Fuzzy Assignment Problem Research Articles

Optimization techniques of Assignment Problem using Trapezoidal Intuitionistic Fuzzy Numbers and Interval Arithmetic

This paper discusses the Assignment problem to optimize the assigning of jobs to workers based on their talents and efficiency. In general, scheduling jobs plays a significant role in manufacturing and is advantageous in real world applications as we face more uncertainty and ambiguity in assigning jobs. The Intuitionistic Fuzzy Assignment problem (IFAP) is employed in circumstances when decision-makers have to deal with uncertainty. The domains are Trapezoidal Intuitionistic Fuzzy Numbers (TrIFNs) and the techniques used are Hungarian Method (HM), Brute Force Method (BFM), and Greedy Method (GM). The suggested model's performance is compared with the existing approach with the help of interval arithmetic operations. Allocating work to the individual is illustrated numerically, the optimal solution of minimizing cost is obtained using R programming and the results of comparative analysis are shown diagrammatically that help viewers to easily understand and generate results from comparisons.

Solving fuzzy assignment problem using nonagonal fuzzy numbers in root mean square method

Assignment Problem is universally used to solve real valued problems. In this paper, the values of the Fuzzy Assignment Problem are considered as nonagonal fuzzy numbers. First the fuzzy numbers are converted into crisp values using Root mean square method. Then the optimum schedule of the Fuzzy Assignment Problem is obtained by usual Hungarian Method. This approach is illustrated by numerical example.

Solving Fuzzy Assignment Problem of Pythagorean Fuzzy Numbers Exploiting a Software Tool

A fresh approach to computing assignment issues in the pythagorean fuzzy domain is the focus of this body of work. Pythagorean fuzzy numbers are utilised in this work for the sake of analysing working hours and working costs. For converting fuzzy sets integers into a crisp number, a new ranking process is used. Optimal solutions have to be found by using software techniques for minimization, maximization and unbalanced assignment problems. In the end, numerical examples are being solved by using the proposed technique.

Solving the trapezoidal fuzzy assignment problem using the novel Dhouib-Matrix-AP1 heuristic

The assignment problem is a famous problem in combinatorial optimization where several objects (tasks) are assigned to different entities (workers) with the goal of minimizing the total assignment cost. In real life, this problem often arises in many practical applications with uncertain data. Hence, this data (the assignment cost) is usually presented as fuzzy numbers. In this paper, the assignment problem is considered with trapezoidal fuzzy parameters and solved using the novel Dhouib-Matrix-AP1 (DM-AP1) heuristic. In fact, this research work presents the first application of the DM-AP1 heuristic to the fuzzy assignment problem, and a step-by-step application of DM-AP1 is detailed for more clarity. DM-AP1 is composed of three simple steps and repeated only once in n iterations. Moreover, DM-AP1 is enhanced with two techniques: a ranking function to order the trapezoidal fuzzy numbers and the min descriptive statistical metric to navigate through the research space. DM-AP1 is developed under the Python programming language and generates a convivial assignment network diagram plan.

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

This article addresses the three-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 environments. 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, a conclusion and future research directions.

Allocation of Subjects in an Educational Institution by Pascal Triangular Approach

The classical assignment problems cannot be successfully used for the real-world situation it is because the work efficiency varies to some extent from person to person hence, the use of fuzzy assignment problems is more appropriate. Based on the performance of the previous record in this study, on taking the scores obtained by the Chairman, by Course Director, by faculty members, and the student’s feedback, we applied Pascal triangular approach in fuzzy assignment problem for allocating the subjects in a department of coming semester. A study of the technique for 4 jobs and 4 persons has been made.

One’s Fixing Method for a Distinct Symmetric Fuzzy Assignment Model

This paper hinges upon the subject of an (n × n) assignment problem and the distinct symmetric fuzzy assignment problem byassigning n machines to n jobs. One’s orientation algorithm is developed for solving the assignment problems based on the position of one’s chosen in every row as well as every column to perform allocations and obtain the assignment cost at every (n − 1) reduced matrix. We also extended the two different symmetric concept to the problem to find the optimum solution based on symmetrical data and also used the ranking concept in our fuzzy assignment problem. In this proposed algorithm, the one’s position is associated with the successor of one in each iteration toobtain the optimal schedule and assignment cost. The comparative analysis is properly considered and discussed. The proposed technique is elaborated with the help of numerical computations and it gives clarity to the idea of this concept.

AN OPTIMAL SOLUTION OF NONAGONAL FUZZY ASSIGNMENT PROBLEM USING AVERAGE RANKING METHOD

The specific case of transportation problem is an assignment problem. The goal of optimal assignment is assign equal number of task to equal number of persons with a minimum cost (time) or maximum profit (sales). In fuzzy assignment problem, the distance (time) are fuzzy values. In this article, a new ranking procedure proposed for ranking the nonagonal fuzzy numbers. The best solution of the nonagonal fuzzy assignment problem is obtained from proposed ranking technique which is compared with existing solution

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

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.

