On Determining the Critical Path of Activity Network with Normalized Heptagonal Fuzzy Data

Khalifa, Hamiden Abd El-Wahed; Alharbi, Majed G.; Kumar, Pavan

doi:10.1155/2021/6699403

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…To enhance sustainability in construction project scheduling Ba'Its et al [19] Combination of CPM and PERT Project schedule development system Liu et al [20] Fuzzy dynamic critical path method Generalised fuzzy similarity for project scheduling Khalifa et al [21] Heptagonal fuzzy CPM The critical path of activity network: Determination Yogashanthi et al [22] Critical path method in intuitionistic fuzzy environment CPM for airfreight ground operation systems Yudiarti et al [23] Fuzzy logic based optimization of time and cost Production of bottled drinking water optimised Yang et al [24] Particle swarm optimization Selection of large-scale features using fuzzy learning Tang et al [25] Based on viewpoints and weight granules…”

Section: Stochastic Processesmentioning

confidence: 99%

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

Parimala,

Prakash,

Al-Quran

et al. 2024

CMES

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The idea of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and optimization under uncertainty. The activity times in the critical path method (CPM) representation procedures approach are initially static, but in the Project Evaluation and Review Technique (PERT) approach, they are probabilistic. This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy (LDF) environment. The LDF expected task time, LDF variance, LDF critical path, and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network. The primary premise of the LDF-PERT approach is to address ambiguities in project network activity times more simply than other approaches such as conventional PERT, Fuzzy PERT, and so on. The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision. We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings. When the available resources and activity times are imprecise and unpredictable, this strategy can help decision-makers make better judgments in a project. A comparison analysis of the proposed technique with the existing techniques has also been discussed. The suggested techniques are demonstrated with two suitable numerical examples.

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Section: Stochastic Processesmentioning

confidence: 99%

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

Parimala,

Prakash,

Al-Quran

et al. 2024

CMES

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“…Bellman and Zadeh [4] introduced the concept of a maximizing decision making problem. Subsequently, fuzzy sets have been extensively studied and applied in various domains such as polynomial form fuzzy numbers [5], transportation problems [6], and critical path activity networks [7].…”

Section: Introductionmentioning

confidence: 99%

Addressing Cost-Efficiency Problems Based on Linear Ordering of Piecewise Quadratic Fuzzy Quotients

El-Wahed Khalifa,

Ali Yousif

2023

JOSA

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Ordering of quotients is a critical aspect of cost-efficiency problems, which hold significant interest and importance for suppliers of goods and services as well as consumers. Comparisons (ordering) are straightforward when dealing with ordinary numbers, yet in many instances, the data are imprecise, vague, or subject to seasonal variations. Consequently, such data may be unknown or derive from expert opinions. Unlike ordinary numbers, fuzzy data render quotients only partially ordered. This study examines the linear ordering of quotients with fuzzy data, expressed in terms of confidence intervals, α-cuts, or piecewise quadratic fuzzy numbers (PQFNs), within the context of cost-efficiency problems. Moreover, the challenges associated with quotient ordering in cost-efficiency problems are introduced.

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“…In addition, the work in [20] investigated a solution method to optimize the fuzzy portfolio selection model. The heptagonal fuzzy numbers (HFNs) were studied by [21][22] to solve the critical path problem as well as the vendor selection problem. In 2020, The work referenced in [23] presented an overview of the interval and fuzzy portfolio selection problems.…”

Section: Introductionmentioning

confidence: 99%

Solving Interval Investment Problem in Vague Environment Using Dynamic Programming Approach

Khalifa

Afifi

Kumar

2022

Frontiers in Artificial Intelligence and Applications

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In financial planning problems, the determination of the best investment is one of the interesting optimization models. In the proposed work, an investment problem (IP) is introduced in vague environment. The vagueness in return parameter is characterized by normalized heptagonal fuzzy number (HFN). One of the suitable interval approximations, namely, an inexact rough interval of a normalized HFN is utilized. Afterward, the inexact rough interval investment problem is considered. A dynamic programming (DP) approach is developed, which is applied for optimizing the fuzzy investment problem. The ideology of “rough interval number” is suggested in the mathematical modeling framework of the proposed problem to show the rough data as an inexact rough interval of piecewise quadratic fuzzy numbers. Afterward, the DP approach is applied to solve and compute a rough interval solution. Finally, a numerical example is yielded for the utility of the approach to apply on real-world problem for the decision-maker. The obtained results consist of the total optimal return with inexact rough intervals on a $ 10 million investments is as follows: $ [[1.69, 2.08]: [1.75, 1.91]] millions.

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On Determining the Critical Path of Activity Network with Normalized Heptagonal Fuzzy Data

Cited by 6 publications

References 23 publications

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

Addressing Cost-Efficiency Problems Based on Linear Ordering of Piecewise Quadratic Fuzzy Quotients

Solving Interval Investment Problem in Vague Environment Using Dynamic Programming Approach

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