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

A framework for generating tunable test functions for multimodal optimization

Abstract  Multimodal function optimization, where the aim is to locate more than one solution, has attracted growing interest especially
in the evolutionary computing research community. To evaluate experimentally the strengths and weaknesse…

Abstract  

Multimodal function optimization, where the aim is to locate more than one solution, has attracted growing interest especially
in the evolutionary computing research community. To evaluate experimentally the strengths and weaknesses of multimodal optimization
algorithms, it is important to use test functions representing different characteristics and various levels of difficulty.
The available selection of multimodal test problems is, however, rather limited and no general framework exists. This paper
describes an attempt to construct a software framework which includes a variety of easily tunable test functions. The aim
is to provide a general and easily expandable environment for testing different methods of multimodal optimization. Several
function families with different characteristics are included. The framework implements new parameterizable function families
for generating desired landscapes. Additionally the framework implements a selection of well known test functions from the
literature, which can be rotated and stretched. The software module can easily be imported to any optimization algorithm implementation
compatible with the C programming language. As an application example, 8 optimization approaches are compared by their ability
to locate several global optima over a set of 16 functions with different properties generated by the proposed module. The
effects of function regularity, dimensionality and number of local optima on the performance of different algorithms are studied.

  • Content Type Journal Article
  • DOI 10.1007/s00500-010-0611-1
  • Authors
    • Jani Rönkkönen, Lappeenranta University of Technology Department of Information Technology P.O. Box 20 Lappeenranta 53851 Finland
    • Xiaodong Li, RMIT University School of Computer Science and Information Technology Melbourne VIC 3001 Australia
    • Ville Kyrki, Lappeenranta University of Technology Department of Information Technology P.O. Box 20 Lappeenranta 53851 Finland
    • Jouni Lampinen, University of Vaasa Department of Computer Science P.O. Box 700 Vaasa 65101 Finland

A possibilistic approach to risk aversion

Abstract  In this paper a possibilistic model of risk aversion based on the lower and upper possibilistic expected values of a fuzzy
number is studied. Three notions of possibilistic risk premium are defined for which calculation formulae in…

Abstract  

In this paper a possibilistic model of risk aversion based on the lower and upper possibilistic expected values of a fuzzy
number is studied. Three notions of possibilistic risk premium are defined for which calculation formulae in terms of Arrow–Pratt
index and a possibilistic variance are established. A possibilistic version of Pratt theorem is proved.

  • Content Type Journal Article
  • Pages 1-7
  • DOI 10.1007/s00500-010-0634-7
  • Authors
    • Irina Georgescu, Academy of Economic Studies Department of Economic Cybernetics P. O. Box 15-432 Piaţa Romana No 6 R 70167, Oficiul Postal 22 014700 Bucharest Romania

On complete fuzzy preorders and their characterizations

Abstract  In the context of crisp or classical relations, one may find several alternative characterizations of the concept of a total
preorder. In this contribution, we first discuss the way of translating those characterizations to the fra…

Abstract  

In the context of crisp or classical relations, one may find several alternative characterizations of the concept of a total
preorder. In this contribution, we first discuss the way of translating those characterizations to the framework of fuzzy
relations. Those new properties depend on t-norms. We focus on two important families of t-norms, namely those that do not
admit zero divisors and those that are rotation invariant. For these families, we study whether or not the properties shown
for fuzzy relations lead to characterizations of complete fuzzy preorders. Special attention is paid to the minimum operator,
which shows the best behaviour in preserving most of the characterizations known for crisp relations.

