Symmetric Trapezoidal Fuzzy Numbers Research Articles

The range of uncertainty on the property market pricing: The case of the city of Shanghai

Property prices around the globe have seen very strong growth over the last two decades. Across various advanced countries, such a rapid and uncontrolled growth in house prices puts their economy in danger, and most importantly, their social integration and interconnectedness at great risk. In this paper, we develop a novel fuzzy linear regression framework using symmetric and asymmetric trapezoidal fuzzy numbers for determining the relationship of particular (non-) policy factors with the house prices. An interviewing questionnaire survey was conducted for collecting real data for the city of Shanghai to illustrate our theoretical treatment.

Solving Linear Fractional Programming Problem in symmetric trapezoidal fuzzy environment

Fuzzy set theory has been applied on different important fields, such as managements, operations research, and control theory. In this paper, we provided a new algorithm to solving a fuzzy fractional linear programming problem (FFlPP) in full fuzzy environments. All the variables and coefficients of both the constraints and the objective function are symmetric trapezoidal fuzzy numbers. The fuzzy linear fractional programming problem (FLFP) has been switched to fuzzy linear programming (FLP) problems, where both of constraint and objective function involve fuzzy numbers as variables and coefficients. Further, using the fuzzy simplex method algorithm to get an optimal fuzzy solution. Finally, we provide illustrative numerical examples.

Fuzzy reliability evaluation of linear <i>m</i>-consecutive weighted-<i>k</i>-out-of-<i>r</i>-from-<i>n</i>: F systems

This paper deals with the introduction and study of fuzzy reliability measures of a linear m-consecutive weighted-k-out-of-r-from-n: F system. The paper provides an algorithm for the evaluation of fuzzy reliability of the proposed system based on application of universal generating function and fuzzy exponential distribution. It is assumed in the study that failure rate follows generalised symmetric trapezoidal fuzzy number in fuzzy exponential distribution. Further, generalised symmetric trapezoidal fuzzy number and its arithmetic operations are defined. Fuzzy mean time to failure and Brinbaum system fuzzy reliability importance is also calculated. A numerical example is also presented to illustrate the proposed approach.

SINGLE MACHINE DUE DATE ASSIGNMENT SCHEDULING PROBLEM WITH PRECEDENCE CONSTRAINTS AND CONTROLLABLE PROCESSING TIMES IN FUZZY ENVIRONMENT

In this paper, a due date assignment scheduling problem with precedence constraints and controllable processing times in uncertain environment is investigated, in which the basic processing time of each job is assumed to be the symmetric trapezoidal fuzzy number, and the linear resource consumption function is used.The objective is to minimize the crisp possibilistic mean (or expected) value of a cost function thatincludes the costs of earliness, tardiness, makespan and resource consumption jointly by scheduling the jobs under precedence constraints and determining the due date and the resource allocation amount satisfying resource constraints for each job. First, the problem is shown to be NP-hard. Furthermore, an optimal algorithm with polynomial time for the special case of this problem is put forward. Moreover, an efficient 2-approximation algorithm is presented based on solving the relaxation of the problem. Finally, the numerical experiment is given, whose results show that our method is promising.

Mehar Method to Find the Fuzzy Optimal Solution of Bounded Fully Fuzzy Linear Programs with Symmetric Trapezoidal Fuzzy Numbers

A new method is proposed to find the fuzzy optimal solution of bounded fully fuzzy linear programs with symmetric trapezoidal fuzzy numbers. Comparative study of various existing methods on different cases is presented to validate the proposed method. A problem representing a real world situation is also solved by using the proposed method.

Forecasting Motorcycle Sales Using Nearest Symmetric Trapezoidal Fuzzy Number

A business activity aimed at obtaining forecasting as an initial step in planning activities helps provide an overview of sales in a business for the coming period based on data available. This research aims to design and develop a motorcycle sales forecasting application using Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Number approach to predict the next period sales of PT Mutiara Motor. To test the accuracy of the method used in application, we used the MSE and MAPE criteria. Based on the results of three experiments taken: (1) monthly ‘All Category’-’All Type’ with MSE = 54.42 and MAPE = 4.28%, (2) monthly ‘Beat CW Fuel Injection’ with MSE = 3.67 and MAPE = 4.04%, and (3) daily ‘All Category’- ’All Type’ with MSE = 1.42 and MAPE = 27.36% we indicate that Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Number approach could give higher accuracy than the Single Exponential Smoothing method as comparison in forecasting motorcycle sales.
 Index Terms—fuzzy time series, nearest symmetric trapezoidal fuzzy number, sales forecasting

