1,720,992 research outputs found
Intuitionistic fuzzy sets in questionnaire analysis
No full textFuzzy sets represent an extension of the concept of set, used to mathematically model veiled and indefinite concepts, such as those of youth, poverty, customer satisfaction and so on. Fuzzy theory introduces a membership function, expressing the degree of membership of the elements to a set. Intuitionistic fuzzy sets and hesitant fuzzy sets are two extensions of the theory of fuzzy sets, in which non-membership degrees and hesitations expressed by a set of experts are, respectively, introduced. In this paper, we apply intuitionistic fuzzy sets to questionnaire analysis, with a focus on the construction of membership, non-membership and uncertainty functions. We also suggest the possibility of considering intuitionistic hesitant fuzzy sets as a valuable theoretical framework. We apply these models to the evaluation of a Public Administration and we assess our results through a sensitivity analysis
Inferential confidence intervals for fuzzy analysis of teaching satisfaction
No full textFuzzy sets are an extension of classical sets, used to mathematically model indefinite concepts, such as that of customer satisfaction. This is obtained by introducing a membership function expressing the degree of membership of the elements to a set. Intuitionistic fuzzy sets represent an extension of the theory of fuzzy sets, in which also a suitable non-membership function is defined. In this paper we aim at quantifying a latent construct, namely satisfaction, using fuzzy sets and intuitionistic fuzzy sets. We put forth a general evaluation method: first, we introduce a fuzzy satisfaction index to obtain membership values. Second, inferential confidence intervals (ICI), calculated through Bootstrap-t and percentile procedures, are used to assess the uncertainty underpinning membership and non-membership estimates. Third, we address the problem of optimal and multiple ICI, as well as their generalization through p values and q-values. In particular, we consider the problem of analyzing the responses to evaluation questionnaires. We apply this new method to a national program of evaluation of University courses and we discuss our framework in comparison with other evaluation techniques
Bootstrap confidence intervals for biodiversity measures based on Gini index and entropy
No full textMonitoring the richness and the diversity of species living in an ecosystem is an important goal of ecology. To this purpose, measures of biodiversity have been introduced as statistical summaries of the abundance vector. In particular, we take into consideration the Gini–Simpson and the Shannon–Wiener indices, along with the effective number of species calculated through these measures, proposed, respectively, by Laakso and Taagepera (Comp Polit Stud 12:3–25, 1979) and Leti (Statistica descrittiva, Bologna, Il Mulino, 1983). It is an open question how to associate to these indices a measure of uncertainty. In this paper we compare confidence intervals based on these measures, calculated through three different bootstrap methods: percentile, -t and accelerated bias-corrected percentile. We recommend to practitioners to use the percentile procedure, as it is straightforward and computationally feasible, providing results very close to those obtained by more complex techniques
Bipolar distributions in fuzzy sets theory
No full textIn this paper we consider the problem of measuring latent variables with ordinal scales and we put forward an original approach to this issue, which combines the use of Intuitionistic Fuzzy Sets with the calculation of bipolar means and bipolar distributions. Intuitionistic Fuzzy theory allows a researcher to model the degree of membership and non-membership to a certain fuzzy set, as well as the residual uncertainty. It is fundamental, for decision making, to properly model such source of variability. We focus on the definition of uncertainty, using bipolar distributions and introducing Intuitionistic Bipolar Fuzzy Sets. This allows us to distinguish between a negative and a positive component of uncertainty, which represents a novelty in Intuitionistic Fuzzy analysis. We apply this method to a national evaluation survey (The Magellano Project) proposed by the Italian Ministry of Public Administration, aimed at involving employees in management decision
Fuzzy theory: Applications and criticism
No full textThe fuzzy theory is a generalization of the standard set theory that is based on the membership function, which expresses, in the fuzzy sense, the membership degree of an element to a set. After a review of the main operations on fuzzy sets, some applications are proposed in various contexts such as in engineering sciences or computational sciences, in automatic systems control or quality evaluation. Special attention is devoted to the applications of fuzzy theory in cognitive sciences by highlighting various critical issues reported in the literature and some responses to these. The intuitionistic and hesitant settings are then introduced and it is shown how these operate the union and intersection of fuzzy sets. In the intuitionistic fuzzy theory; along with a membership function, a non-membership function is defined and uncertainty is modeled. Besides, the hesitant fuzzy theory allows to express the uncertainty of one or more decision makers
The ordinal inter-rater agreement in the evaluation of University courses