  • Content Type Journal Article
  • DOI 10.1007/s00500-010-0630-y
  • Authors
    • Ignacio Montes, University of Oviedo Department of Statistics and Operational Research, U. T. S. of Industrial E. 33203 Gijón Spain
    • Susana Díaz, University of Oviedo Department of Statistics and Operational Research, Faculty of Science Calvo Sotelo s/n 33071 Oviedo Spain
    • Susana Montes, University of Oviedo Department of Statistics and Operational Research, U. T. S. of Industrial E. 33203 Gijón Spain

Guest editorial: special issue on “Intelligent Systems, Design and Applications (ISDA’2009)”

Guest editorial: special issue on “Intelligent Systems, Design and Applications (ISDA’2009)”
Content Type Journal ArticleDOI 10.1007/s00500-010-0622-yAuthors
José Manuel Benítez, Universidad de Granada Department of Computer Science and Arti…

Guest editorial: special issue on “Intelligent Systems, Design and Applications (ISDA’2009)”

  • Content Type Journal Article
  • DOI 10.1007/s00500-010-0622-y
  • Authors
    • José Manuel Benítez, Universidad de Granada Department of Computer Science and Artificial Intelligence, CITIC-UGR Granada Spain
    • Sabrina Senatore, University of Salerno Department of Mathematics and Informatics Salerno Italy
    • Ajith Abraham, Machine Intelligence Research Labs Washington USA

Dynamic combinatorial optimisation problems: an analysis of the subset sum problem

Abstract  The field of evolutionary computation has traditionally focused on static optimisation problems. Recently, many new approaches
have been proposed that adapt traditional evolutionary algorithms to the dynamic domain to deal with the…

Abstract  

The field of evolutionary computation has traditionally focused on static optimisation problems. Recently, many new approaches
have been proposed that adapt traditional evolutionary algorithms to the dynamic domain to deal with the task of tracking
high-quality solutions as the search space changes over time. These novel algorithms are subsequently evaluated on a wide
range of different optimisation problems, including well-specified benchmark generators. However, due to a lack of theoretical
results, as well as a general lack of references to actual real-world scenarios, it is not entirely clear whether these benchmarks
capture any of the characteristics found in NP-hard dynamic optimisation problems. In this paper, we extensively analyse the
properties of the NP-hard (dynamic) subset sum problem. In particular, we highlight the correlation between the dynamic parameters
of the problem and the resulting movement of the global optimum. It is shown by empirical means that the degree to which the
global optimum moves in response to the underlying dynamics is correlated only in specific cases. Furthermore, the role of
the representation used to encode the problem, as well as the impact of the formulation of the objective function on the dynamics
are also discussed.

  • Content Type Journal Article
  • DOI 10.1007/s00500-010-0616-9
  • Authors
    • Philipp Rohlfshagen, University of Birmingham School of Computer Science Birmingham B15 2TT UK
    • Xin Yao, University of Birmingham School of Computer Science Birmingham B15 2TT UK

Coalitional game with fuzzy payoffs and credibilistic core

Abstract  As an important branch of game theory, coalitional game deals with situations that involve cooperation among the players.
This paper deals with this topic further by incorporating the fuzzy payoff information. Based on the credibil…

Abstract  

As an important branch of game theory, coalitional game deals with situations that involve cooperation among the players.
This paper deals with this topic further by incorporating the fuzzy payoff information. Based on the credibility theory, we
introduce two decision criteria to define the preferences of players, which leads to two definitions of credibilistic cores—the
solution of coalitional game with fuzzy transferable payoffs. Meanwhile, we give a sufficient and necessary condition to ensure
non-emptiness of the credibilistic cores. Finally, an example is provided for illustrating the usefulness of the theory developed
in this paper.

