Narrow Results

We consider a lattice-based model in multiattribute decision making, where preferences are represented by global utility functions that evaluate alternatives in a lattice structure (which can account for situations of indifference as well as of incomparability). Essentially, this evaluation is obtained by first encoding each of the attributes (nominal, qualitative, numeric, etc.) of each alternative into a distributive lattice, and then aggregating such values by lattice functions. We formulate version spaces within this model (global preferences consistent with empirical data) as solutions of an interpolation problem and present their complete descriptions accordingly. Moreover, we consider the computational complexity of this interpolation problem, and show that up to 3 attributes it is solvable in polynomial time, whereas it is NP complete over more than 3 attributes. Our results are then illustrated with a concrete example.

To evaluate the pronunciation skills of spoken English is one of the key tasks for computer-aided spoken language learning (CALL). While most of the researchers focus on improving the speech recognition techniques to build a reliable evaluation system, another important aspect of this task has been ignored, i.e. the pronunciation evaluation model that integrates both the reliabilities of existing speech processing systems and the learner's pronunciation personalities. To take this aspect into consideration, a Sugeno integral-based evaluation model is introduced in this paper. At first, the English phonemes that are hard to be distinguished (HDP) for Chinese language learners are grouped into different HDP sets. Then, the system reliabilities for distinguishing the phonemes within a HDP set are computed from the standard speech corpus and are integrated with the phoneme recognition results under the Sugeno integral framework. The fuzzy measures are given for each subset of speech segments that contains n occurrences of phonemes within a HDP set. Rather than providing a quantity of scores, the linguistic descriptions of evaluation results are given by the model, which is more helpful for the users to improve their spoken language skills. To get a better performance, generic algorithm (GA)-based parameter optimization is also applied to optimize the model parameters. Experiments are conducted on the Sphinx-4 speech recognition platform. They show that, with 84.7% of average recognition rate of the SR system on standard speech corpus, our pronunciation evaluation model has got reasonable and reliable results for three kinds of test corpora.

Previous work has shown that the Choquet integral w.r.t. a symmetric k-order additive fuzzy measure is characterized as a weighted sum, with possibly negative weights, of k specific OWA operators, and that the Sugeno integral w.r.t. a symmetric k-order maxitive fuzzy measure is characterized as a weighted maximum of k order statistics. In this paper, these characterizations are extended to the general, non-symmetric case, thereby providing additional insight in the symmetric case. More specifically, a new general decomposition of the Choquet integral w.r.t. a k-order additive fuzzy measure and of the Sugeno integral w.r.t. a k-order maxitive fuzzy measure are established.

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a preference functional is presented in the qualitative framework of two decision paradigms: multi-criteria decision-making and decision-making under uncertainty. The parallelism between the representation theorems in both settings is stressed, even if a basic requirement like the idempotency of the aggregation scheme should be explicitely stated in multi-criteria decision-making, while its counterpart is implicit in decision under uncertainty by equating the utility of a constant act with the utility of its consequence. Important particular cases of Sugeno integrals such as prioritized minimum and maximum operators, their ordered versions, and Boolean max-min functions are studied.

The Choquet and Sugeno (fuzzy) integrals are examples of piecewise linear functions on a finite dimensional space ℝⁿ. In this paper we consider piecewise linear functions as aggregation functions and establish a Max-Min polynomial representation of these functions.

In this work, we prove a Prékopa-Leindler type inequality for the Sugeno integral. More precisely, if 0 < λ < 1 and h((1-λ)x+λy) ≥ f(x)^1-λg(y)^λ, ∀ x,y ∈ ℝⁿ, where h, f and g are nonnegative μ-measurable functions on ℝⁿ, then , for any concave fuzzy measure μ. Also, we derive a general Brunn-Minkowski inequality (standard form) for any homogeneous quasiconcave fuzzy measure μ on ℝⁿ.

The time or space complexity may considerably increase for a single classifier if all features are taken into account. Thus, it is reasonable to train a single classifier by partial features. Then, a set of multiple classifiers can be generated, and an aggregation of outputs from different classifiers is subsequently performed. The aim of this paper is to propose a classification system with a heuristic fusion scheme in which multiple fuzzy association rule-based classifiers with partial features are combined, and show the feasibility and effectiveness of fusing multiple classifiers through the Sugeno integral extended by ordered weighted averaging operators. In comparison with the Sugeno integral by computer simulations on the iris data and the appendicitis data show that the overall classification accuracy rate could be improved by the Sugeno integral with ordered weighted averaging operators. The experimental results further demonstrate that the proposed method performs well in comparison with other fuzzy or non-fuzzy classification methods.

