Pei-Chun Lin

Kolmogorov-Smirnov Two Sample Test with Continuous Fuzzy Data

The Kolmogorov-Smirnov two-sample test (K-S two sample test) is a goodness-of-fit test which is used to determine whether two underlying one-dimensional probability distributions differ. In order to find the statistic pivot of a K-S two-sample test, we calculate the cumulative function by means of empirical distribution function. When we deal with fuzzy data, it is essential to know how to find the empirical distribution function for continuous fuzzy data. In our paper, we define a new function, the weight function that can be used to deal with continuous fuzzy data. Moreover we can divide samples into different classes. The cumulative function can be calculated with those divided data. The paper explains that the K-S two sample test for continuous fuzzy data can make it possible to judge whether two independent samples of continuous fuzzy data come from the same population. The results show that it is realistic and reasonable in social science research to use the K-S two-sample test for continuous fuzzy data.

A Fuzzy Random Variable Approach to Restructuring of Rough Sets through Statistical Test

Usually it is hard to classify the situation where randomness and fuzziness exist simultaneously. This paper presents a method based on fuzzy random variables and statistical t-test to restructure a rough set. The algorithms of rough set and statistical t-test are used to distinguish whether a subset can be classified in the object set or not. The expected-value-approach is also applied to calculate the fuzzy value with probability into a scalar value.

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.

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.

Hypothesis test for identifying the vague factors from consolidated income

This study proposes a statistical hypothesis test with fuzzy data which is represented in a form of interval data to perform one-way analysis of variance (ANOVA) test with fuzzy data. We adopt 2015 LEGO consolidated income as an empirical study for analyzing the main factors that affecting the LEGO annual profit by using one-way ANOVA Test with interval data. The results shown that each impact factor has different influence levels by means of testing their means. To confirm the most influential impact factor of 2015 LEGO annual profit, we provided the pair-wise comparisons in the evaluation. The comparison results shown that the greater financial income is decided from revenue factor and the most risk will be revealed from expenses factor. We concluded that the proposed method is able to assist an enterprise in identifying the main impact factors which are crucial for financial decision making.

Decision making of a portfolio selection model based on fuzzy statistic test

The objective of our research is to build a statistical test that can evaluate the sensitivity of a portfolio selection model with fuzzy data. The central point and radius are used to determine the portfolio selection model and we make a decision for the best return by a fuzzy statistical test. Empirical studies are presented to illustrate the risk of the portfolio selection model with interval values. We conclude that the evaluation by the fuzzy statistical test enables us to obtain a stable expected return and low risk investment with different choices based on the risk level k, which is taken for the risk level.

An Algorithm Design of Kansei Recommender System

We propose an algorithm design for a Recommender System based on a Kansei model in this paper, we called this algorithm as Kansei Recommender System (hereafter, we denoted as KRS algorithm). The purpose of KRS algorithm is to support designers to pre-know the appearance feeling (Kansei) of products from consumers. To complete this algorithm, we divide the algorithm design into three parts: (1) Extract Kansei factors and evaluation factors from consumers’ shopping items. (2) Determine a Kansei model for KRS algorithm. (3) Making decision by using KRS algorithm. We also give a concept map of paradigm by using KRS algorithm. In conclusion, we remain the future work to implement the KRS algorithm in real case studies with different fields of enterprises.

Confidence interval calculator for fuzzy random regression

The software tool namely Confidence Interval Calculator (CIC) presented in this paper is designed to compute confidential interval of fuzzy random regression (FRR) model. FRR model uses fuzzy random input-output data to construct confidential interval for prediction. Manual calculation by hand of FRR however requires lengthy time to compute the result. Hence, CIC is introduced to alleviate computational difficulties and to reduce the computational time. The tool provides a function to capture input (fuzzy random) data and to calculate the expected value, and the variance. Technical formulation is embedded in the tool which enables the tool to compute the result correctly. The solution of a technical problem is described with numerical example.

An Enhanced Possibilistic Programming Model with Fuzzy Random Confidence-Interval for Multi-objective Problem

Mathematical models are established to represent real-world problems. Since the real-world faces various types of uncertainties, it makes mathematical model suffers with insufficient uncertainties modeling. The existing models lack of explanation in dealing uncertainties. In this paper, construction of mathematical model for decision making scenario with uncertainties is presented. Primarily, fuzzy random regression is applied to formulate a corresponding mathematical model from real application of a multi-objective problem. Then, a technique in possibilistic theory, known as modality optimization is used to solve the developed model. Consequently, the result shows that a well-defined multi-objective mathematical model is possible to be formulated for decision making problems with the uncertainty. Indeed, such problems with uncertainties can be solved efficiently with the presence of modality optimization.

Facility location problems with fuzzy demands based on parametric assessment

We discuss uncertainty included in demands in facility location problem in this paper. The uncertain demand is named as fuzzy demand in the paper. In the facility location model, the parameters of fuzzy demand are determined by calculating the estimated expected value of the fuzzy demand, which is obtained by using estimated parameters of underlying probability distribution function of fuzzy data. Moreover, we propose a defuzzification formula of the fuzzy demand named a realization of fuzzy demand. The defuzzification formula of fuzzy demand composes the upper bound of fuzzy demand and the lower bound of fuzzy demand. Moreover, an error of fuzzy demand is assessed as mean absolute percentage error of fuzzy demand. Empirical studies show that we can solve the real-life location problem by using the defuzzification formula of fuzzy demand and get higher profit in our facility location model than conventional methods.