Supplementarity measures on fuzzy sets.

In this paper, we commence the study of the so called supplementarity measures. They are introduced axiomatically and are then related to incompatibility measures by antonyms. To do this, we have to establish what we mean by antonymous measure. We then prove that, under certain conditions, supplementarity and incompatibility measuresare antonymous. Besides, with the aim of constructing antonymous measures, we introduce the concept of involution on the set made up of all the ordered pairs of fuzzy sets. Finally, we obtain some antonymous supplementarity measures from incompatibility measures by means of involutions.

A new similarity function for generalized trapezoidal fuzzy numbers

Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawback for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature.

An interactive method of fuzzy probability elicitation in risk analysis

Expert knowledge is used to assign probabilities to events in many risk analysis models. However, experts sometimes find it hard to provide specific values for these probabilities, preferring to express vague or imprecise terms that are mapped using a previously defined fuzzy number scale. The rigidity of these scales generates bias in the probability elicitation process and does not allow experts to adequately express their probabilistic judgments. We present an interactive method for extracting a fuzzy number from experts that represents their probabilistic judgments for a given event, along with a quality measure of the probabilistic judgments, useful in a final information filtering and analysis sensitivity process.

Fuzzy data envelopment analysis:a discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on a-cut. One drawback of the a-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the a-cut approach. We introduce the concept of "local a-level" to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.

A fuzzy levelised energy cost method for renewable energy technology assessment

Renewable energy project development is highly complex and success is by no means guaranteed. Decisions are often made with approximate or uncertain information yet the current methods employed by decision-makers do not necessarily accommodate this. Levelised energy costs (LEC) are one such commonly applied measure utilised within the energy industry to assess the viability of potential projects and inform policy. The research proposes a method for achieving this by enhancing the traditional discounting LEC measure with fuzzy set theory. Furthermore, the research develops the fuzzy LEC (F-LEC) methodology to incorporate the cost of financing a project from debt and equity sources. Applied to an example bioenergy project, the research demonstrates the benefit of incorporating fuzziness for project viability, optimal capital structure and key variable sensitivity analysis decision-making. The proposed method contributes by incorporating uncertain and approximate information to the widely utilised LEC measure and by being applicable to a wide range of energy project viability decisions. © 2013 Elsevier Ltd. All rights reserved.

Document similarity:a new measure using OWA

In this paper, we propose a new similarity measure to compute the pair-wise similarity of text-based documents based on patterns of the words in the documents. First we develop a kappa measure for pair-wise comparison of documents then we use ordered weighting averaging operator to define a document similarity measure for a set of documents.

A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

Assessing productive efficiency of banks using integrated Fuzzy-DEA and bootstrapping:a case of Mozambican banks

Performance analysis has become a vital part of the management practices in the banking industry. There are numerous applications using DEA models to estimate efficiency in banking, and most of them assume that inputs and outputs are known with absolute precision. Here, we propose new Fuzzy-DEA α-level models to assess underlying uncertainty. Further, bootstrap truncated regressions with fixed factors are used to measure the impact of each model on the efficiency scores and to identify the most relevant contextual variables on efficiency. The proposed models have been demonstrated using an application in Mozambican banks to handle the underlying uncertainty. Findings reveal that fuzziness is predominant over randomness in interpreting the results. In addition, fuzziness can be used by decision-makers to identify missing variables to help in interpreting the results. Price of labor, price of capital, and market-share were found to be the significant factors in measuring bank efficiency. Managerial implications are addressed.

Critério de correntropia no treinamento de redes fuzzy wavelet neural networks para identificação de sistemas dinâmicos não lineares

The great interest in nonlinear system identification is mainly due to the fact that a large amount of real systems are complex and need to have their nonlinearities considered so that their models can be successfully used in applications of control, prediction, inference, among others. This work evaluates the application of Fuzzy Wavelet Neural Networks (FWNN) to identify nonlinear dynamical systems subjected to noise and outliers. Generally, these elements cause negative effects on the identification procedure, resulting in erroneous interpretations regarding the dynamical behavior of the system. The FWNN combines in a single structure the ability to deal with uncertainties of fuzzy logic, the multiresolution characteristics of wavelet theory and learning and generalization abilities of the artificial neural networks. Usually, the learning procedure of these neural networks is realized by a gradient based method, which uses the mean squared error as its cost function. This work proposes the replacement of this traditional function by an Information Theoretic Learning similarity measure, called correntropy. With the use of this similarity measure, higher order statistics can be considered during the FWNN training process. For this reason, this measure is more suitable for non-Gaussian error distributions and makes the training less sensitive to the presence of outliers. In order to evaluate this replacement, FWNN models are obtained in two identification case studies: a real nonlinear system, consisting of a multisection tank, and a simulated system based on a model of the human knee joint. The results demonstrate that the application of correntropy as the error backpropagation algorithm cost function makes the identification procedure using FWNN models more robust to outliers. However, this is only achieved if the gaussian kernel width of correntropy is properly adjusted.

Modulating membership grades to gain consensus for fuzzy set uncertainty values in a clinical decision support system

This paper deals with a very important issue in any knowledge engineering discipline: the accurate representation and modelling of real life data and its processing by human experts. The work is applied to the GRiST Mental Health Risk Screening Tool for assessing risks associated with mental-health problems. The complexity of risk data and the wide variations in clinicians' expert opinions make it difficult to elicit representations of uncertainty that are an accurate and meaningful consensus. It requires integrating each expert's estimation of a continuous distribution of uncertainty across a range of values. This paper describes an algorithm that generates a consensual distribution at the same time as measuring the consistency of inputs. Hence it provides a measure of the confidence in the particular data item's risk contribution at the input stage and can help give an indication of the quality of subsequent risk predictions. © 2010 IEEE.

A Fuzzy Decision Strategy for Topic Identification and Dynamic Selection of Language Models

International audience