Amrit Das

Defuzzification of trapezoidal type-2 fuzzy variables and its application to solid transportation problem

The main proposal of this paper is to derive two different reduction process for a trapezoidal type-2 fuzzy number. The first reduction method is based on critical values and the second method is based on α-cut of fuzzy number. As an application a multi-objective solid transportation problem, minimizing the cost and time has been developed using trapezoidal type-2 fuzzy number as system parameters and hereby solved. Finally after solving the proposed multi-objective problem by intuitionistic fuzzy programming technique a comparison between the two proposed reduction methods are discussed briefly. The proposed models and techniques are finally illustrated by providing numerical examples at the end. Also this paper present a comparative study between the proposed method to the KM algorithm and NT method for type reduction.

A Profit Maximizing Solid Transportation Model Under a Rough Interval Approach

This study attempts to establish an innovative solid transportation problem that intends to maximize profit under the rough interval approximation methodology. Two transportation problems were constructed in this regard with interval coefficients corresponding to the upper approximations and the lower approximations of the rough intervals under study. Furthermore, from the contingent solid transportation problems, four different classical solid transportation problems were derived, which were subsequently solved on the LINGO iteration platform. The concepts of completely satisfactory solution and rather satisfactory solution, surely optimal range, possibly optimal range, and rough optimal range have been discussed with a perspective to its relevance to real-world practical problems. The rough chance-constrained programming and the expected value operator for rough interval have been applied to solve the problem under study. The distinct advantages of the proposed method over those existing have been outlined. Numerical examples have also been provided to illustrate the solution procedure and the methodologies adopted.

Defuzzification and application of trapezoidal type-2 fuzzy variables to green solid transportation problem

The main objective of this investigation is to propose a defuzzification process of a trapezoidal type-2 fuzzy variable centred on critical value-based reduction method and nearest interval approximation, i.e.

A Bi-Objective Solid Transportation Model Under Uncertain Environment

\alpha

A carbon emission optimization model with reduction method of type-2 zigzag uncertain variable

α-cut of fuzzy number. In this context, this paper proposes some theorems with proof. Also as an application of the proposed defuzzification process, a new multi-objective green solid transportation model has been formulated with all of its parameters as trapezoidal type-2 fuzzy variables, where the objectives are profit maximization and minimization of carbon emission produced by the modes of transport depending upon their loads, fuel type used, type of engine, driving characteristics, etc. After defuzzification, to solve the equivalent crisp multi-objective solid transportation problem the intuitionistic fuzzy programming technique is used. Also we have proposed the MOGA and LINGO 13.0 iterative platform for the soft computation related to the problem. At the end, proposed methodologies are finally illustrated by providing numerical examples which incorporate some real-life data and demonstrate how a decision maker makes a balance between the maximum profit and minimum carbon emission. Also a comparative study with N–T method has been provided, and some managerial decisions are drawn.

A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission

This paper is based on two mathematical models for multi-item multi-stage solid transportation problem with budget on total transportation cost in Gaussian type-2 fuzzy environment considering the fixed opening charge and operating cost in distribution center. The first model is about transportation of breakable/damageable items, and the second one considers non breakable/damageable items. The main aspect here is to develop the mathematical formulation of multi stage related solid transportation problem where several items are available for transportation. In order to deal with the Gaussian type-2 fuzziness, two chance-constrained programming models are developed based on generalized credibility measures for the objective function as well as the constraints sets with the help of the CV-based reductions method. Finally the reduced model is turned into its equivalent parametric programming problem. The problem is of high complexity and is difficult to find the optimal solution by any classical method and hence a time and space based meta-heuristic Genetic Algorithm has been proposed. Also the equivalent crisp models are solved using GA and LINGO 13.0 and after comparison, GA results are better. The proposed models and techniques are finally illustrated by providing numerical examples. Some sensitivity analysis and particular cases are presented and discussed. Degrees of efficiency is also evaluated for both the techniques.

Defuzzication method of type-2 gamma fuzzy variables and its application to transportation problem

In this paper, we study a solid transportation problem with uncertain cost and uncertain time, where the supplies, the demands, the conveyance capacities are regarded as uncertain in nature. For the first time we minimize the uncertain transportation time. According to the inverse uncertainty distribution, the model can be transformed into a deterministic form by taking expected value on objective functions and confidence level on the constraint functions. We solve the uncertain solid transportation problem by fuzzy programming technique and using the LINGO 13.0 software. Finally, this paper is illustrated by a numerical example on uncertain solid transportation problem to show the application of the model.

Profit Maximization Solid Transportation Problem with Trapezoidal Interval Type-2 Fuzzy Numbers

The main purpose of the paper is to present the reduction process of type-2 zigzag uncertain variables with an application to a two stage solid transportation problem (STP). The problem under consideration has been described with all its parameters are in type-2 zigzag uncertain variables. To solve the problem, we have used the proposed reduction method which is based on expected value of the type-2 zigzag uncertain variables. Whole the research will describe the superiority to use the uncertain variables in transportation problem. In connection with the real life situation, we have encountered a numerical example with the help of practical data to show the use of our proposed reduction method in two-stage STP. All the soft computations regarding the numerical problem solution are performed in Lingo 13.0 iterative platform. At the last, the overall contribution, iteration and managerial facts have been outlined following the result.