Nureize Arbaiy

Approximation of Goal Constraint Coefficients in Fuzzy Goal Programming

It is sometimes difficult in real situations to estimate the coefficients of decision variables in multi-objective model. Even though mathematical analysis may contribute to determine these coefficients, historical data used may contain fuzzy and random properties and should be treated properly. Thus, this paper introduces a fuzzy random regression to approximate the coefficients; specifically the goal constraints of goal programming model. We propose a two phase-based approach for the solution model; first, we construct the goal constraints using fuzzy random regression model and, second, we solve the multi-objective problem with a fuzzy additive goal programming. A numerical example is presented to illustrate the model.

Multi-Attribute Decision Making in Contractor Selection Under Hybrid Uncertainty

The successful of a construction industry project depends on contractor evaluation and selection. Further, human judgment and unknown evaluation risk make evaluation and selection increasingly complex. Such situations show that a contractor selection is influenced by multiple attributes that often have the hybrid uncertainty of fuzziness and probability. The objective of this study is therefore to propose a fuzzy random variable based multi-attribute decision scheme that enables us to solve such problems within the bounds of hybrid uncertainty by using a fuzzy random regression model. The proposed model is explained in examples and its usefulness is clarified. This decision model is facilitated in its use by evaluating alternatives and enables us to indicate the optimum choice in the presence of hybrid uncertainty.

Constructing Fuzzy Random Goal Constraints for Stochastic Fuzzy Goal Programming

This paper attempts to estimate the coefficient of the goal constraints through a fuzzy random regression model which plays a pivotal role in solving a stochastic fuzzy additive goal programming.We propose the two phase-based solutions; in the first phase, the goal constraints are constructed by fuzzy random-based regression model and, in the second phase, the multi-objective problem is solved with a stochastic fuzzy additive goal programming model. Further, we apply the model to a multi-objective decision-making scheme’s use in palm oil production planning and give a numerical example to illustrate the model.

Estimation of Confidence-Interval for Yearly Electricity Load Consumption Based on Fuzzy Random Auto-Regression Model

Many models have been implemented in the energy sectors, especially in the electricity load consumption ranging from the statistical to the artificial intelligence models. However, most of these models do not consider the factors of uncertainty, the randomness and the probability of the time series data into the forecasting model. These factors give impact to the estimated model’s coefficients and also the forecasting accuracy. In this paper, the fuzzy random auto-regression model is suggested to solve three conditions above. The best confidence interval estimation and the forecasting accuracy are improved through adjusting of the left-right spreads of triangular fuzzy numbers. The yearly electricity load consumption of North-Taiwan from 1981 to 2000 are examined in evaluating the performance of three different left-right spreads of fuzzy random auto-regression models and some existing models, respectively. The result indicates that the smaller left-right spread of triangular fuzzy number provides the better forecast values if compared with based line models.

Weighted value assessment of linear fractional programming for possibilistic multi-objective problem

Determining the weight values is crucial in developing problems mathematical model. The value of the models weight must be determined before the model is solved. Nevertheless, the developed mathematical model is troublesome when the weight values are not exactly known, as relevant data are sometimes not given or difficult to obtain or estimate. Since numerous researches focusing in finding the solution of the model, this paper focuses on determining the weight value and a weighting method specifically for linear fractional programming to solve possibilistic programming of the multi-objective decision-making problem. Fuzzy random regression approach is applied to estimate the multi-objective models weight value. Meanwhile, the minimal and maximal values of the objective function are utilised in determination for objective function weight value. Since most of the weight values in the developed model discusses in this paper are estimated from real data, assessment to these weights value in the objective function is executed. The weight value assessment uses weight absolute percentage error of fuzzy demand WAPE_FD. This analysis concludes that it is worthwhile to pursue proposed solution approach to the multi-objective evaluation scheme, which addresses some limitation to determine and assess the weight values within fuzzy circumstances.