Implementation of Modified Best Candidate Method in Fuzzy Assignment Problem

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.

Using the Geometric Mean Method to Finding the Optimal Solution for the Unbalanced Fuzzy Assignment Problem with Practical Application

Using the Geometric Mean Method to Finding the Optimal Solution for the Unbalanced Fuzzy Assignment Problem with Practical Application

Comparison of effectiveness of models for solvingfuzzy assignment problem

The task of assigning particular task to a particular person can be solved using assignment problem. If the problem is considered under fuzzy environment, then uncertainty can be minimized which is usually involved in human complex problem. There are various modelsfor solving fuzzy assignment problem. In this paper, the triangular fuzzy assignment problem is formulated. It is then solved by the fuzzy Hungarian method, Hungarian and direct method. The results are obtained and comparison of optimal solution among these methods is done for the effectiveness of the method. The method is illustrated by numerical example based on real life data.

Novel Fuzzy Assignment Problem Using Hexagonal Fuzzy Numbers

In this paper, a hexagonal fuzzy assignment problem employing a fuzzy new ranking technique is applied. This method requires less number of iterations to succeed in an optimality solution compared to the prevailing methods. Numerical examples show the effectiveness of the proposed fuzzy hexagonal assignment problem.

A NOVEL APPROACH FOR THE SOLUTION OF GENERALIZED FUZZY ASSIGNMENT PROBLEM

In engineering and other fields, generalised assignment problem plays a vital role. It has widespread applications in routing problems, knapsack problems and other complicated models. In real world problems, the available data may not be known with certainty. Hence to model and solve practical problems, we must deal with uncertainty and vagueness. Fuzzy sets play a vital role to tackle these uncertainty and vagueness. The generalised fuzzy assignment problem became popular and has gained its importance too. In this paper, we consider a generalised fuzzy assignment problem which has restrictions both on tasks and on persons with respect to his/her efficiency/qualification. We propose a unique approach for the solution of generalised fuzzy assignment problem with restrictions without converting the problem to a corresponding crisp form. Costs for handling jth task by the ith person are taken to be trapezoidal fuzzy numbers. The trapezoidal fuzzy numbers are first represented in its parametric form. In view of the decision maker's preference, a new ranking method and arithmetic operations are used to bring a desirable solution. A numerical example is given to illustrate the proposed method.

A novel approach for the solution of generalised fuzzy assignment problem

A novel approach for the solution of generalised fuzzy assignment problem

Assignment and Travelling Salesman Problems with Coefficients as LR Fuzzy Parameters

Mukherjee and Basu (Application of fuzzy ranking method for solving assignment problems with fuzzy costs, International Journal of Computational and Applied Mathematics, 5, 2010, 359-368) proposed a new method for solving fuzzy assignment problems. In this paper, some fuzzy assignment problems and fuzzy travelling salesman problems are chosen which cannot be solved by using the fore-mentioned method. Two new methods are proposed for solving such type of fuzzy assignment problems and fuzzy travelling salesman problems. The fuzzy assignment problems and fuzzy travelling salesman problems which can be solved by using the existing method, can also be solved by using the proposed methods. But, there exist certain fuzzy assignment problems and fuzzy travelling salesman problems which can be solved only by using the proposed methods. To illustrate the proposed methods, a fuzzy assignment problem and a fuzzy travelling salesman problem is solved. The proposed methods are easy to understand and apply to find optimal solution of fuzzy assignment problems and fuzzy travelling salesman problems occurring in real life situations.

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

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 solution approach for a fully fuzzy assignment problem

We solve a fully fuzzy assignment problem (FAP) where the costs are triangular fuzzy numbers. The FAP has gained its importance in the recent years. We have represented the fuzzy numbers in their parametric form and then solved it through ones assignment method. To the best of our knowledge, several authors have acquired the solution for a FAP by converting the problem to its crisp form. We have proposed an algorithm where we have used our ranking method and arithmetic operations to obtain a desirable solution without converting to an equivalent crisp form. The solution we acquired is represented in terms of location index and fuzziness index functions which enables the decision maker to decide his/her preference of solution. An example is given to explain the proposed methodology.

A new approach for optimality of fully fuzzy assignment problems

In this paper, we developed an efficient approach for the solution of fully fuzzy assignment problems involving imprecise information without transforming to equivalent precise form. Here, the imprecise information are represented as triangular fuzzy numbers and optimal solution is obtained applying branch and bound method and a new type of arithmetic operations, ranking on triangular fuzzy numbers. The proposed method is validated using a real life numerical example.

ON OPTIMAL SOLUTION OF FUZZY ASSIGNMENT PROBLEM WITH RANKING METHODS

ON OPTIMAL SOLUTION OF FUZZY ASSIGNMENT PROBLEM WITH RANKING METHODS