fuzzy number in assignment problem

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A solution approach for a fully fuzzy assignment problem

E. Melita Vinoliah 1 and K. Ganesan 1

Published under licence by IOP Publishing Ltd IOP Conference Series: Materials Science and Engineering , Volume 912 , Multidisciplinary Citation E. Melita Vinoliah and K. Ganesan 2020 IOP Conf. Ser.: Mater. Sci. Eng. 912 062046 DOI 10.1088/1757-899X/912/6/062046

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1 Department of Mathematics, Faculty of Engineering & Technology, SRM institute of science & Technology, Kattankulathur–603 203, Chennai, Tamilnadu, India.

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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.

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• DOI: 10.12988/AMS.2013.34228
• Corpus ID: 125542518

Fuzzy Assignment Problem with Generalized Fuzzy Numbers

• Y. Thorani , N. R. Shankar
• Published 2013
• Mathematics, Computer Science
• Applied mathematical sciences

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34 Citations

A new approach for solving balanced and/or unbalanced intuitionistic fuzzy assignment problems, new algorithm for solving mixed intuitionistic fuzzy assignment problem, an algorithm for solving assignment problems with costs as generalized trapezoidal intuitionistic fuzzy numbers, a method for finding an optimal solution of an assignment problem under mixed intuitionistic fuzzy environment, a method for solving balanced intuitionistic fuzzy assignment problem, on solving fuzzy assignment problem based on distance method for ranking of generalized trapezoidal fuzzy numbers using centroid of incenters and an index of modality, an approach for solving fuzzyassignment problem using branch andbound technique, fuzzy optimal solution for a fuzzy assignment problem with octagonal fuzzy numbers, a new ranking method for solving hexadecagonal fuzzy assignment problem, an algorithm for solving unbalanced intuitionistic fuzzy assignment problem using triangular intuitionistic fuzzy number, 25 references, a labeling algorithm for the fuzzy assignment problem, fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads, fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, a fuzzy vehicle routing assignment model with connection network based on priority-based genetic algorithm, fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm, a new method for handling multicriteria fuzzy decision-making problems using fn-iowa operators, solution method for fuzzy assignment problem with restriction of qualification, a two-objective fuzzy k -cardinality assignment problem, ordering generalized trapezoidal fuzzy numbers using orthocentre of centroids.

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An extended assignment problem considering multiple inputs and outputs

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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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• 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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'Ludicrous': Donors leave call with Kamala Harris frustrated and annoyed

PROVINCETOWN, Mass. — A call Friday featuring Vice President Kamala Harris and about 300 major Democratic donors left many who dialed in frustrated, with one donor declaring it “ludicrous” shortly before it ended, according to two sources familiar with the call.

One person on the call referred to it as “mismanaged” and “rushed.” They added expectations had not been managed well and some participants left feeling admonished.

That person and two other sources said many donors joined hoping to get an insider’s view of how to move forward in the wake of President Joe Biden’s dismal debate performance and the growing number of Democrats calling for him to drop out of the race. Instead, they said donors left the call feeling disappointed and like they had not gained any new insights or helpful information.

“It was a total failure,” said one source who was on the call and who spoke on the condition of anonymity to provide a candid assessment. “It was damaging. It was poor planning.”

The call had been organized by Jen O’Malley Dillon, the chair of Biden’s campaign, and not by the campaign’s finance team, according to a source familiar with the planning. One of the sources who was on the call said the donors who participated represented a wide range of views — some die-hard Biden fans, some unconvinced about his path forward and many views in between.

At the end of the call, hundreds of participants were unmuted, and one person declared that the call was “ludicrous,” according to two of the sources.

One source stressed that they took the comment to mean that the call was poorly run and not as a criticism of Harris.

During the call, Harris, who was asked to join the call by Biden’s senior advisers, praised Biden, according to campaign officials.

“We know which candidate in this election puts the American people first: our president, Joe Biden,” she said, according to the campaign officials. “With every decision he makes in the Oval Office, he thinks about how it will impact working Americans. And I witness it every day.”

Harris also spoke positively about Democrats’ chances of beating former President Donald Trump. “Something I believe in my heart of hearts,” Harris said, according to campaign officials. “It is something I feel strongly you should all hear and should take with you when you leave. And tell your friends too. We are going to win this election. We are going to win.”

NBC News reached out to the Biden campaign for comment.

The fallout from the call comes as donations to the Biden-Harris campaign and Democratic groups have plummeted and as Harris has been deployed several times to speak with donors as questions swirl over Biden’s future on the ticket.

The call with donors started with presentations from field organizers who expressed anger at the ongoing debate within the Democratic Party about backing Biden, given what they’ve seen and heard from voters on the ground, according to one source with direct knowledge of the discussion.

One source said before Harris joined there seemed to be an effort to stall, which they said is normal for events with high-ranking officials. But what angered many donors, this source said, was that during the wait — which was about 20 minutes — donors were “admonished.” Participants of the call were told they needed to “lock in and get behind” Biden and to not pursue efforts to push out the president.

“Please help us turn down the volume on this conversation publicly,” Melissa Morales, founder and president of Somos Votantes, said on the call, according to a transcript obtained by NBC News. “It’s time to stop the leaks and the rampant rumors. Your message has been heard and received. But every day that we continue this publicly chaotic conversation, we come closer to a loss — no matter who the nominee is.”

That didn’t sit well with some on the call.

“These are donors who are not used to getting admonished and told what to do,” the source said.

Another source who was on the call and is supportive of Harris being the Democratic nominee pushed back on the donor’s feelings of frustrations.

