scholarly journals Calculating the Fuzzy Project Network Critical Path

2012 ◽  
Vol 1 (2) ◽  
pp. 58 ◽  
Author(s):  
Nasser Shahsavari Pour ◽  
Samira Zeynali ◽  
Mansoor Kheradmand
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Special Importance ◽  
Activity Time ◽  
Simple Method ◽  
Project Completion ◽  
Project Network ◽  
Ranking Of Fuzzy Numbers

A project network consists of various activities. To determine the length of project time and the amount of the needed sources, the time of project completion must correctly and exactly be calculated, so the critical path is calculated. The activities on this path have no floating. It means that there is no delay on these activities. As a result the calculation of the critical path in a project network has a special importance. In this paper a simple method for calculation the critical path is proposed. Assignment an exact time on any activity in real world is not correct; So the fuzzy and uncertainty theories are used to assigned a length of time on any activities. In the present study the trapezoidal fuzzy numbers are assigned to the length of activity time, and the total time of the project is also a fuzzy number. In addition, to compare the fuzzy numbers, ranking of fuzzy numbers are used. Finally a practical example will show the efficiency of the method.

scholarly journals The Intelligence of Octagonal Fuzzy Number to Determine the Fuzzy Critical Path: A New Ranking Method

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
S. Narayanamoorthy ◽  
S. Maheswari
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Ranking Method ◽  
Triangular Fuzzy Numbers ◽  
Activity Time ◽  
Numerical Example ◽  
Modified Method ◽  
Project Network ◽  
Negative Time

This research paper proposes a modified ranking approach to determine the critical path in fuzzy project network, where the duration of each activity time is represented by an octagonal fuzzy number. In this method, a modified subtraction formula is carried out on fuzzy numbers. This modified method works well on fuzzy backward pass calculations as there will be no negative time. The analysis is expected to show that the fuzzy number which is used in this paper is more effective in determining the critical path in a fuzzy project network and possibility of meeting the project time. A numerical example is given and compared with trapezoidal, triangular fuzzy numbers through proposed ranking method.

Ranking of Fuzzy Numbers by using Scaling Method

2019 ◽  
Vol 3 (2) ◽  
pp. 137-143
Author(s):  
Ayad Mohammed Ramadan
Keyword(s):  
Multidimensional Scaling ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Scaling Method ◽  
Ranking Of Fuzzy Numbers ◽  
First Time

In this paper, we presented for the first time a multidimensional scaling approach to find the scaling as well as the ranking of triangular fuzzy numbers. Each fuzzy number was represented by a row in a matrix, and then found the configuration points (scale points) which represent the fuzzy numbers in . Since these points are not uniquely determined, then we presented different techniques to reconfigure the points to compare them with other methods. The results showed the ability of ranking fuzzy numbers

Planning of a Project with Imprecise Activity Time

2016 ◽  
pp. 505-515
Author(s):  
Sk. Md. Abu Nayeem ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Numbers ◽  
Critical Path ◽  
Project Evaluation ◽  
Triangular Fuzzy Numbers ◽  
Activity Time ◽  
Ranking Methods ◽  
Mathematical Techniques ◽  
Activity Times

A project where activity times are characterized by intervals or triangular fuzzy numbers is considered in this chapter. Classical project evaluation and review technique (PERT) cannot be directly applied to such projects. Comparison of two intervals or two triangular fuzzy numbers plays an important role in this problem. Ranking methods based on some fuzzy mathematical techniques are discussed and two algorithms for finding the critical path for such a project are given. An illustrative example is also provided.

scholarly journals Using Metric Distance Ranking Method to Find Intuitionistic Fuzzy Critical Path

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
P. Jayagowri ◽  
G. Geetharamani
Keyword(s):  
Fuzzy Numbers ◽  
Critical Path ◽  
Method Comparison ◽  
Critical Length ◽  
Ranking Method ◽  
Critical Path Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Project Network ◽  
Metric Distance

Network analysis is a technique which determines the various sequences of activities concerning a project and the project completion time. The popular methods of this technique which is widely used are the critical path method and program evaluation and review techniques. The aim of this paper is to present an analytical method for measuring the criticality in an (Atanassov) intuitionistic fuzzy project network. Vague parameters in the project network are represented by (Atanassov) intuitionistic trapezoidal fuzzy numbers. A metric distance ranking method for (Atanassov) intuitionistic fuzzy numbers to a critical path method is proposed. (Atanassov) Intuitionistic fuzzy critical length of the project network is found without converting the (Atanassov) intuitionistic fuzzy activity times to classical numbers. The fuzzified conversion of the problem has been discussed with the numerical example. We also apply four different ranking procedures and we compare it with metric distance ranking method. Comparison reveals that the proposed ranking method is better than other raking procedures.