In this paper, we generalize Ying's model of linguistic quantifiers [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence, 170 (2006) 581-606] to intuitionistic linguistic quantifiers. An intuitionistic linguistic quantifier is represented by a family of intuitionistic fuzzy-valued fuzzy measures and the intuitionistic truth value (the degrees of satisfaction and non-satisfaction) of a quantified proposition is calculated by using intuitionistic fuzzy-valued fuzzy integral. Description of a quantifier by intuitionistic fuzzy-valued fuzzy measures allows us to take into account differences in understanding the meaning of the quantifier by different persons. If the intuitionistic fuzzy linguistic quantifiers are taken to be linguistic fuzzy quantifiers, then our model reduces to Ying's model. Some excellent logical properties of intuitionistic linguistic quantifiers are obtained including a prenex norm form theorem. A simple example is presented to illustrate the use of intuitionistic linguistic quantifiers.

Comonotone maxitivity and minitivity of Sugeno integral can be seen as commuting of the Sugeno integral and max, resp. min operator for comonotone functions. In the paper, we look for the other operators commuting with the Sugeno integral when comonotone functions are considered. We give full description of all such commuting operators, which can be classified into 18 classes.

The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L₁ (Lipschitz stability) and L_∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization of stochastically increasing Archimedean copulas is also given.

In this paper, a two-dimensional Hardy type inequality for fuzzy integrals is proved. Also, some illustrative examples are presented.

In this paper we consider Steffensen's integral inequality for the Sugeno integral

Generalizing a first approach by L. A. ZADEH (J. Math. Anal. Appl. 23, 1968), expected values of fuzzy events are studied which are (up to standard boundary conditions) only required to be monotone. They can be seen as an extension of capacities, i.e., monotone set functions satisfying standard boundary conditions. Some of these expected values can be characterized axiomatically, others are based on some distinguished integrals (Choquet, Sugeno, Shilkret, universal, and decomposition integral).

This paper propose a Berwald type inequality and a Favard type inequality for Sugeno integrals. That is, we first show that

A Fuzzy Decision Tree is a classification method consisting of a set of rules defined on fuzzy variables. The final class assignment is done according to the output of all the rules of the tree. Generally, the maximum operator is used to aggregate the results of the rules. However, some approaches based on more complex aggregation operators have appeared recently. In this work we propose to use Sugeno and Choquet integrals together with a Hierarchically ⊥-Decomposable Fuzzy Measure (HDFM) to aggregate the rules' values. The HDFM exploits the hierarchical structure of the fuzzy decision tree and takes into account the confidence value of the output together with the classification ambiguity of the rules. The HDFM is built using Sugeno-Weber t-conorms.We validate this approach on several classification problems and make a comparison of the performance with the state of art aggregation operators. Finally, a case study with a real dataset of diabetic patients is analyzed to predict the risk of suffering from diabetic retinopathy.

It is well known that the Choquet and Sugeno integrals w.r.t. a discrete fuzzy measure can be considered as aggregation operators. In this paper, we study in detail two special cases of symmetric fuzzy measures, i.e. fuzzy measures of which the values only depend upon the cardinality of the arguments. The first case is that of a symmetric k-order additive fuzzy measure, i.e. a fuzzy measure of which the Möbius transform vanishes in sets with cardinality greater than k. A new increasing sequence of binomial OWA operators is introduced. It is recalled that weighted sums of aggregation operators, with possibly negative weights, may also lead to aggregation operators. The Choquet integral w.r.t. a symmetric k-order additive fuzzy measure is then characterized as such a weighted sum of the first k binomial OWA operators. The second case is that of a symmetric k-order maxitive fuzzy measure, i.e. a fuzzy measure of which the possibilistic Möbius transform vanishes in sets with cardinality greater than k. The Sugeno integral w.r.t. a symmetric k-order maxitive fuzzy measure is then characterized as a weighted maximum of the last k order statistics.