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

A modified learning algorithm for the multilayer neural network with multi-valued neurons based on the complex QR decomposition

Abstract  In this paper, a modified learning algorithm for the multilayer neural network with the multi-valued neurons (MLMVN) is presented.
The MLMVN, which is a member of complex-valued neural networks family, has already demonstrated a nu…

Abstract  

In this paper, a modified learning algorithm for the multilayer neural network with the multi-valued neurons (MLMVN) is presented.
The MLMVN, which is a member of complex-valued neural networks family, has already demonstrated a number of important advantages
over other techniques. A modified learning algorithm for this network is based on the introduction of an acceleration step,
performing by means of the complex QR decomposition and on the new approach to calculation of the output neurons errors: they
are calculated as the differences between the corresponding desired outputs and actual values of the weighted sums. These
modifications significantly improve the existing derivative-free backpropagation learning algorithm for the MLMVN in terms
of learning speed. A modified learning algorithm requires two orders of magnitude lower number of training epochs and less
time for its convergence when compared with the existing learning algorithm. Good performance is confirmed not only by the
much quicker convergence of the learning algorithm, but also by the compatible or even higher classification/prediction accuracy,
which is obtained by testing over some benchmarks (Mackey–Glass and Jenkins–Box time series) and over some satellite spectral
data examined in a comparison test.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-13
  • DOI 10.1007/s00500-011-0755-7
  • Authors
    • Igor Aizenberg, Texas A&M University-Texarkana, 7101 University Ave., Texarkana, TX 75503, USA
    • Antonio Luchetta, Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, 50139 Florence, Italy
    • Stefano Manetti, Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, 50139 Florence, Italy

Consensus reaching models of linguistic preference relations based on distance functions

Abstract  In group decision making (GDM) using linguistic preference relations to obtain the maximum degree of agreement, it is desirable
to develop a consensus process prior to the selection process. This paper proposes two consensus models…

Abstract  

In group decision making (GDM) using linguistic preference relations to obtain the maximum degree of agreement, it is desirable
to develop a consensus process prior to the selection process. This paper proposes two consensus models with linguistic information
to support the GDM consensus reaching process. Two different distance functions between linguistic preference relations are
introduced to measure both individual consistency and group consensus. Based on these measures, the consensus reaching models
are developed. The two models presented have the same concept that the expert whose preference is farthest from the group
preference needs to update their opinion according to the group preference relation. In addition, the convergence of the models
is proved. After achieving the predefined consensus level, each expert’s consistency indexes are still acceptable under the
condition that the initial preference relations are of satisfactory consistency. Finally, an example is given to show the
effectiveness of the models and to verify the theoretical results.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-13
  • DOI 10.1007/s00500-011-0756-6
  • Authors
    • Zhibin Wu, Uncertain Decision-making Laboratory, Sichuan University, Chengdu, 610064 China
    • Jiuping Xu, Uncertain Decision-making Laboratory, Sichuan University, Chengdu, 610064 China

Residuated bilattices

Abstract  We introduce a new product bilattice construction that generalizes the well-known one for interlaced bilattices and others
that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kin…

Abstract  

We introduce a new product bilattice construction that generalizes the well-known one for interlaced bilattices and others
that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of
an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization
for it and characterize the congruences of its members in terms of those of their lattice factors. Finally, we show how to
employ our product construction to define first-order definable classes of bilattices corresponding to any first-order definable
subclass of residuated lattices.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-12
  • DOI 10.1007/s00500-011-0752-x
  • Authors
    • Ramon Jansana, Departament of Logic, History and Philosophy of Science, Faculty of Philosophy, University of Barcelona, c/ Montalegre, 6, 08001 Barcelona, Spain
    • Umberto Rivieccio, School of Computer Science, University of Birmingham, Edgbaston, Birmingham, B15 2TT UK

Variable mesh optimization for continuous optimization problems

Abstract  Population-based meta-heuristics are algorithms that can obtain very good results for complex continuous optimization problems
in a reduced amount of time. These search algorithms use a population of solutions to maintain an accept…

