fuzzy number in assignment problem

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8 Method for solving intuitionistic fuzzy assignment problem

From the book soft computing.

• Laxminarayan Sahoo

The method to find an answer for assignment problem (AP) under intuitionistic fuzzy domain is proposed in this chapter. Due to the irregular rising and falling of the present market economy, here we have assumed that the assignment costs are not always fixed. Therefore, the assignment costs are imprecise in nature. In the existing literature, different approaches have been used, which are interval, fuzzy, stochastic, and fuzzy-stochastic approaches to represent the impreciseness. In this chapter, we have represented impreciseness taking intuitionistic fuzzy numbers (IFN). The proposed method is hinged on ranking of IFN and use of wellknown Hungarian method. Here, we have used a newly proposed centroid concept ranking method for IFNs. In this chapter, we have solved AP where costs for assignment are taken as triangular IFNs. A numerical example has been considered to derive the optimal result and also to adorn the applicability of the suggested method. In the end, concluding remarks and future research of the proposed approach have been presented.

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A New Method for Solving Fuzzy Assignment Problems

• P. Pandian , K. Kavitha
• Published 2012
• Computer Science, Mathematics

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10 Citations

An approach for solving fuzzyassignment problem using branch andbound technique.

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HAAR HUNGARIAN ALGORITHM TO SOLVE FUZZY ASSIGNMENT PROBLEM

A solution approach for a fully fuzzy assignment problem, an algorithm for solving assignment problems with costs as generalized trapezoidal intuitionistic fuzzy numbers, a simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers, 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, placement of staff in lic using fuzzy assignment problem, optimization of fuzzy bi-objective fractional assignment problem, trapezoidal neutrosophic assignment problem with new interval arithmetic costs, solving fuzzy linear fractional programming problem using lu decomposition method, 19 references, a new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, a labeling algorithm for the fuzzy assignment problem.

• Highly Influential

A two-objective fuzzy k -cardinality assignment problem

A primal method for the assignment and transportation problems, an algorithm for fractional assignment problems, fuzzy integer transportation problem, solution of assignment problem of restriction of qualification, an integer fuzzy transportation problem, interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: a case study, a fuzzy approach to the transportation problem, related papers.

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• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology

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DOI : 10.17485/ijst/2016/v9i20/88691

Year : 2016, Volume : 9, Issue : 20, Pages : 1-4

Original Article

Solving Fuzzy Assignment Problem using Ranking of Generalized Trapezoidal Fuzzy Numbers

P. Malini 1* and M. Ananthanarayanan 2

1 Department of Mathematics, Jeppiaar Engineering College, Chennai - 600119, India; [email protected]                                                                                                     2 Department of Mathematics, A. M. Jain College, Chennai - 600114, India; [email protected]

*Author for correspondence P. Malini Department of Mathematics, Jeppiaar Engineering College, Chennai - 600119, India; [email protected]  

Background/Objectives: The fuzzy optimal solution is totally based on ranking or comparing fuzzy numbers. Ranking fuzzy numbers play an vital role in decision making problems, data analysis and socio economics systems. The aim is to optimize the total cost of assigning all the jobs to the available persons. Ranking fuzzy number offers an powerful tool for handling fuzzy assignment problems. Methods/Statistical analysis: In this paper we used Hungarian method for solving fuzzy assignment problems using generalized trapezoidal fuzzy numbers. By using the ranking procedure we convert the fuzzy assignment problem to a crisp value assignment problem which then can be solved using Hungarian Method to find the fuzzy optimal solution. We presented the method which is not only simple in calculation but also gives better approximation and satisfactory results which is illustrated through the numerical examples. Findings: We propose a new ranking method which discriminates the fuzzy numbers where as few of the existing method fails to discriminates the fuzzy numbers. This method ranks all types of fuzzy numbers i.e. normal and generalized fuzzy numbers. Both triangular and trapezoidal fuzzy numbers). It is evident from the numerical examples that the proposed ranking measure for a fuzzy assignment problem is easy to compute and cost effective and gives much more optimal value. Applications/Improvements: The proposed ranking procedure can be applied in various decision making problems. This ranking method could also be used to solve other types of problems like game theory, project schedules, transportation problems. 

Keywords: Fuzzy Assignment Problem, Ranking Function, Trapezoidal Fuzzy Numbers

14 May 2020

How to cite this paper

Malini and Ananthanarayanan, Solving Fuzzy Assignment Problem using Ranking of Generalized Trapezoidal Fuzzy Numbers . Indian Journal of Science and Technology. 2016: 9(20);1-4

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Fuzzy Assignment problems

2020, Journal of science - Misurata

In this paper, we deal with solving a fuzzy Assignment Problem (FAP), in this problem C denotes the cost for assigning the n jobs to the n workers and C has been considered to be triangular fuzzy numbers. The Hungarian method is used for solving FAP by using ranking function for fuzzy costs. A numerical example is considered by incorporating a fuzzy numbers into the costs.

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iaeme iaeme

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To solve the problems of Engineering and Management Science Generalized Assignment Problem (GAP) plays a very important role. The GAP is a classical example of a difficult combinatorial optimization problem that has received considerable attention over the years due to its widespread applications. In many instances it appears as a substructure in more complicated models, including routing problems, facility location models, knapsack problems, computer networking applications etc. Recently, Fuzzy Generalized Assignment Problem (FGAP) became very popular because in real life, data may not be known with certainty. So, to consider uncertainty in real life situations fuzzy data instead of crisp data is more advantageous. In this paper, cost for assigning the j-th job to the i-th person is taken as triangular fuzzy numbers. Further we have put a restriction on the total available cost which makes the problem more realistic and general. The problem is solved by modified Fuzzy Extremum Diff...

