A New Approach for Solving Type-2-Fuzzy Transportation Problem

Maity, Somnath; Roy, Sankar Kumar

doi:10.33889//ijmems.2019.4.3-054

Cited by 6 publications

(6 citation statements)

References 20 publications

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“…This paper is motivated by [17,21] it will be very useful in solving decision making problems. There are no optimization models in literature based on this topic.…”

Section: Resultsmentioning

confidence: 99%

“…In this piece of work, a goal programming technique for solving duality fuzzy fractional transportation problem by interval-valued triangular and trapezoidal intuitionistic fuzzy numbers by using a special type of non-linear (hyperbolic) membership functions. This paper is motivated by [17,21]. In our research, we have attempted for the first time solving fractional transportation problem using duality method.…”

Section: Introductionmentioning

confidence: 99%

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Type-2 Duality Trapezoidal Fuzzy Fractional Transportation Problem using Fuzzy Optimization Techniques

Priyadharshini*,

Anju

2020

IJRTE

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The authors focused goal programming technique for solving type-2 duality fuzzy fractional transportation problem by using interval-valued triangular intuitionistic fuzzy numbers. The proposed method solves three types of models in which variables are taken as type-2 fuzzy variables which have spring up to the fuzzy fractional transportation problem. In these models, duality is applied and a particular type of non-linear membership functions are used to resolve duality fractional transportation problem including fuzzy parameters. A numerical example for examining the performance of the proposed model is envisaged here.

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“…This paper is motivated by [17,21] it will be very useful in solving decision making problems. There are no optimization models in literature based on this topic.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Type-2 Duality Trapezoidal Fuzzy Fractional Transportation Problem using Fuzzy Optimization Techniques

Priyadharshini*,

Anju

2020

IJRTE

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“…In recent years, many experts have utilized the concept of T2FS in decision-making problems. Maity and Roy (2019) developed a new technique for solving TP with T2FS. Sinha et al (2016) considered a solid TP with profit maximization and time minimization objectives with T2FS and used interactive fuzzy satisficing technique to obtain the optimum solution.…”

Section: Literature Reviewmentioning

confidence: 99%

Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

et al. 2021

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The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

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“…[12] used LPP with some Multi-Choice Fuzzy Parameters (FP). [13] suggested A New Approach for Solving the Type-2-Fuzzy Transportation Problem. [14] studied analytical preparations' level-dependent weighted average value of discrete trapezoidal fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

An Application Model for Linear Programming with an Evolutionary Ranking Function

Mitlif

2022

IHJPAS

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One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This method is simple in structure and is based on crisp linear programming. To solve the fuzzy linear programming problem (FLPP), a new ranking function (RF) with the trapezoidal fuzzy number (TFN) is devised in this study. The fuzzy quantities are de-fuzzified by applying the proposed ranking function (RF) transformation to crisp value linear programming problems (LPP) in the objective function (OF). Then the simplex method (SM) is used to determine the best solution (BS). To demonstrate our findings, we provide a numerical example (NE).

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A New Approach for Solving Type-2-Fuzzy Transportation Problem

Cited by 6 publications

References 20 publications

Type-2 Duality Trapezoidal Fuzzy Fractional Transportation Problem using Fuzzy Optimization Techniques

Type-2 Duality Trapezoidal Fuzzy Fractional Transportation Problem using Fuzzy Optimization Techniques

Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

An Application Model for Linear Programming with an Evolutionary Ranking Function

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