Fuzzy Majority Algorithms for the 1-Median and 2-Median Problems on a Fuzzy Tree

Taleshian, Fatemeh; Fathali, Jafar; Taghi-Nezhad, Nemat Allah

doi:10.1080/16168658.2018.1517976

Cited by 10 publications

(6 citation statements)

References 43 publications

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“…There are many papers on fuzzy location models, see e.g. [5], [6], [21], [22] , [23] and [24]. Guo and Tanaka [11] presented a possible linear programming model in which the coefficients of the definite decision variables and the variables themselves are obtained from fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Balanced Allocation Problem with Efficiency on Servers

Azodi

Fathali

Ghiyasi

et al. 2021

Preprint

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This paper deals with the problem of allocation customers to servers with regards to some fuzzy parameters. In this problem each customer is allocated to the nearest server, and assignment of a customer to a server involves the cost to the customer, which is due to the customer's fuzzy distance to the server. Each server has a fuzzy efficiency which is calculated by the data envelopment analysis method with fuzzy parameters. The higher efficiency of the server to which a customer is assigned, cause more profit for the customer. The goal is allocation of all customers to the servers such that the profitability of the least profits for the customers is maximized. In addition, to prevent queuing in some servers, we consider the balancing on allocation customers to the servers. Therefore, the second goal is minimizing the difference between the maximum and minimum number of customers that are assigned to different servers. A fuzzy bi-objective programming model is presented for the problem, then two fuzzy approaches are proposed for solving this model.

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Section: Introductionmentioning

confidence: 99%

Fuzzy Balanced Allocation Problem with Efficiency on Servers

Azodi

Fathali

Ghiyasi

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since in some problems defining the membership value may yet involve hesitancy, in such class of problems, hesitant fuzzy sets (HFS) are dealt with. As a result, introducing hesitancy in mathematical models or equations opens both a new field and constitutes a challenge for researchers (see Buckley, 1991, andthen Nasseri et al, 2014;Taghi-Nezhad, 2019;Taleshian, Fathali and Taghi-Nezhad, 2018;Babakordi, Allahviranloo and Adabitabarfirozja, 2016;Allahviranloo and Babakordi, 2017;Xu, 2015;Babakordi, 2020a).…”

Section: Introductionmentioning

confidence: 99%

Introducing and solving the hesitant fuzzy system AX = B

Babakordi

Allahviranloo

2021

Control and Cybernetics

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In this paper the solution for hesitant fuzzy system as AX = B is introduced where A is an n × n known hesitant fuzzy matrix, B is an n × 1 known hesitant fuzzy vector and X is an n × 1 unknown hesitant fuzzy vector. First, L ∞-norm and L 1-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ’almost equal’ and ’less than’ and ’equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.

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“…Therefore, the parameters of such systems are often non-deterministic and the uncertainty must be considered in modeling these systems. One approach to uncertainty quantification is to consider a fuzzy set as an encoding of uncertainty (see, for instance, Khalili Goodarzi, Taghinezhad and Nasseri et al, 2014;Taghi-Nezhad, 2019;Taleshian, Fathali and Taghi-Nezhad, 2018;Babakordi, Allahviranloo and Adabitabarfirozja, 2016;or Allahviranloo and Babakordi, 2017). Fuzzy set theory is considered in different areas, and many new results are being continuously obtained, such as those reported, for instance, in Viattchenin, Owsiński and Kacprzyk (2018), Begnini et al (2018), Kalshetti and Dixit (2018), or Hesamian (2017).…”

Section: Introductionmentioning

confidence: 99%

Introducing hesitant fuzzy equations and determining market equilibrium price

Babakordi

Taghi-Nezhad

2021

Control and Cybernetics

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A vast majority of research has been performed in the field of hesitant fuzzy sets (HFSs), involving the introduction of some properties, operations, relations and modifications of such sets or considering the application of HFSs in MCDM (multicriteria decision making). On the other hand, no research has been performed in the field of fully hesitant fuzzy equations. Therefore, in this paper, fully hesitant fuzzy equations and dual hesitant fuzzy equations are introduced. First, a method is proposed to solve one-element hesitant fuzzy equations. Then, the proposed method is extended to solve n-element hesitant fuzzy equations effectively. Moreover, to show the applicability of the proposed method, it is used to solve a real world problem. Thus, the proposed method is applied to determine market equilibrium price. Also, some other numerical examples are presented to better show the performance of the proposed method.

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Fuzzy Majority Algorithms for the 1-Median and 2-Median Problems on a Fuzzy Tree

Cited by 10 publications

References 43 publications

Fuzzy Balanced Allocation Problem with Efficiency on Servers

Fuzzy Balanced Allocation Problem with Efficiency on Servers

Introducing and solving the hesitant fuzzy system AX = B

Introducing hesitant fuzzy equations and determining market equilibrium price

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