K. Ruth Isabels

This paper presents an assignment problem with fuzzy costs, where the objective is to minimize the cost. Here each fuzzy cost is assumed as triangular or trapezoidal fuzzy number. Yager’s ranking method has been used for ranking the fuzzy numbers. The fuzzy assignment problem has been transformed into a crisp one, using linguistic variables and solved by Hungarian technique. The use of linguistic variables helps to convert qualitative data into quantitative data which will be effective in dealing with fuzzy assignment problems of qualitative nature. A numerical example is provided to demonstrate the proposed approach.

SRMS Journal of Mathmetical Science

Anju Khandelwal

The recruitment process in any departments or organizations is usually decided by traditional criteria. Lacking of theoretical basis, it is often difficult to achieve the desired result. In this paper we use triangular fuzzy number in delegation of recruitment process with the help of modified approach of assignment. For finding the optimal assignment, we make the balanced assignment problem, if unbalanced is given, then it is transformed into crisp assignment problem in linear programming by using the Robust’s ranking method. Finally the solution is obtained by modified method of assignment. This method is easier than the existing technique i.e. easier than the Hungarian Method and by this approach the numbers of iterations are reduced so that time taken by this method is less than the Hungarian method

Journal of the Operational Research Society

anchal choudhary

I n the literature, there are various methods to solve assignment problems in which parameters are represented by triangular or trapezoidal fuzzy numbers. This paper presents an assignment problem with fuzzy costs, where the objective is to minimize the cost. Here each fuzzy cost is assumed as trapezoidal fuzzy number. A new ranking method has been used for ranking the fuzzy trapezoidal numbers. The fuzzy assignment problem has been transformed into a crisp one using ranking function and solved by branch and bound method. A numerical example is provided to demonstrate the proposed approach.

Applied Mathematical Modelling

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY

Anil Gotmare

In this paper Branch and bound technique is applied to assignment problem with fuzzy cost with objective to minimise cost, fuzzy cost is assumed as triangular fuzzy number, Yager’s ranking method has been used for ranking the fuzzy numbers, after transforming assignment problem into a crisp one using linguistic variables, assignment problem is solved by branch and bound technique. To deal with fuzzy assignment problem with qualitative data, linguistic variable helps to convert qualitative data into quantitative data.

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Optimal Solution for Fuzzy Assignment Problem and Applications

• Conference paper
• First Online: 17 October 2019
• Cite this conference paper

• Sanjivani M. Ingle 18 &
• Kirtiwant P. Ghadle 18  

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1025))

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Assignment problem is the biggest significant problem in decision-making. In this paper, a novel technique is planned to discover the best possible solution to a balanced fuzzy assignment problem (FAP). We derive two formulae; one is related to the odd number of fuzzy numbers and another is related to the even number of fuzzy numbers to discover better answer from the existing answer to the FAP. Proposed technique give the best possible solution to balanced FAP in the fewer number of iteration than existing techniques. An algebraic illustration is specified to authenticate the process of proposed technique which is based on industrial environment and education domain.

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Ingle, S.M., Ghadle, K.P. (2020). Optimal Solution for Fuzzy Assignment Problem and Applications. In: Iyer, B., Deshpande, P., Sharma, S., Shiurkar, U. (eds) Computing in Engineering and Technology. Advances in Intelligent Systems and Computing, vol 1025. Springer, Singapore. https://doi.org/10.1007/978-981-32-9515-5_15

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Fuzzy multi-objective, multi-period integrated routing–scheduling problem to distribute relief to disaster areas: a hybrid ant colony optimization approach.

1. Introduction

2. literature review, 2.1. multi-period relief distribution, 2.2. multi-objective relief distribution, 2.3. relief distribution with the uncertain problem, 3. fuzzy multi-objective multi-period integer programming model.

• Limited number of periods is given;
• Number of depots is fixed;
• Heterogeneous fleet of vehicles is available;
• Capacity of vehicles is predetermined;
• Demand of each customer in each period is specified as a fuzzy parameter;
• Number of customers that should be serviced in each period is defined;
• Customers of each period are different from those of other periods;
• Distance-dependent transportation costs are assumed;
• Each vehicle starts its journey from one depot and ends at another depot, although the starting and ending depots could be also be identical;
• Symmetric transportation network is considered;
• Traversing cost and customer’s demand are considered as fuzzy parameters.

4. Hybrid Multi-Objective Ant Colony System and Simulated Annealing Algorithm

4.1. pheromone structure, 4.2. heuristic information, 4.3. quasi-random probability rule, 4.4. pheromone update, 5. numerical results, 6. conclusions and future directions, author contributions, data availability statement, conflicts of interest.

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Niksirat, M.; Saffarian, M.; Tayyebi, J.; Deaconu, A.M.; Spridon, D.E. Fuzzy Multi-Objective, Multi-Period Integrated Routing–Scheduling Problem to Distribute Relief to Disaster Areas: A Hybrid Ant Colony Optimization Approach. Mathematics 2024 , 12 , 2844. https://doi.org/10.3390/math12182844

Niksirat M, Saffarian M, Tayyebi J, Deaconu AM, Spridon DE. Fuzzy Multi-Objective, Multi-Period Integrated Routing–Scheduling Problem to Distribute Relief to Disaster Areas: A Hybrid Ant Colony Optimization Approach. Mathematics . 2024; 12(18):2844. https://doi.org/10.3390/math12182844

Niksirat, Malihe, Mohsen Saffarian, Javad Tayyebi, Adrian Marius Deaconu, and Delia Elena Spridon. 2024. "Fuzzy Multi-Objective, Multi-Period Integrated Routing–Scheduling Problem to Distribute Relief to Disaster Areas: A Hybrid Ant Colony Optimization Approach" Mathematics 12, no. 18: 2844. https://doi.org/10.3390/math12182844

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