Search

Hydroforming is a relatively new technology of forming and profiling. So far, the application of this method has been limited by the costs of die production. The cost of the dies and the long production start-up time made this method economically viable for the production of hundreds of products. The approach change to the tool design for profile shaping techniques has allowed to develop the new hydroforming method perfectly suited to low-volume or even unit production. In traditional solutions, the die is rigid and does not deform during the expansion of the profile. In the newly patented RTH (Rapid Tube Hydroforming) method, the die undergoes controlled deformation during the process. The specificity of the granular materials used for the production of the dies makes modeling the behavior of the die during the expansion of the profile a remarkable problem. This contribution presents considerations on the fuzzy inference method used to model the technological process. As a result, it was possible to more accurately determine the importance of individual die parameters (geometry and material properties), and thus better predict the final shape of the formed profile. The main goal is to understand the effect of shaped profile on the matrix and to recognize the influence of granular material in the matrix under the compaction conditions of the expanded profile on its final geometry.

A new statistical goodness-of-fit for comparing distributions of two or more populations and based on fuzzy data is proposed. Its idea goes back to the k-nearest neighbor technique applied in pattern recognition, where it simply consists in classifying an object by the majority vote of its neighbors. In our paper we show that by an appropriate test statistic construction which counts the number of nearest neighbors between and within samples it is possible to check whether available fuzzy samples come or not from the same distribution. It is worth underlying that the suggested testing procedure is completely distribution-free which seems to be of extreme importance in statistical reasoning with fuzzy data. Our test proposal is completed with a study of its properties and a case study related to quality assessment.

In 2011 Grzegorzewski introduced two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications. They are based on copulas and make a bridge between probability theory and fuzzy logic. Another family of fuzzy conditional implication operators was proposed by Dolati et al. in 2013. In this paper we consider some properties of these three classes of fuzzy implications like the law of contrapositions and the law of importation. Moreover, we examine intersections of these families of implications with R-implications, ( S, N)-implications, QL-operations and Yager’s f- and g-generated implications.

A fuzzy least squares estimator in the multiple with fuzzy-input&ndash, fuzzy-output linear regression model is considered. The paper provides a formula for the L2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

In this paper we firstly review the definition of fuzzy semi-numbers and study some of their properties. Then, we consider some methods for converting fuzzy semi-numbers to fuzzy numbers in order to find the distance between fuzzy semi-numbers. By presenting a new distance function, we also find the distance between fuzzy semi-numbers directly without any change to their originality. Finally, we prove some properties of the presented distance and study a practical motivational medical case study along with some numerical examples.

Probabilistic implications and probabilistic S-implications, introduced recently by Grzegorzewski, have attracted attention of researchers engaged in fuzzy implications. Since these two families are based on copulas, they form a kind of bridge between probability theory and fuzzy logic. In this paper we generalize the aforementioned two classes and propose a new approach for constructing fuzzy implications which combines a given a priori fuzzy implication and a semicopula.

Recently, Grzegorzewski (2011) introduced two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In his previous articles author gave a motivation to his idea and indicates some interesting connections between new families of multivalued implications and the dependence structure of the underlying environment. In this paper the laws of contraposition, the law of importation and T-conditionality are studied for these families of fuzzy implications. Furthermore, we discuss the intersections of both new families of implications with R-implications, (S,N)-implications and QL-operations.

A new methodology for processing non-normal fuzzy sets is proposed. To break the predominant constraint on normality of fuzzy numbers the concept of fuzzy semi-numbers is introduced Then it is shown how to generalize operations defined on fuzzy numbers onto a family of fuzzy semi-numbers with possibly different heights.

One of the key problems in statistics is to get information about the form of the population from which a sample is drawn. To check compatibility of a set of observed values with a presumed distribution one can apply various, so called, goodness-of-fit tests. It seems that the goodness-of-fit testing problem becomes much more complicated in the presence of imprecise observations. Actually, although many statistical procedure dedicated for specified types of distributions were generalized to fuzzy environment, still there are not too many tools that help under fuzzy data from the unknown distribution. Therefore, in the paper we suggest how to generalize the well-known one-sample goodness-of-fit tests based on the empirical distribution function, like the Kolmogorov test, the Cramer-von Mises test or the Anderson-Darling test, for fuzzy data.

A novel approach for detecting patterns in price time series is shown. The proposed system for identifying consolidation phases is based on fuzzy geometric protoforms and classification trees. Promising results of the empirical studies prove that the suggested fuzzy geometric protoforms are very useful for identifying patterns in graphical visualizations of data. Moreover, the architecture of the system enables successful incorporation of genetic optimization what enables capturing various data sets structure and unstable conditions on financial markets.

The multiple fuzzy linear regression model with fuzzy input–fuzzy output is considered. Assuming that fuzzy inputs and fuzzy outputs are modeled by triangular fuzzy numbers, we prove the consistency and asymptotic normality of the least squares estimators.

Recently, fuzzy implications based on copulas, i.e. probabilistic implications and probabilistic S-implications, were introduced and their properties were explored. However, the reverse problem of copulas derived from fuzzy implications, suggested by Massanet et al. [11, 12], is also of interest. In the paper we consider geometric properties of those fuzzy implications that generate copulas. Moreover, we consider the reverse problem for some generalizations of copulas like quasi-copulas and semi-copulas.

