A Method of Computing Functions of Trapezoidal Fuzzy Variable and Its Application to Fuzzy Calculus

This paper introduces a method of computing functions of trapezoidal fuzzy variable. The method is based on the implementation of an unconstrained optimisation technique over the α -cut of fuzzy interval. To show the effectiveness of the proposed method, we provide several numerical examples in computing the solutions of linear and non-linear fuzzy differential equations. The final results showed that the proposed method is capable to generate convex fuzzy solutions on time domain

A New Approach to solve Fuzzy Transportation Problem for Trapezoidal Number

In this paper we are study on fuzzy transportation problem for industries to reduce the transportation cost of commodity from one source to another source. In this paper we are taking transportation cost, demand and supply all are in fuzzy trapezoidal number because the fuzzy number satisfy the condition of vagueness. Here we are using the propose algorithm to obtained the fuzzy optimal solution of fuzzy transportation problem with membership function. The solution procedure is illustrated with numerical example

Solving the four index fully fuzzy transportation problem

In this paper, we will solve the four index fully fuzzy transportation problem (textit{FFTP$_{4}$}) with some adapted classical methods. All problem\u27s data will be presented as fuzzy numbers. In order to defuzificate these data, we will use the ranking function procedure. Our method to solve the textit{FFTP$_{4}$} composed of two phases; in the first one, we will use an adaptation of well-known algorithms to find an initial feasible solution, which are the least cost, Russell\u27s approximation and Vogel\u27s approximation methods. In the second phase, we will test the optimality of the initial solution, if it is not optimal, we will improve it. A numerical analysis of the proposed methods is performed by solving different examples of different sizes; it is determined that they are stable, robust, and efficient. A proper comparative study between the adapted methods identifies the suitable method for solving textit{FFTP$_{4}$}

Approximate Membership Function Shapes of Solutions to Intuitionistic Fuzzy Transportation Problems

In this paper, proposing a mathematical model with disjunctive constraint system, and providing approximate membership function shapes to the optimal values of the decision variables, we improve the solution approach to transportation problems with trapezoidal fuzzy parameters. We further extend the approach to solving transportation problems with intuitionistic fuzzy parameters; and compare the membership function shapes of the fuzzy solutions obtained by our approach to the fuzzy solutions to full fuzzy transportation problems yielded by approaches found in the literature

A Fuzzy Approach Using Generalized Dinkelbach’s Algorithm for Multiobjective Linear Fractional Transportation Problem

We consider a multiobjective linear fractional transportation problem (MLFTP) with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time, and its two properties are source and destination. Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem. To do this, first, we present a theorem which shows that MLFTP is always solvable. And then, reducing MLFTP to the Zimmermann’s “min” operator model which is the max-min problem, we construct Generalized Dinkelbach’s Algorithm for solving the obtained problem. Furthermore, we provide an illustrative numerical example to explain this fuzzy approach

Two-stage based dynamic earth-rock transportation assignment problem under fuzzy random environment to earth-rock dam construction

This paper discusses a two-stage based dynamic transportation assignment problem (TS-based DTAP) under a fuzzy random environment in an earth-rock transportation system. This problem is a multi-objective dynamic programming optimization process for minimizing total operational cost, transportation duration and total waste. Triangular fuzzy random numbers are used for the uncertain parameters, and a hybrid crisp approach and an expected value operator are introduced to deal with these uncertainties. A dynamic programming based contraction particle swarm optimization is developed to solve the proposed expected value model for TS-based DTAP. Then, the earth-rock dam construction at Pubugou Hydropower project is used as a practical application to verify the proposed approach. Results and analysis are presented to highlight the performance of the proposed TS-based DTAP model and the optimization method, which proves to be effective and relatively efficient compared to the models under other environments and a standard PSO algorithm

An overview of fuzzy techniques in supply chain management: bibliometrics, methodologies, applications and future directions

Every practice in supply chain management (SCM) requires decision making. However, due to the complexity of evaluated objects and the cognitive limitations of individuals, the decision information given by experts is often fuzzy, which may make it difficult to make decisions. In this regard, many scholars applied fuzzy techniques to solve decision making problems in SCM. Although there were review papers about either fuzzy methods or SCM, most of them did not use bibliometrics methods or did not consider fuzzy sets theory-based techniques comprehensively in SCM. In this paper, for the purpose of analyzing the advances of fuzzy techniques in SCM, we review 301 relevant papers from 1998 to 2020. By the analyses in terms of bibliometrics, methodologies and applications, publication trends, popular methods such as fuzzy MCDM methods, and hot applications such as supplier selection, are found. Finally, we propose future directions regarding fuzzy techniques in SCM. It is hoped that this paper would be helpful for scholars and practitioners in the field of fuzzy decision making and SCM

Improving the cost model development process using fuzzy logic

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