The person said while many donors thought they were going to get insightful and confidential information, they immediately went to the media and proved why they shouldn’t get it.

Meanwhile, on Saturday, Harris spoke at a campaign fundraiser in Provincetown, Massachusetts, and praised Biden as one the most consequential presidents in history.

Harris garnered applause at various parts of her speech in which she talked about her and Biden’s record, including advocating for the rights of the LGBTQ community.

But the loudest applause from the crowd came when someone in the crowd of 1,000 people shouted, “Go get him, Kamala,” as Harris criticized Trump.

The applause lasted for several seconds as Harris smiled and looked out onto the cheering crowd of some 1,000 people.

After Harris left the stage, Lennie Alickman, 63, said she wanted to see Biden step aside.

“She is on a tightrope. She has to be very careful not to alienate Biden,” Alickman said when asked about Harris praising Biden throughout the speech. “I actually would like to see Kamala at the top of the ticket. She could carry out and continue the policies of the Biden administration. I love Biden but I’m not sure he is up to the job. And I’m worried he is going to lose against Trump.”

John Newton, 75, who attended the fundraiser, also said he believes Biden needs to drop out of the race and wants to see Harris become the party’s nominee.

“I love Joe,” Newton said. “In a business context, it’s like your 81-year-old salesman that’s goofed up at the convention and not making his numbers. And you gotta go in and tell him, ‘Judy is replacing you.’ It’s no fun. But sadly that has to happen.”

Harris closed her speech at the event, which was said to have raised $2 million, by talking about her campaign manager when she ran for district attorney in San Francisco.

She said he told her, “You must recognize what you’re up against — and know that those who oppose progress will always try to suggest that a movement for freedom is somehow subversive and that it undermines who we are as a nation or our traditions. But what we know is that it strengthens who we are as a nation when we fight to expand rights.”

Yamiche Alcindor is an NBC News Washington correspondent.

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After a Shaky Start, Harris Is Suddenly on Brink of Leading Democratic Ticket

Vice President Kamala Harris got off to a rocky start in office. She is now at the heart of a political drama that could make her the first woman of color to become a major party presidential nominee.

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• July 21, 2024

Vice President Kamala Harris, who has struggled for nearly four years in President Biden’s shadow, was thrust on Sunday into the center of a remarkable political drama that could culminate with her becoming the first woman of color at the top of a major-party presidential ticket.

Mr. Biden’s decision to abandon his re-election bid and endorse Ms. Harris to succeed him puts her in a powerful, but not certain, position to become the new face of the Democratic Party, charged with preventing former President Donald J. Trump from returning to the Oval Office for another four years.

“Today I want to offer my full support and endorsement for Kamala to be the nominee of our party this year. Democrats — it’s time to come together and beat Trump,” Mr. Biden wrote in a social media post after he announced his decision to step aside. “Let’s do this.”

Ms. Harris and her team are likely to move swiftly to try to seize that mantle even as uncertainty swirled about whether other Democrats would seek to challenge her for the nomination at the party’s convention in Chicago next month.

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A novel fuzzy twin support vector machine based on centered kernel alignment

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• Published: 24 July 2024

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• Jialiang Xie 1 ,
• Jianxiang Qiu 1 ,
• Dongxiao Zhang 1 &
• Ruping Zhang 2  

Twin Support Vector Machine (TSVM) transforms a single large quadratic programming problem (QPP) in support vector machine (SVM) into two smaller QPPs by finding two non-parallel classification hyperplanes, so that its computational time is reduced to a quarter of what the traditional SVM takes. However, TSVM ignores the data distribution of class, which makes TSVM sensitive to noise. In this paper, a fuzzy twin support vector machine based on centered kernel alignment (FTSVM-CKA) is proposed to solve the problem that TSVM is sensitive to noise. Firstly, a feature-weighted kernel function is constructed by using the information gain, and it is applied to the calculation of the centered kernel alignment (CKA). This assigns greater weight to strongly correlated features, emphasizing their classification importance over weakly correlated features. Secondly, the CKA method is utilized to derive a heuristic function for calculating the dependency between samples and their corresponding labels, which assigns fuzzy membership to different samples. Based on this, a fuzzy membership assignment strategy is proposed that can effectively address the sensitivity of TSVM to noise. Thirdly, this strategy is combined with TSVM to propose the FTSVM-CKA model. Moreover, this study employs a coordinate descent strategy with shrinking by active set to tackle the computational complexity arising from high-dimensional inputs. This can effectively accelerate the training speed of the model while ensuring classification performance. In order to evaluate the performance of FTSVM-CKA, this study conducts experiments designed on artificial and UCI datasets. The results demonstrate that FTSVM-CKA can efficiently and quickly solve binary classification problems with noise.

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Acknowledgements

This paper would like to thank the editors and the anonymous referees for their professional comments, which improved the quality of the manuscript.

This work was supported in part by the National Natural Science Foundation of China (Nos. 12271211, 12071179), the National Natural Science Foundation of Fujian Province (Nos. 2021J01861, 2020J01710), the Youth Innovation Fund of Xiamen City (3502Z20206020), the Open Fund of Digital Fujian Big Data Modeling and Intelligent Computing Institute, Pre-Research Fund of Jimei University.

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Jialiang Xie, Jianxiang Qiu & Dongxiao Zhang

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Xie, J., Qiu, J., Zhang, D. et al. A novel fuzzy twin support vector machine based on centered kernel alignment. Soft Comput (2024). https://doi.org/10.1007/s00500-024-09917-3

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• Classification
• Twin support vector machine
• Membership function
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