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

Recently, in Dvurečenskij (http://arxiv.org/submit/103087, 2011), it was shown that if a pseudo effect algebra satisfies a kind of the Riesz decomposition property (RDP), then its state
space is either empty or a nonempty simplex. This will allow us to prove a Yosida–Hewitt type and a Lebesgue type decomposition
for measures on pseudo effect algebra with RDP. The simplex structure of the state space will entail not only the existence
of such a decomposition but also its uniqueness.

Evolutionary Algorithms (EAs) have been recognized to be well suited to approximate the Pareto front of Multi-objective Optimization
Problems (MOPs). In reality, the Decision Maker (DM) is not interested in discovering the whole Pareto front rather than finding
only the portion(s) of the front that matches at most his/her preferences. Recently, several studies have addressed the decision-making
task to assist the DM in choosing the final alternative. Knee regions are potential parts of the Pareto front presenting the
maximal trade-offs between objectives. Solutions residing in knee regions are characterized by the fact that a small improvement
in either objective will cause a large deterioration in at least another one which makes moving in either direction not attractive.
Thus, in the absence of explicit DM’s preferences, we suppose that knee regions represent the DM’s preferences themselves.
Recently, few works were proposed to find knee regions. This paper represents a further study in this direction. Hence, we
propose a new evolutionary method, denoted TKR-NSGA-II, to discover knee regions of the Pareto front. In this method, the
population is guided gradually by means of a set of mobile reference points. Since the reference points are updated based
on trade-off information, the population converges towards knee region centers which allows the construction of a neighborhood
of solutions in each knee. The performance assessment of the proposed algorithm is done on two- and three-objective knee-based
test problems. The obtained results show the ability of the algorithm to: (1) find the Pareto optimal knee regions, (2) control
the extent (We mean by extent the breadth/spread of the obtained knee region.) of the obtained regions independently of the
geometry of the front and (3) provide competitive and better results when compared to other recently proposed methods. Moreover,
we propose an interactive version of TKR-NSGA-II which is useful when the DM has no a priori information about the number
of existing knees in the Pareto optimal front.

Fuzzy linear regression is an active area of research. In the literature, fuzziness is considered in outputs and/or in inputs.
This paper focuses on both fuzzy inputs and fuzzy outputs. First, some approximations for multiplication of two triangular
fuzzy numbers are introduced. Then, to evaluate the fuzzy linear regression, the best approximation is selected to minimize
a suitable function via goal programming. An important feature of the proposed model is that it takes into account the centers
of fuzzy data as well as their spreads. Moreover, it is flexible to deal with both symmetric and non-symmetric data. Furthermore,
it can handle the crisp inputs and trapezoidal fuzzy outputs easily. To show the efficiency of the proposed model, some numerical
examples are solved and compared with some earlier methods.

Attribute reduction and reducts are important notions in rough set theory that can preserve discriminatory properties to the
highest possible extent similar to the entire set of attributes. In this paper, the relationships among 13 types of alternative
objective functions for attribute reduction are systematically analyzed in complete decision tables. For inconsistent and
consistent decision tables, it is demonstrated that there are only six and two intrinsically different objective functions
for attribute reduction, respectively. Some algorithms have been put forward for minimal attribute reduction according to
different objective functions. Through a counterexample, it is shown that heuristic methods cannot always guarantee to produce
a minimal reduct. Based on the general definition of discernibility function, a complete algorithm for finding a minimal reduct
is proposed. Since it only depends on reasoning mechanisms, it can be applied under any objective function for attribute reduction
as long as the corresponding discernibility matrix has been well established.

Protein-DNA bindings are essential activities. Understanding them forms the basis for further deciphering of biological and
genetic systems. In particular, the protein-DNA bindings between transcription factors (TFs) and transcription factor binding
sites (TFBSs) play a central role in gene transcription. Comprehensive TF-TFBS binding sequence pairs have been found in a
recent study. However, they are in one-to-one mappings which cannot fully reflect the many-to-many mappings within the bindings.
An evolutionary algorithm is proposed to learn generalized representations (many-to-many mappings) from the TF-TFBS binding
sequence pairs (one-to-one mappings). The generalized pairs are shown to be more meaningful than the original TF-TFBS binding
sequence pairs. Some representative examples have been analyzed in this study. In particular, it shows that the TF-TFBS binding
sequence pairs are not presumably in one-to-one mappings. They can also exhibit many-to-many mappings. The proposed method
can help us extract such many-to-many information from the one-to-one TF-TFBS binding sequence pairs found in the previous
study, providing further knowledge in understanding the bindings between TFs and TFBSs.

In this paper, a new hybrid method based on fuzzy neural network (FNN) for approximate solution of fuzzy linear systems of
the form

Ax=d,

where

A

is a square matrix of fuzzy coefficients,

x

and

d

are fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing
or soft computing. Moreover, in order to find the approximate solution of an

n×n

system of fuzzy linear equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of
the FNN is proposed. Finally, we illustrate our approach by some numerical examples.