Fuzzy Goal Programming for Multi-level Multi-objective Problem: An Additive Model

The coordination of decision authority is noteworthy especially in a complex multi-level structured organization, which faces multi-objective problems to achieve overall organization targets. However, the standard formulation of mathematical programming problems assumes that a single decision maker made the decisions. Nevertheless it should be appropriate to establish the formulations of mathematical models based on multi-level programming method embracing multiple objectives. Yet, it is realized that sometimes estimating the coefficients of objective functions in the multi-objective model are difficult when the statistical data contain random and fuzzy information. Hence, this paper proposes a fuzzy goal programming additive model, to solve a multi-level multi-objective problem in a fuzzy environment, which can attain a satisfaction solution. A numerical example of production planning problem illustrates the proposed solution approach and highlights its advantages that consider the inherent uncertainties in developing the multi-level multi-objective model.

Multi-level multi-objective decision problem through fuzzy random regression based objective function

A multi-level decision making problem confronts several issues especially in coordinating decision in hierarchic processes and in compromising conflicting objectives for each decision level. Therefore, its mathematical model plays a pivotal role in solving such problem, and is influencing to the final result. However, it is sometimes difficult to estimate the coefficients of objective functions of the model in real situations specifically when the statistical data contain random and fuzzy information. Thus, decision making scheme should provide an appropriate method to handle the presence of such uncertainties. Hence, this paper proposes a fuzzy random regression method to estimate the coefficients value for the objective functions of multi-level multi-objective model. The algorithm is constructed to obtain a satisfaction solution, which fulfills at least weak Pareto optimality. A numerical example illustrates the proposed solution procedure.

One-Way ANOVA Model with Fuzzy Data for Consumer Demand

This paper presents a statistical method which could distinguish the customer’s demand into different type whereby fuzzy data is in consideration. A one-way analysis of variance (ANOVA) model for fuzzy data is introduced with hypothesis test, \( F \)-test, which is the pivot statistic in ANOVA model. In the experiment, several different factors in testing with one-way ANOVA model are considered. The results of this study indicate that the solution method introduced in this paper could give decision maker a result with favorable degree of each factor. This kind of result is beneficial to the decision maker and retailer to distinguish which factor is the most critical for the customer and with how much amount of products would be allocated for customers.

Fuzzy Random Regression to Improve Coefficient Determination in Fuzzy Random Environment

Determining the coefficient value is important to measure relationship in algebraic expression and to build a mathematical model though it is complex and troublesome. Additionally, providing precise value for the coefficient is difficult when it deals with fuzzy information and the existence of random information increase the complexity of deciding the coefficient. Hence, this paper proposes a fuzzy random regression method to estimate the coefficient values for which statistical data contains simultaneous fuzzy random information. A numerical example illustrates the proposed solution approach whereby coefficient values are successfully deduced from the statistical data and the fuzziness and randomness were treated based on the property of fuzzy random regression. The implementation of the fuzzy random regression method shows the significant capabilities to estimate the coefficient value to further improve the model setting of production planning problem which retain simultaneous uncertainties.

A new procedure in stock market forecasting based on fuzzy random auto-regression time series model

Various models used in stock market forecasting presented have been classified accord- ing to the data preparation, forecasting methodology, performance evaluation, and perfor- mance measure. However, these models have not sufficiently discussed in data prepara- tion to overcome randomness, as well as uncertainty and volatility of stock prices issues in achieving high forecasting accuracy. Therefore, the focus of this paper is the data prepa- ration procedure of triangular fuzzy number to build an improved fuzzy random auto- regression model using non-stationary stock market data for forecasting purposes. The im- proved forecasting model considers two types of input, which are data with low-high and single point values of stock market prices. Even though, low-high data present variabil- ity and volatility in nature, the single data has to be form in symmetry left-right spread to present variability and standard error. Then, expectations and variances, confidence- intervals of fuzzy random data are constructed for fuzzy input-output data. By using the input-output data and simplex approach, parameters of the model can be estimated. In this study, some real data sets were used to represent both types of inputs, which are the Kuala Lumpur stock exchange and Alabama University enrollment. The study found that variability and spread adjustment are important factors in data preparation to improve ac- curacy of the fuzzy random auto-regression model.