Abstract  

Population-based meta-heuristics are algorithms that can obtain very good results for complex continuous optimization problems
in a reduced amount of time. These search algorithms use a population of solutions to maintain an acceptable diversity level
during the process, thus their correct distribution is crucial for the search. This paper introduces a new population meta-heuristic
called “variable mesh optimization” (VMO), in which the set of nodes (potential solutions) are distributed as a mesh. This
mesh is variable, because it evolves to maintain a controlled diversity (avoiding solutions too close to each other) and to
guide it to the best solutions (by a mechanism of resampling from current nodes to its best neighbour). This proposal is compared
with basic population-based meta-heuristics using a benchmark of multimodal continuous functions, showing that VMO is a competitive
algorithm.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-15
  • DOI 10.1007/s00500-011-0753-9
  • Authors
    • Amilkar Puris, Department of Computer Science, Universidad Central de las Villas, Santa Clara, Cuba
    • Rafael Bello, Department of Computer Science, Universidad Central de las Villas, Santa Clara, Cuba
    • Daniel Molina, Department of Computer Languages and Systems, University of Cadiz, Cadiz, Spain
    • Francisco Herrera, Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain

Quotients and weakly algebraic sets in pseudoeffect algebras

Abstract  In the paper, we show that the quotient

[E]I
of a lattice-ordered pseudoeffect algebra

E
with respect to a normal weak Riesz ideal

I
is linearly ordered if and only if

I
is a prime normal weak Riesz ideal, and

[E]I
is…

Abstract  

In the paper, we show that the quotient

[E]I

of a lattice-ordered pseudoeffect algebra

E

with respect to a normal weak Riesz ideal

I

is linearly ordered if and only if

I

is a prime normal weak Riesz ideal, and

[E]I

is a representable pseudo MV-algebra if and only if

I

is an intersection of prime normal weak Riesz ideals. Moreover, we introduce the concept of weakly algebraic sets in pseudoeffect
algebras, discuss the characterizations of weakly algebraic sets and show that weakly algebraic sets in pseudoeffect algebra

E

are in a one-to-one correspondence with normal weak Riesz ideals in pseudoeffect algebra

E.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-8
  • DOI 10.1007/s00500-011-0750-z
  • Authors
    • Hai-Yang Li, Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China
    • Ji-Gen Peng, Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China

Extension of the DEMATEL method in an uncertain linguistic environment

Abstract  The decision making trial and evaluation laboratory (DEMATEL) method is a useful tool for analyzing correlations among factors
using crisp values. However, the crisp values are inadequate to model real-life situations due to the fu…

Abstract  

The decision making trial and evaluation laboratory (DEMATEL) method is a useful tool for analyzing correlations among factors
using crisp values. However, the crisp values are inadequate to model real-life situations due to the fuzziness and uncertainty
that are frequently involved in judgments of experts. The aim of this paper is to extend the DEMATEL method to an uncertain
linguistic environment. In this paper, the correlation information among factors provided by experts is in the form of uncertain
linguistic terms. A formula is first presented to transform correlation information from uncertain linguistic terms to trapezoidal
fuzzy numbers. Then, we aggregate the transformed correlation information of each expert into group information using the
operations of trapezoidal fuzzy numbers. The importance and classification of factors are determined via fuzzy matrix operations.
Furthermore, a causal diagram is constructed to vividly show the different roles of factors. Finally, an example is used to
illustrate the procedure of the proposed method.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-13
  • DOI 10.1007/s00500-011-0751-y
  • Authors
    • Wei-Lan Suo, Department of Management Science and Engineering, School of Business Administration, Northeastern University, Shenyang, 110819 China
    • Bo Feng, Department of Decision Sciences, School of Business Administration, South China University of Technology, Guangzhou, 510640 China
    • Zhi-Ping Fan, Department of Management Science and Engineering, School of Business Administration, Northeastern University, Shenyang, 110819 China

Some comments on fuzzy variables with different membership functions

Abstract  Hong and Kim (Fuzzy Sets Syst 93:121–124, 1998) presented a membership function of a finite sum of mutually unrelated fuzzy variables with a common membership function.
In this paper, we extend the fuzzy variables with a common m…

Abstract  

Hong and Kim (Fuzzy Sets Syst 93:121–124, 1998) presented a membership function of a finite sum of mutually unrelated fuzzy variables with a common membership function.
In this paper, we extend the fuzzy variables with a common membership function to those with different membership functions
and then present the membership function of a finite sum of mutually unrelated fuzzy variables with different membership functions.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-5
  • DOI 10.1007/s00500-011-0749-5
  • Authors
    • Shunqin Li, School of Science, Tianjin University of Commerce, Tianjin, 300134 China

Complexity reduction and interpretability improvement for fuzzy rule systems based on simple interpretability measures and indices by bi-objective evolutionary rule selection