A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers

The aim of this paper is to develop an effective method for solving matrix game with payoffs of trapezoidal fuzzy numbers (TrFNs). The method always assures that players’ gain-floor and loss-ceiling have a common TrFN-type fuzzy value and hereby any matrix game with payoffs of TrFNs has a TrFN-type fuzzy value. The matrix game is first converted to a fuzzy linear programming problem, which is converted to three different optimization problems, which are then solved to get the optimum value of the game. The proposed method has an edge over other method as this focuses only on matrix games with payoff element as symmetric trapezoidal fuzzy number, which might not always be the case. A numerical example is given to illustrate the method.

Stratified simplex method for solving fuzzy multi-objective linear programming problem

This paper is to deal with a kind of fuzzy multi-objective linear programming (FMOLP) problem with symmetric trapezoidal fuzzy numbers. Several methods has been proposed in order to obtain fuzzy efficient solution to FMOLP problem. In this paper, we change FMOLP problem into the complete stratified fuzzy linear programming problem, then use the stratified simplex method to obtain the fuzzy optimal solution directly without converting them to crisp linear programming problem. We then prove that this fuzzy optimal solution is the fuzzy efficient solution of the original FMOLP problem. A numerical example is given to illustrate the proposed method.

FFLP problem with symmetric trapezoidal fuzzy numbers

Article history: Received December 10, 2014 Received in revised format: January 4, 2015 Accepted January 5, 2015 Available online January 5 2015 The most popular approach for solving fully fuzzy linear programming (FFLP) problems is to convert them into the corresponding deterministic linear programs. Khan et al. (2013) [Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2), 536546.] claimed that there had been no method in the literature to find the fuzzy optimal solution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Others showed that the fuzzy arithmetic operation used by Khan et al. (2013) had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al. (2014) [Ezzati, R., Khorram, E., & Enayati, R. (2014). A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5), 2333-2358.] defined a new operation on symmetric trapezoidal fuzzy numbers and proposed a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multiobjective linear programming problem by using new fuzzy arithmetic operations, but their model was not fully fuzzy optimization. In this paper, a new method, by using Ezzati et al. (2014)’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm, is proposed for solving FFLP problem whose parameters are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method, the fuzzy optimal solution of FFLP problem can be easily obtained. A numerical example is provided to illustrate the proposed method. Growing Science Ltd. All rights reserved. 5 © 201

A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers

Linear programming (LP) is a widely used optimization method for solving real-life problems because of its efficiency. Although precise data are fundamentally indispensable in conventional LP problems, the observed values of the data in real-life problems are often imprecise. Fuzzy sets theory has been extensively used to represent imprecise data in LP by formalizing the inaccuracies inherent in human decision-making. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand-side, and/or the elements of the coefficient matrix. We propose a new method for solving FLP problems in which the coefficients of the objective function and the values of the right-hand-side are represented by symmetric trapezoidal fuzzy numbers while the elements of the coefficient matrix are represented by real numbers. We convert the FLP problem into an equivalent crisp LP problem and solve the crisp problem with the standard primal simplex method. We show that the method proposed in this study is simpler and computationally more efficient than two competing FLP methods commonly used in the literature.

Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method) is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions

In this paper, based on two new fuzzy arithmetic operations i.e. Multiplication and Division and fuzzy ordering on symmetric trapezoidal fuzzy numbers, a new algorithm is proposed to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming FLMOLP problem and a properly fuzzy efficient solution of a fuzzy multi-objective linear programming FMOLP problem. Also, in optimality conditions, it is shown that how the FLMOLP problem can be solved by employing the preceding computations if the degree of priority of the fuzzy objective functions is changed. It should be noted that this permutation of fuzzy objective functions is a kind of sensitivity analysis which it may be happen due to the change in the management strategy with the passing of time.

