Search

This paper presents a comprehensive study of the signed distance metric for fuzzy numbers. Due to the property of directionality, this measure has been widely used. However, it has a main drawback in handling asymmetry and irregular shapes in fuzzy numbers. To overcome this rather bad feature, we introduce two new distances, the balanced signed distance (BSGD) and the generalised signed distance (GSGD), seen as generalisations of the classical signed distance. The developed distances successfully and effectively take into account the shape, the asymmetry and the overlap of fuzzy numbers. The GSGD is additionally directional, while the BSGD satisfies the requirements for being a metric of fuzzy quantities. Analytical simplifications of both distances in the case of often-used particular types of fuzzy numbers are provided to simplify the computation process, making them as simple as the classical signed distance but more realistic and precise. We empirically analyse the sensitivity of these distances. Considering several scenarios of fuzzy numbers, we also numerically compare these distances against established metrics, highlighting the advantages of the BSGD and the GSGD in capturing the shape properties of fuzzy numbers. One main finding of this research is that the defended distances capture with great precision the distance between fuzzy numbers; additionally, they are theoretically appealing and are computationally easy for traditional fuzzy numbers such as triangular, trapezoidal, Gaussian, etc., making these metrics promising. [ABSTRACT FROM AUTHOR]

In several research areas, ratings data and response times have been successfully used to unfold the stagewise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regard to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameters triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers leads to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures. [ABSTRACT FROM AUTHOR]

Three organic fertilizers of manure sheep, sewage sludge and municipal waste were mixed with soil at the rates of 0%, 1.25% and 2.5% (w/w), respectively. In a greenhouse experiment, corn seed were grown on pots of 3 kg treated contaminated soils and irrigated. Sixty days after sowing, the aerial plant parts were harvested and analyzed for Cadmium (Cd) and Lead (Pb) contents. Since all of data in this research are fuzzy, we need an extended version of analysis of variance (ANOVA) to investigate on these fuzzy observations. In this paper, as a method to compare several populations, the fuzzy analysis of variance (FANOVA) has been used where the collected data considered fuzzy rather than crisp numbers and therefore all calculations are based on FANOVA method. Although, ANOVA based on vague data can lead to a fuzzy decision, but measuring the vagueness of this fuzzy decision is one of advantages of proposed method from the applied point of view. [ABSTRACT FROM AUTHOR]

Background: The fuzzy rating scale was introduced to cope with the imprecision of human thought and experience in measuring attitudes in many fields of Psychology. The flexibility and expressiveness of this scale allow us to properly describe the answers to many questions involving psychological measurement. Method: Analyzing the responses to a fuzzy rating scale-based questionnaire is indeed a critical problem. Nevertheless, over the last years, a methodology is being developed to analyze statistically fuzzy data in such a way that the information they contain is fully exploited. In this paper, a summary review of the main procedures is given. Results: The methods are illustrated by their application on the dataset obtained from a case study with nine-year-old children. In this study, children replied to some questions from the well-known TIMSS/ PIRLS questionnaire by using a fuzzy rating scale. The form could be filled in either on the computer or by hand. Conclusions: The study indicates that the requirements of background and training underlying the fuzzy rating scale are not too demanding. Moreover, it is clearly shown that statistical conclusions substantially often differ depending on the responses being given in accordance with either a Likert scale or a fuzzy rating scale. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions, namely, ideal statistical convergence and ideal lacunary statistical convergence for fuzzy numbers, their relationship and also make some observations about these classes. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to use soft computing technique and fuzzy statistical tool to evaluate people's performance on the marketing research and time management. Design/methodology/approach – Through standardized measurement system, the authors come up with real-value data to satisfy not the current needs but data itself. This is when fuzzy classification stands out and highlights the area of in-between and undefined. Findings – The proposed metric system helps the authors to assess the distance among trapezoidal fuzzy data. The index of efficiency between observed time and ideal time is also presented. Originality/value – With the ranking of fuzzy sample, the authors can examine the decision process by non-parametric testing hypothesis. [ABSTRACT FROM AUTHOR]