Abstract  The aim of this paper is to develop a general post-processing methodology to reduce the complexity of data-driven linguistic
fuzzy models, in order to reach simpler fuzzy models preserving enough accuracy and better fuzzy linguisti…

Abstract  

The aim of this paper is to develop a general post-processing methodology to reduce the complexity of data-driven linguistic
fuzzy models, in order to reach simpler fuzzy models preserving enough accuracy and better fuzzy linguistic performance with
respect to their initial values. This post-processing approach is based on rule selection via the formulation of a bi-objective
problem with one objective focusing on accuracy and the other on interpretability. The latter is defined via the aggregation
of several interpretability measures, based on the concepts of similarity and complexity of fuzzy systems and rules. In this
way, a measure of the fuzzy model interpretability is given. Two neuro-fuzzy systems for providing initial fuzzy models, Fuzzy
Adaptive System ART based and Neuro-Fuzzy Function Approximation and several case studies, data sets from KEEL Project Repository,
are used to check this approach. Both fuzzy and neuro-fuzzy systems generate Mamdani-type fuzzy rule-based systems, each with
its own particularities and complexities from the point of view of the fuzzy sets and the rule generation. Based on these
systems and data sets, several fuzzy models are generated to check the performance of the proposal under different restrictions
of complexity and fuzziness.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-20
  • DOI 10.1007/s00500-011-0748-6
  • Authors
    • Marta Galende-Hernández, CARTIF Centro Tecnológico, Parque Tecnológico de Boecillo, parcela 205, 47151 Boecillo, Valladolid, Spain
    • Gregorio I. Sainz-Palmero, CARTIF Centro Tecnológico, Parque Tecnológico de Boecillo, parcela 205, 47151 Boecillo, Valladolid, Spain
    • Maria J. Fuente-Aparicio, Department of Systems Engineering and Control, School of Industrial Engineering, University of Valladolid, Paseo del Cauce s/n, 47011 Valladolid, Spain

Deriving weights from a pairwise comparison matrix over an alo-group

Abstract  In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered
group, the related subgroup of

\odot

-normal vectors, the relation of

\odot

-pro…

Abstract  

In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered
group, the related subgroup of


\odot

-normal vectors, the relation of


\odot

-proportionality and the corresponding quotient group. Then, we apply the achieved results to the groups of reciprocal and
consistent matrices over divisible Abelian linearly ordered groups; this allows us to deal with the problem of deriving a
weighting ranking for the alternatives from a pairwise comparison matrix. The proposed weighting vector has several advantages;
it satisfies, for instance, the independence of scale-inversion condition.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-14
  • DOI 10.1007/s00500-011-0746-8
  • Authors
    • Bice Cavallo, University of Naples Federico II, Naples, Italy
    • Livia D’Apuzzo, University of Naples Federico II, Naples, Italy

Learning-enhanced differential evolution for numerical optimization

Abstract  Differential evolution (DE) is a simple and powerful population-based search algorithm, successfully used in various scientific
and engineering fields. However, DE is not free from the problems of stagnation and premature convergen…

Abstract  

Differential evolution (DE) is a simple and powerful population-based search algorithm, successfully used in various scientific
and engineering fields. However, DE is not free from the problems of stagnation and premature convergence. Hence, designing
more effective search strategies to enhance the performance of DE is one of the most salient and active topics. This paper
proposes a new method, called learning-enhanced DE (LeDE) that promotes individuals to exchange information systematically.
Distinct from the existing DE variants, LeDE adopts a novel learning strategy, namely clustering-based learning strategy (CLS).
In CLS, there are two levels of learning strategies, intra-cluster learning strategy and inter-cluster learning strategy.
They are adopted for exchanging information within the same cluster and between different clusters, respectively. Experimental
studies over 23 benchmark functions show that LeDE significantly outperforms the conventional DE. Compared with other clustering-based
DE algorithms, LeDE can obtain better solutions. In addition, LeDE is also shown to be significantly better than or at least
comparable to several state-of-art DE variants as well as some other evolutionary algorithms.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-28
  • DOI 10.1007/s00500-011-0744-x
  • Authors
    • Yiqiao Cai, Department of Computer Science, Sun Yat-sen University, Guangzhou Higher Education Mega Center, Guangzhou, 510006 China
    • Jiahai Wang, Sun Yat-sen University, Guangzhou Higher Education Mega Center, Guangzhou, 510006 China
    • Jian Yin, Department of Computer Science, Sun Yat-sen University, Guangzhou Higher Education Mega Center, Guangzhou, 510006 China