Tag: Soft Computing – A Fusion of Foundations, Methodologies and Applications

In the last few years, several papers have exploited multi-objective evolutionary algorithms (MOEAs) to generate Mamdani fuzzy
rule-based systems (MFRBSs) with different trade-offs between interpretability and accuracy. In this framework, a common approach
is to distinguish between interpretability of the rule base (RB), also known as complexity, and interpretability of fuzzy
partitions, also known as integrity of the database (DB). Typically, complexity has been used as one of the objectives of
the MOEAs, while partition integrity has been ensured by enforcing constraints on the membership function (MF) parameters.
In this paper, we propose to adopt partition integrity as an objective of the evolutionary process. To this aim, we first
discuss how partition integrity can be measured by using a purposely defined index based on the similarity between the partitions
learned during the evolutionary process and the initial interpretable partitions defined by an expert. Then, we introduce
a three-objective evolutionary algorithm which generates a set of MFRBSs with different trade-offs between complexity, accuracy
and partition integrity by concurrently learning the RB and the MF parameters of the linguistic variables. Accuracy is assessed
in terms of mean squared error between the actual and the predicted values, complexity is calculated as the total number of
conditions in the antecedents of the rules and integrity is measured by using the purposely defined index. The proposed approach
has been experimented on six real-world regression problems. The results have been compared with those obtained by applying
the same MOEA, but with only accuracy and complexity as objectives, both to learn only RBs, and to concurrently learn RBs
and MF parameters, with and without constraints on the parameter tuning. We show that our approach achieves the best trade-offs
between interpretability and accuracy. Finally, we compare our approach with a similar MOEA recently proposed in the literature.

Three ways for generating the optimal transitive approximations or a suboptimal transitive approximation are given in this
paper. The first one can obtain all the optimal transitive approximations for any proximity relation. However, trying to find
all the optimal transitive approximations can be very expensive. The second one gives a method to obtain a suboptimal transitive
approximation which can frequently generate an optimal transitive approximation. Furthermore, starting from the transitive
closure the third method is proposed which can obtain a locally optimal transitive approximation. Finally, numerical experiments
are carried out to show the abilities of these algorithms and compare them to other existing approximation algorithms.

This paper proposes a novel approach to attribute reduction in consistent decision tables within the framework of dependence
spaces. For a consistent decision table

(U,AÈ{d}),

an equivalence relation r on the conditional attribute set A and a congruence relation R on the power set of A are constructed, respectively. Two closure operators, T

_r
and T

_R
, and two families of closed sets,

Cr

and

CR,

are then constructed with respect to the two equivalence relations. After discussing the properties of

Cr

and

CR,

the necessary and sufficient condition for

Cr=CR

is obtained and employed to formulate an approach to attribute reduction in consistent decision tables. It is also proved,
under the condition

Cr=CR,

that a relative reduct is equivalent to a

R

-reduction defined by Novotny and Pawlak (Fundam Inform 16:275–287, 1992).

The persistence and evolution of systems essentially depend on their adaptivity to new situations. As an expression of intelligence,
adaptivity is a distinguishing quality of any system that is able to learn and to adjust itself in a flexible manner to new
environmental conditions and such ability ensures self-correction over time as new events happen, new input becomes available,
or new operational conditions occur. This requires self-monitoring of the performance in an ever-changing environment. The
relevance of adaptivity is established in numerous domains and by versatile real-world applications. The present paper presents
an incremental fuzzy rule-based system for classification purposes. Relying on fuzzy min–max neural networks, the paper explains
how fuzzy rules can be continuously online generated to meet the requirements of non-stationary dynamic environments, where
data arrives over long periods of time. The approach proposed to deal with an ambient intelligence application. The simulation
results show its effectiveness in dealing with dynamic situations and its performance when compared with existing approaches.

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions.
DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from
premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation
resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed
up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence
rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that
fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with
the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance
of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities
and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show
that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison
with basic DE and several other contemporary optimization algorithms.