Nonparametric statistical tests are a distribution-free method without any assumption that data are drawn from a particular probability distribution. In this paper, to identify the distribution difference between two populations of fuzzy data, we derive a function that can describe continuous fuzzy data. In particular, the Kolmogorov-Smirnov two-sample test is used for distinguishing two populations of fuzzy data. Empirical studies illustrate that the Kolmogorov-Smirnov two-sample test enables us to judge whether two independent samples of continuous fuzzy data are derived from the same population. The results show that the proposed function is successful in distinguishing two populations of continuous fuzzy data and useful in various applications. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

The aging of the population in today's society has become a worldwide phenomenon. The elderly population is increasing. Care for the elderly people has become an important issue in the national policy. It is important to pay attention to and then analyze elderly people's leisure lifestyle issues. For different age groups and different residence, exploring the time of outgoing and watching TV, ideal retirement age, and the situation successful aging, etc. Unlike traditional statistical methods, we used fuzzy theory and soft Computing, proposed the counter-fuzzy transformation, and, by using the median test and variance test, established a nonparametric fuzzy statistical model for small-sized samples and for parameters of the fuzzy number or fuzzy interval types. Then, we made recommendations for elderly issues policy to decisions. [ABSTRACT FROM AUTHOR]

This paper extends the Wilcoxon signed-rank test to the case where the available observations are imprecise quantities, rather than crisp. To do this, the associated test statistic is extended, using the α-cuts approach. In addition, the concept of critical value is generalized to the case when the significance level is given by a fuzzy number. Finally, to accept or reject the null hypothesis of interest, a preference degree between two fuzzy sets is employed for comparing the observed fuzzy test statistic and fuzzy critical value. [ABSTRACT FROM AUTHOR]

Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis. The simplest type of ANOVA is one-way ANOVA for comparison among means of several populations. In this article, we extend one-way ANOVA to a case where observed data are fuzzy observations rather than real numbers. Two real-data examples are given to show the performance of this method. [ABSTRACT FROM AUTHOR]

In several works, Buckley (Soft Comput 9:512-518, ; Soft Comput 9:769-775 ; Fuzzy statistics, Springer, Heidelberg, ) have introduced and developed an approach to the estimation of unknown parameters in statistical models. In this paper, we introduce an improved method for the estimation of parameters for cases in which the Buckley's approach presents some drawbacks, as for example when the underlying statistic has a non-symmetric distribution. [ABSTRACT FROM AUTHOR]

We introduce the notions of fuzzy ternary subsemiring, fuzzy ideal and quasi-ideal in ternary semirings and study some properties of these two ideals. We also study the properties of fuzzy ideal and fuzzy quasi-ideal of ternary semirings. [ABSTRACT FROM AUTHOR]

As a fuzzification of the Choquet integral, the defuzzified choquet integral with fuzzy-valued integrand (DCIFI) takes a fuzzy-valued integrand and gives a crisp-valued integration result. In this paper, the DCIFI acts as a projection to project high-dimensional heterogeneous fuzzy data to one-dimensional crisp data to handle the classification problems involving different data forms, such as crisp data, interval values, fuzzy numbers, and linguistic variables, simultaneously. The nonadditivity of the signed fuzzy measure applied in the DCIFI can represent the interaction among the measurements of features towards the discrimination of classes. Values of the signed fuzzy measure in the DCIFI are considered to be unknown parameters which should be learned before the classifier is used to classify new data. We have implemented a genetic algorithm (GA)-based adaptive classifier-learning algorithm to optimally learn the signed fuzzy measure values and the classified boundaries simultaneously. The performance of our algorithm has been tested both on synthetic and real data. The experimental results are satisfactory and outperform those of existing methods, such as the fuzzy decision trees and the fuzzy-neuro networks. [ABSTRACT FROM AUTHOR]

This paper constitutes a first step towards an extension of correspondence analysis with fuzzy data (FCA). At this stage, our main objective is to lay down the algebraic foundations for this fuzzy extension of the usual correspondence analysis. A two-step method is introduced to convert the fuzzy eigenvalue problem to an ordinary one. We consider a fuzzy matrix as the set of its cuts. Each such cut is an interval-valued matrix viewed as a line-segment in the matrix space. In this way, line-segments of cut-matrices are transformed into intervals of eigenvalues. Therefore, the two-step method is essentially a reduction of the fuzzy eigenvalue problem to an ordinary one. We illustrate the FCA-fuzzy eigenvalue problem with a simple numerical example. We hope upon the completion of this project in near future, to be able to supply the necessary tools for the end user of the correspondence analysis with fuzzy data. [Copyright &y& Elsevier]