A new interactive approach for solving fully fuzzy mixed integer linear programming

Khalili, F; Naseri, S H; Taghi-Nezhad, Nemat Allah

doi:10.2298/yjor181015025k

Cited by 7 publications

(3 citation statements)

References 27 publications

(35 reference statements)

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“…When the fuzzy variables are special fuzzy numbers, such as triangular fuzzy numbers and trapezoidal fuzzy numbers, which are widely used in modeling fuzziness, this ranking method is easier to apply. The use of fuzzy credibility programming in fuzzy mathematical programming problems whose parameters are triangular or trapezoidal fuzzy numbers has been studied by a number of researchers ( [14], [25], [30]). Proposition 1.…”

Section: Possibility Relation Is Very Optimistic But Necessity Relation Is Very Pessimisticmentioning

confidence: 99%

Knapsack problem in fuzzy nature: Different models based on credibility ranking method

Niksirat

Nasseri

2022

YUGOSLAV J OPERATION

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This paper deals with knapsack problem in fuzzy nature, where both the objective function and constraints are considered to be fuzzy. Three different models for fuzzy knapsack problem are proposed including, expected value model, chance-constrained model, and dependent-chance model. Credibility ranking method is applied to convert the fuzzy models into a crisp equivalent linear one considering triangular and trapezoidal fuzzy numbers. The solution of the fuzzy problem is obtained with respect to different satisfaction degrees in the objective function and constraints. Several numerical examples are given to demonstrate different models and concepts. The proposed approaches are applied to model and to solve a fuzzy pre-disaster investment decision problem.

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Section: Possibility Relation Is Very Optimistic But Necessity Relation Is Very Pessimisticmentioning

confidence: 99%

Knapsack problem in fuzzy nature: Different models based on credibility ranking method

Niksirat

Nasseri

2022

YUGOSLAV J OPERATION

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“…Khalili Goudarzi et al [47] proposed a solution approach to FF-MILP problems. First, they formulate a crisp three-objective problem, and find the positive and negative ideal solutions to each objective.…”

Section: Principle They Analyzed One Of Ezzati Et Al's Examples and C...mentioning

confidence: 99%

Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Stanojević

Nădăban

2021

Mathematics

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Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process.

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“…Linear programming can solve various problems, including finding the shortest part on the graph, maximizing network flow, transportation problems, task problems, portfolio optimization, dynamic programming, and integer programming [6], [14]. Integer programming is one of the linear programming languages where some or all decision variables must be non-negative integers [15]. All decision variables must be non-negative integers.…”

Section: Introductionmentioning

confidence: 99%

Optimization of bakery production by using branch and bound approach

Rahimullaily¹,

Darwas²,

Purwasih³

2023

Comput. Sci. Inf. Technol.

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Mommy Ai Kitchen is one the businesses specializing in the bakery business, producing cupcakes, birthday cakes, brownies, and donuts. However, it does not optimally determine each bakery’s production quantity, so it offers fewer profits and becomes a problem. This research aims to find the optimal production quantity so that this business maximizes profits. The method used was integer programming using the branch and bound approach, which counts the decision variable value using the simplex method. This research was based on the number of raw materials on hand-wheat flour, sugar, eggs, modal, and the profits of each bakery. Based on the analysis of the branch and bound approach, it was known that the maximum profit value was IDR 253,200, with eight alternative options for the bakeries that were produced. One of them was Mommy Ai Kitchen, which could produce three cupcakes, five birthday cakes, one brownie, and nine donuts to get that maximum profit. Meanwhile, Mommy Ai Kitchen’s estimation could produce one cupcake, one brownie, and six donuts using available materials with a profit of IDR 78,800. As a result, the profit difference before and after integer programming was IDR 174,400.

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A new interactive approach for solving fully fuzzy mixed integer linear programming

Cited by 7 publications

References 27 publications

Knapsack problem in fuzzy nature: Different models based on credibility ranking method

Knapsack problem in fuzzy nature: Different models based on credibility ranking method

Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Optimization of bakery production by using branch and bound approach

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