scholarly journals On Fuzzy Critical Path Method Based On Ranking Of Various Type-2 Fuzzy Quantities Using Centroid Of Centroids

2019 ◽  
Vol 8 (6) ◽  
pp. 910-920
Keyword(s):  
Path Analysis ◽  
Explicit Form ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Simple Approach ◽  
Membership Functions ◽  
Project Network ◽  
Generalized Type ◽  
Activity Times

This paper proposes a simple approach to critical path analysis in a project network with activity times being intervals and which are converted into various Type-2 fuzzy quantities. The idea is based on generalized type-2 trapezoidal, hexagonal and octagonal fuzzy numbers and its ranking. The explicit form of membership functions of the type-2 fuzzy activity times is not required in the proposed approach. Moreover, the method is very simple and the numerical example is given for demonstrating and comparing the proposed approach with generalized type-2 trapezoidal, hexagonal and octagonal fuzzy numbers through proposed ranking function.

scholarly journals Defuzzification Formula for Modelling and Scheduling A Furniture Fuzzy Project Network

2019 ◽  
Vol 9 (1S5) ◽  
pp. 279-283
Keyword(s):  
Fuzzy Numbers ◽  
Critical Path ◽  
Numerical Example ◽  
Research Article ◽  
Duration Time ◽  
Project Network

-This research article presents a new defuzzification formula for deciding the critical path in a proposed network. Here we introduce an octagonal fuzzy numbers for representing the duration time. It is shown that it is better to use octagonal fuzzy numbers towards determining the critical path. A numerical example is given and the proposed formula as compared with the existing fuzzy numbers.

On the Latest Times and Float Times of Activities in a Fuzzy Project Network with LR Fuzzy Numbers

2012 ◽  
Vol 2 (2) ◽  
pp. 91-101 ◽  
Author(s):  
V. Sireesha ◽  
N. Ravi Shankar ◽  
K. Srinivasa Rao ◽  
P. Phani Bushan Rao
Keyword(s):  
Project Scheduling ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Real Life ◽  
New Method ◽  
Scheduling Problem ◽  
Forward Pass ◽  
Project Scheduling Problem ◽  
Project Network ◽  
Activity Times

In this paper, the authors propose a new method to compute the fuzzy latest times and float times of activities for a project scheduling problem with fuzzy activity times. The authors have considered LR fuzzy numbers to represent the activity times. As the data of the problem are LR fuzzy numbers, the authors have shown that the results are also in terms of LR fuzzy numbers. Total float time of each activity can be found by this method without using the forward pass and backward pass computations. The authors use an example to illustrate the method. This paper shows the advantages of this method over the existing methods with great clarity. The proposed method illustrates its application to fuzzy critical path problems occurring in real life situations.

Fuzzy Number Approximation

1998 ◽  
Vol 06 (01) ◽  
pp. 69-78 ◽  
Author(s):  
Mariano Jiménez ◽  
Juan Antonio Rivas
Keyword(s):  
Initial Data ◽  
Economic Model ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Membership Functions ◽  
Simple Method ◽  
Non Linear

As the number of parameters involved in an economic model is often uncertain, we propose that it be estimated using fuzzy numbers. Since we move in an environment of uncertainty, it is logical to leave room for deviation in estimating membership functions. We should recall that when soft max-min operators are used, the resulting deviation is never greater than the variation introduced in estimating the initial data. Often, the result of our calculations is not a triangular fuzzy number. In this paper we study the value of approximating the resulting non-linear fuzzy number using a triangular fuzzy number having the same support and kernel. Finally, we present a simple method for weighing this approximation.

scholarly journals Oriented Fuzzy Numbers vs. Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 523
Author(s):  
Krzysztof Piasecki ◽  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Formal Model ◽  
Original Study ◽  
Portfolio Analysis ◽  
Algebraic Structures ◽  
Equivalent Models ◽  
Real World Problems

A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems.

scholarly journals Generalization and ranking of fuzzy numbers by relative preference relation

2021 ◽  
Author(s):  
Kavitha Koppula ◽  
Babushri Srinivas Kedukodi ◽  
Syam Prasad Kuncham
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Preference Relation ◽  
Multi Criteria Decision Making ◽  
Fuzzy Preference Relation ◽  
Trapezoidal Fuzzy Numbers ◽  
Relative Preference ◽  
Decision Making Model ◽  
Ranking Of Fuzzy Numbers

AbstractWe define $$2n+1$$ 2 n + 1 and 2n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$ 2 n + 1 and 2n fuzzy numbers. When the data is representable in terms of $$2n+1$$ 2 n + 1 fuzzy number, we generalize the FMCDM (fuzzy multi-criteria decision making) model constructed with TOPSIS and relative preference relation. Lastly, we give an example from telecommunications to present the proposed FMCDM model and validate the results obtained.

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