ◽  
Optimum Design ◽  
Fuzzy Numbers ◽  
Fuzzy Optimization ◽  
Design Parameters ◽  
Numerical Examples ◽  
Design Variables ◽  
Conventional Methods

Abstract In this study, we summerize the method of fuzzy optimization using fuzzy numbers as design variables. In order to detect flaw in fuzzy calculation, we use LR-fuzzy numbers, which is known as its simplicity in calculation. We also use simple fuzzy numbers’ operations, which was proposed in the previous papers. The proposed method has unique characteristics that we can obtain fuzzy sets in design variables (results of the design) directly from single numerical optimizing process. Which takes a large number of numerical optimizing processes when we try to obtain similar results in the conventional methods. In the numerical examples, we compare the proposed method with several other methods taking imprecision in design parameters into account, and demonstrate the effectiveness of the proposed method.

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