A novel approach for sensitivity analysis in linear programs with trapezoidal fuzzy numbers

There are several methods in the literature to deal with the sensitivity analysis of fuzzy linear programming (FLP) problems. In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method is proposed to handle the sensitivity analysis of that kind of FLP problems in which the elements of the coefficient matrix of the constraints are represented by real numbers, and the remaining parameters are represented by symmetric trapezoidal fuzzy numbers. To the best of our knowledge, till now there is no method in the literature to deal with the sensitivity analysis of such FLP problems without converting them to the crisp linear programming problems. The advantages of the proposed method over existing methods are discussed. To illustrate the approach a numerical example is examined by using the proposed method and the obtained results are discussed. The method is easy to understand and to apply for dealing with the sensitivity analysis of the same problems occurring in real life situations.

NEAREST SYMMETRIC TRAPEZOIDAL FUZZY NUMBER APPROXIMATION PRESERVING EXPECTED INTERVAL

Fuzzy number approximation has been investigated by many researchers. It is still useful to develop new approximations in order to better fit real world problems. This paper proposes a method for symmetric trapezoidal fuzzy number approximation which preserves the expected interval. Some properties of approximation are proved and a fuzzy partition is generated by using the proposed method.

Tableau form of the fuzzy primal-dual simplex algorithm for solving linear programmes with trapezoidal fuzzy numbers

Recently, Ebrahimnejad (2011) generalised the primal-dual simplex algorithm for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems. In this paper, we describe the fuzzy primal-dual algorithm in tableau form and illustrate our approach by a numerical example. If there is no uncertainty among parameters then the proposed approach gives the same result as in crisp FLP problems. Since the proposed method is a direct extension of classical method so it is very easy to understand and apply the proposed method to find the fuzzy optimal solution of FLP problems occurring in the real life situations.

The dual simplex method and sensitivity analysis for fuzzy linear programming with symmetric trapezoidal numbers

In this paper, we first extend the dual simplex method to a type of fuzzy linear programming problem involving symmetric trapezoidal fuzzy numbers. The results obtained lead to a solution for fuzzy linear programming problems that does not require their conversion into crisp linear programming problems. We then study the ranges of values we can achieve so that when changes to the data of the problem are introduced, the fuzzy optimal solution remains invariant. Finally, we obtain the optimal value function with fuzzy coefficients in each case, and the results are described by means of numerical examples.

Intuitionistic Fuzzy Simplex Method

paper deals with Intuitionistic Fuzzy Linear Programming Problems(IFLPPs) using Symmetric Trapezoidal Intuitionistic Fuzzy Numbers(STIFNs) and the arithmetic operations defined on them. A special ranking function is presented in project environment to rank STIFN. An attempt has been made to solve the given IFLPP without converting them to crisp linear programming problems by using intuitionistic fuzzy simplex method and the algorithm is effective and reasonable as is evident from the results of a numerical example.

Linear programmes with trapezoidal fuzzy numbers: a duality approach

Solving fuzzy linear programming problems have received a great deal of attention. Recently, Ganesan and Veeramani (2006) developed a new method for solving a kind of these problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems based on primal simplex method. But their method has no efficient when a primal basic feasible solution is not at hand. In this paper, we develop a new dual simplex algorithm to overcome this shortcoming by using the duality results which has been proposed by Nasseri and Mahdavi-Amiri (2009) and Nasseri et al. (2010). This algorithm starts with a dual basic feasible solution, but primal basic infeasible solution and walks to an optimal solution by moving among adjacent dual basic feasible solution.

Some new results in linear programs with trapezoidal fuzzy numbers: Finite convergence of the Ganesan and Veeramani’s method and a fuzzy revised simplex method

In a recent paper, Ganesan and Veermani [K. Ganesan, P. Veeramani, Fuzzy linear programs with trapezoidal fuzzy numbers, Ann. Oper. Res. 143 (2006) 305–315] considered a kind of linear programming involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems and then proved fuzzy analogues of some important theorems of linear programming that lead to a new method for solving fuzzy linear programming (FLP) problems. In this paper, we obtain some another new results for FLP problems. In fact, we show that if an FLP problem has a fuzzy feasible solution, it also has a fuzzy basic feasible solution and if an FLP problem has an optimal fuzzy solution, it has an optimal fuzzy basic solution too. We also prove that in the absence of degeneracy, the method proposed by Ganesan and Veermani stops in a finite number of iterations. Then, we propose a revised kind of their method that is more efficient and robust in practice. Finally, we give a new method to obtain an initial fuzzy basic feasible solution for solving FLP problems.

A Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers

Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.