No full textIn this paper we consider the problem of the evaluation of undergraduate and graduate courses, in the context of Italian universities. We present a descriptive measure of ordinal inter-rater agreement that can be associated with a suitable index of satisfaction. This measure is a modification of a previously proposed index, which avoids the problem of paradoxes of both Cohen’s and Fleiss’ kappa statistics. We apply our results to the evaluation of the Bachelors and Masters of Sciences in Economics at the University of Milan-Bicocca
A Measure of Ordinal Concordance for the Evaluation of University Courses
No full textAbstractIn this paper we apply the s* statistic, aimed to measure the inter-rater agreement between observers in case of ordinal variables, to the evaluation of the quality of University courses. The objective is to measure the inter-rater agreement between students, along with their satisfaction, in order to verify the consistency of judgments expressed by independent observers. s* is a modification of a previously proposed index, which avoids the problem of paradoxes of Cohen's and Fleiss’ kappa statistics. We present the s* index from both a descriptive and an inferential point of view. In particular, as far as statistical inference is concerned, we show that s* is a biased estimator of the inter-rater agreement in the population and, under the null hypothesis of inter-rater agreement by chance, s* is asymptotically normally distributed
Fuzzy Analysis of Students’ Ratings
No full textBackground: Intuitionistic fuzzy sets (IFS) represent a methodology for quantifying latent variables in questionnaire analysis through membership and non-membership functions, which are linked by an uncertainty function. Objectives: We aim to apply an IFS approach to the problem of students’ satisfaction of university teaching. Such framework can take into account a source of uncertainty related to items and another related to subjects. Results: A new technique for IFS analysis is set forth and generalized to a multivariate scenario. Potential advantages of the IFS perspective with respect to other nonfuzzy approaches are provided. Application: We apply this method to a national program of university courses evaluation and we focus, in particular, on the outcomes of two Masters in Statistics
Assessing the inter-rater agreement for ordinal data through weighted indexes
No full textAssessing the inter-rater agreement between observers, in the case of ordinal variables, is an important issue in both the statistical theory and biomedical applications. Typically, this problem has been dealt with the use of Cohen's weighted kappa, which is a modification of the original kappa statistic, proposed for nominal variables in the case of two observers. Fleiss (1971) put forth a generalization of kappa in the case of multiple observers, but both Cohen's and Fleiss' kappa could have a paradoxical behavior, which may lead to a difficult interpretation of their magnitude. In this paper, a modification of Fleiss' kappa, not affected by paradoxes, is proposed, and subsequently generalized to the case of ordinal variables. Monte Carlo simulations are used both to testing statistical hypotheses and to calculating percentile and bootstrap-t confidence intervals based on this statistic. The normal asymptotic distribution of the proposed statistic is demonstrated. Our results are applied to the classical Holmquist et al.'s (1967) dataset on the classification, by multiple observers, of carcinoma in situ of the uterine cervix. Finally, we generalize the use of s∗ to a bivariate case
Anatomical and spatial matching in imitation: Evidence from left and right brain-damaged patients.
No full textImitation is a sensorimotor process whereby the visual information present in the model's movement has to be coupled with the activation of the motor system in the observer. This also implies that greater the similarity between the seen and the produced movement, the easier it will be to execute the movement, a process also known as ideomotor compatibility. Two components can influence the degree of similarity between two movements: the anatomical and the spatial component. The anatomical component is present when the model and imitator move the same body part (e.g., the right hand) while the spatial component is present when the movement of the model and that of the imitator occur at the same spatial position. Imitation can be achieved by relying on both components, but typically the model's and imitator's movements are matched either anatomically or spatially. The aim of this study was to ascertain the contribution of the left and right hemisphere to the imitation accomplished either with anatomical or spatial matching (or with both). Patients with unilateral left and right brain damage performed an ideomotor task and a gesture imitation task. Lesions in the left and right hemispheres gave rise to different performance deficits. Patients with lesions in the left hemisphere showed impaired imitation when anatomical matching was required, and patients with lesions in the right hemisphere showed impaired imitation when spatial matching was required. Lesion analysis further revealed a differential involvement of left and right hemispheric regions, such as the parietal opercula, in supporting imitation in the ideomotor task. Similarly, gesture imitation seemed to rely on different regions in the left and right hemisphere, such as parietal regions in the left hemisphere and premotor, somatosensory and subcortical regions in the right hemisphere
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