This volume presents recent research, challenging problems and solutions in Intelligent Systems covering the following disciplines: artificial and computational intelligence, fuzzy logic and other non-classic logics, intelligent database systems, information retrieval, information fusion, intelligent search (engines), data mining, cluster analysis, unsupervised learning, machine learning, intelligent data analysis, (group) decision support systems, intelligent agents and multi-agent systems, knowledge-based systems, imprecision and uncertainty handling, electronic commerce, distributed systems, etc. The book defines a common ground for sometimes seemingly disparate problems and addresses them by using the paradigm of broadly perceived intelligent systems. It presents a broad panorama of a multitude of theoretical and practical problems which have been successfully dealt with using the paradigm of intelligent computing.

Trapezoidal approximation of fuzzy numbers is discussed in relation to data aggregation. An important problem whether it is better to simplify initial data before using an aggregation operator or conversely, to aggregate original fuzzy values and then to simplify the output is addressed.

In this paper, we present the novel concept of fuzzy semi-numbers. Then, a method for assigning distance between every pair of fuzzy semi-numbers is given. Moreover, it is shown that this distance is a metric on the set of all trapezoidal fuzzy semi-numbers with the same height and is a pseudo-metric on the set of all fuzzy semi-numbers. Also, with utilizing this distance we propose an approximation of a fuzzy seminumber with given height and apply this approximation method in a medical case study.

The traditional query languages used in database management systems require precise and unambiguous queries only. Fuzzy querying was introduced to relax this rigidity and allow the user more natural information retrieval. In this article we suggest how to enrich fuzzy querying by the use of IF-sets. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 587–597, 2007.

Fuzzy opinions are very common in surveys performed by social sciences. A fuzzy multinomial distribution for modeling such opinions is proposed. Next, a method for constructing a generalized version of the chi-square test of homogeneity which allows fuzzy data is proposed.

Recently, Grzegorzewski [5-7] introduced two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In the same article [7] author gives a motivation to his idea and indicates some interesting connections between new families of implications and the dependence structure of the underlying environment. In this paper the laws of contraposition and the law of importation are studied for these families of fuzzy implications.

A problem of defuzzification of a fuzzy test for testing statistical hypotheses with vague data is considered. Two defuzzification operators are discussed. It is shown that the superposition of a fuzzy test and these operators leads to decision strategies equivalent to the classical crisp tests. Moreover, another source of randomization in hypothesis testing is indicated, and a new ground for the randomized tests application is given. Advice to practitioners – how to defuzzify – is also given.

A definition of fuzzy test for testing statistical hypotheses with vague data is proposed. Then the general method for the construction of fuzzy tests for hypotheses concerning an unknown parameter against one-sided or two-sided alternative hypotheses is shown. This fuzzy test, contrary to the classical approach, leads not to the binary decision: to reject or to accept given null hypothesis, but to a fuzzy decision showing a grade of acceptability of the null and the alternative hypothesis, respectively. However, it is a natural generalization of the traditional test, i.e. if the data are precise, not vague, we get a classical statistical test with the binary decision. A measure of fuzziness of the considered fuzzy test is suggested and the robustness of that test is also discussed.

Since fuzzy numbers are not linearly ordered a median of a fuzzy sample cannot be determined directly as it happens with crisp observations. Even the very notion of a median of a fuzzy sample is not well established. Therefore we propose some definitions of the fixed-shape fuzzy median of a fuzzy sample as a member of a given class of fuzzy numbers which minimizes the distance to the sample. We also prove the existence of such fixed-shape median for the most important subfamilies of fuzzy numbers and the broad class of metrics.

A new family of implication operators, called probabilistic implications, are discussed. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that probabilistic fuzzy implications have some interesting properties, especially those connected with the dependence structure of the underlying environment. Therefore, it seems that probabilistic implications might be a useful tool in approximate reasoning, knowledge extraction and decision making.

The problem of trend detection in fuzzy time series is considered. Two fuzzy tests are suggested and their basic properties are examined. Moreover, the general problem of fuzziness in statistical data which might be either inherent or imposed is discussed.

The problem of measuring degree of inclusion between intuitionistic fuzzy sets is discussed. A simple subsethood measure based on the Hamming distance between intuitionistic fuzzy sets is suggested.

The problem of testing fuzzy hypotheses in the presence of vague data is considered. A new method based on the necessity index of strict dominance (NSD) is suggesteded. An example how to apply the proposed test in statistical quality control is shown.

Part I: Introductory Papers.- Part II: Soft Methods in Probability - Fundamentals.- Part III: Soft Methods in Statistics - Fuzzy Stochastic Models.- Part IV: Soft Methods in Data Analysis - Fuzzy, Rough and Other Approaches.

The paper is devoted to nonclassical approaches to hypotheses testing. We consider testing statistical hypotheses in fuzzy environment, i.e. tests with vague data, tests for fuzzy hypotheses and tests for fuzzy hypotheses with vague data. We also present a possibilistic interpretation of statistical tests.

A method for designing single sampling plans by attributes with relaxed producer’s and consumer’s risks and quality levels is suggested. Since small deviations of the parameter (risk, quality level) from its target value are very often of no importance this soft method for designing sampling plans is more flexible than the conventional one.

Life tests for vague data expressed, e.g. by plain words, are considered. It is shown how to handle with fuzzy lifetimes and fuzzy censoring in order to find estimates, fuzzy confidence intervals and verify hypotheses concerning the mean lifetime. Different strategies corresponding to the decision-maker’s attitude to the life data is considered.

International audience; In evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibility and rough partitions, which are recovered as special cases. Different algorithms to generate a credal partition are reviewed. We also describe different ways in which a credal partition, such as produced by the EVCLUS or ECM algorithms, can be summarized into any of the simpler clustering structures.