A Posynomial Geometric Programming Restricted to a System of Fuzzy Relation Equations

Singh, Garima; Pandey, Dhaneshwar; Thapar, Antika

doi:10.1016/j.proeng.2012.06.400

Cited by 7 publications

(4 citation statements)

References 21 publications

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“…The results of this model offer a framework for decision-makers to achieve an acceptable time frame with minimal cost and loss of quality. Thapar, Singh, and Pandey [20] resolved a polynomial geometric optimization problem using max-min fuzzy relational equations (FRE). After solving optimization problems, a single optimal solution was determined.…”

Section: Literature Reviewmentioning

confidence: 99%

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The Road to Sustainable Logistics: Using the Fuzzy Nonlinear Multi-Objective Optimization Model to Build Photovoltaic Stations in Taiwan’s Logistics Centers

Wang,

Chiang,

Pan

et al. 2023

Sustainability

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In Taiwan, numerous company logistics centers have embraced installing solar photovoltaic power stations (SPPSs) on their rooftops. The primary objective of this study is to expedite the generation of green electricity for sale, bolstering the logistics center’s income and enhancing its environmental, social, and governance (ESG) profile. How can we secure solar photovoltaic power station (SPPS) projects with expedited construction timelines, reduced investment costs, and heightened quality aligned with the long-term ESG objectives? The study applies the critical path method (CPM) to determine the item’s path. Next, the mothed leverages Zimmermann’s mathematical models for nonlinear multi-objectives and Yager’s fuzzy sets to enhance project efficiency, minimizing completion time and cost while maximizing the quality ratio. Subsequently, the project uses Liou and Wang’s defuzzification values and incorporates Dong’s fuzzy to accelerate calculations. In this case, Project HP’s item J, the construction time is reduced from 24.3 to 3.2 days, ensuring that construction quality meets an 85% standard. Item J necessitates expanding the fuzzy cost interval (4549.90, 15,416.65, 26,283.41) (it refers to a scope of possible costs). It becomes evident that construction time plays a pivotal role in controlling costs. For Project HP’s item H, the unit time quality decision ranges from TWD 238,000 to 240,000, to turn into a cost interval of TWD 215,100, 239,000, and 262,900. Consequently, cost transformation transitions from an active to a more passive role, with quality and construction time becoming the driving components. This study uses a fuzzy nonlinear multi-objective model to guide the decision analysis of SPPSs within logistics centers. This strategy enables decision-makers to streamline logistics center operations, ensuring time, cost, and quality (TCQ) alignment during SPPS installation, thereby advancing ESG sustainability goals.

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Section: Literature Reviewmentioning

confidence: 99%

“…From the literature [18][19][20][21][22] in the previous paragraph, it is evident that the choice of method is closely tied to the nature of the problem. Different problems necessitate different solutions.…”

Section: Literature Reviewmentioning

confidence: 99%

The Road to Sustainable Logistics: Using the Fuzzy Nonlinear Multi-Objective Optimization Model to Build Photovoltaic Stations in Taiwan’s Logistics Centers

Wang,

Chiang,

Pan

et al. 2023

Sustainability

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“…To deal with such problem, some researchers improved the existing methods, or proposed some novel resolution methods [27][28][29][30][31][32][33]. In recent years, some Complexity researchers have turned their attentions to the fuzzy relation nonlinear optimization problems [34][35][36][37][38][39][40][41], especially to the fuzzy relation geometric programming problems [42][43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

“…. ,* 6 by(47). * 1 = { ∈ | 1 = * 1 } = { ∈ | 1 = 1} = {1} , * 2 = { ∈ | 2 = * 2 } = { ∈ | 2 = 0.86} = {6} , * 3 = { ∈ | 3 = * 3 } = { ∈ | 3 = 0.93} = {6} , * 4 = { ∈ | 4 = * 4 } = { ∈ | 4 = 0.8} = {7} , * 5 = { ∈ | 5 = * 5 } = { ∈ | 5 = 0.79} = {3, 8} , * 6 = { ∈ | 6 = * 6 } = { ∈ | 6 = 0.9} = {8} .…”

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Maximin Optimization Problem Subject to Min‐Product Fuzzy Relation Inequalities with Application in Supply and Demand Scheme

et al. 2019

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In a supply chain system, the prices with which the suppliers supply its local commodity to the retailers should satisfy the requirements of the retailers and the consumers. The supply and demand scheme satisfying these requirements is reduced into fuzzy relation inequalities (FRIs) with min-product composition. Due to the difference between the min-product composition and the classical max-t-norm one, we first study the resolution of such min-product FRI system. For optimization management in the supply chain system, we further investigate a maximin programming problem subject to the min-product FRIs. An algorithm is proposed to obtain the optimal solution based on the quasi-maximal matrix and corresponding index set. To illustrate the efficiency of our proposed algorithm, we provide a simple numerical example. The obtained optimal solution reflects an optimal pricing scheme, which maximizes the minimum prices of the commodity from the suppliers.

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A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality constraints

Molai

2014

Computers & Industrial Engineering

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A Posynomial Geometric Programming Restricted to a System of Fuzzy Relation Equations

Cited by 7 publications

References 21 publications

The Road to Sustainable Logistics: Using the Fuzzy Nonlinear Multi-Objective Optimization Model to Build Photovoltaic Stations in Taiwan’s Logistics Centers

The Road to Sustainable Logistics: Using the Fuzzy Nonlinear Multi-Objective Optimization Model to Build Photovoltaic Stations in Taiwan’s Logistics Centers

Maximin Optimization Problem Subject to Min‐Product Fuzzy Relation Inequalities with Application in Supply and Demand Scheme

A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality constraints

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