  • Content Type Journal Article
  • DOI 10.1007/s00500-010-0632-9
  • Authors
    • Puchen Shen, Renmin University of China Uncertain Systems Lab, School of Information Beijing 100872 China
    • Jinwu Gao, Renmin University of China Uncertain Systems Lab, School of Information Beijing 100872 China

On some sets of difference sequences of fuzzy numbers

Abstract  In this paper we define the sequence space

wF(f,p,\Updelta)

which is called the space of strongly

\Updelta p

-Cesàro summable sequences with modulus f. Furthermore the fuzzy Δ-statistically pre-Cauchy sequen…

Abstract  

In this paper we define the sequence space


wF(f,p,\Updelta)

which is called the space of strongly


\Updelta p

-Cesàro summable sequences with modulus f. Furthermore the fuzzy Δ-statistically pre-Cauchy sequence is defined and the necessary and sufficient conditions are given
for a sequence of fuzzy numbers to be fuzzy


\Updelta

-statistically pre-Cauchy and to be fuzzy


\Updelta

-statistically convergent. Also some relations between


wF(f,p,\Updelta)

and


SF(\Updelta)

are given.

  • Content Type Journal Article
  • Pages 1-7
  • DOI 10.1007/s00500-010-0633-8
  • Authors
    • R. Çolak, Firat University Department of Mathematics 23119 Elazig Turkey
    • Y. Altın, Firat University Department of Mathematics 23119 Elazig Turkey
    • M. Mursaleen, Aligarh Muslim University Department of Mathematics Aligarh 202002 India

An IVFS-based image segmentation methodology for rat gait analysis

Abstract  In this work, image segmentation is addressed as the starting point within a motion analysis methodology intended for rat
biomechanics behavior characterization. First, we propose a general segmentation framework that uses interval…

Abstract  

In this work, image segmentation is addressed as the starting point within a motion analysis methodology intended for rat
biomechanics behavior characterization. First, we propose a general segmentation framework that uses interval valued fuzzy
sets (IVFSs) to determine the optimal image threshold value. The amplitude values of the IVFSs are used for representing the
unknowledge/ignorance of an expert on determining whether a pixel belongs to the background or to the object of the image.
Then, we introduce an extension of this methodology that uses a heuristic-based multi-threshold approach to determine the
optimal threshold. Experimental results are presented.

  • Content Type Journal Article
  • Pages 1-8
  • DOI 10.1007/s00500-010-0626-7
  • Authors
    • Pedro Couto, CITAB, UTAD University Vila Real Portugal
    • Aranzazu Jurio, Universidad Publica de Navarra Pamplona Spain
    • Artur Varejão, UTAD University Vila Real Portugal
    • Miguel Pagola, Universidad Publica de Navarra Pamplona Spain
    • Humberto Bustince, Universidad Publica de Navarra Pamplona Spain
    • Pedro Melo-Pinto, CITAB, UTAD University Vila Real Portugal

A general inequality of Chebyshev type for semi(co)normed fuzzy integrals

Abstract  Generalization of the Chebyshev inequality for semi(co)normed fuzzy integrals on an abstract fuzzy measure space based on
a binary operation is given. Also, Minkowski’s and Hölder’s inequalities for semi(co)normed fuzzy integr…

Abstract  

Generalization of the Chebyshev inequality for semi(co)normed fuzzy integrals on an abstract fuzzy measure space based on
a binary operation is given. Also, Minkowski’s and Hölder’s inequalities for semi(co)normed fuzzy integrals are studied in
a rather general form. The main results of this paper generalize some previous results. Finally, a conclusion is drawn and
an open problem for further investigations is given.

  • Content Type Journal Article
  • Pages 1-10
  • DOI 10.1007/s00500-010-0621-z
  • Authors
    • Hamzeh Agahi, Shahid Bahonar University of Kerman Department of Statistics, Faculty of Mathematics and Computer Kerman Iran
    • Esfandiar Eslami, Shahid Bahonar University of Kerman Department of Mathematics and Computer Science Kerman Iran

HILK++: an interpretability-guided fuzzy modeling methodology for learning readable and comprehensible fuzzy rule-based classifiers

Abstract  This work presents a methodology for building interpretable fuzzy systems for classification problems. We consider interpretability
from two points of view: (1) readability of the system description and (2) comprehensibility of the…

Abstract  

This work presents a methodology for building interpretable fuzzy systems for classification problems. We consider interpretability
from two points of view: (1) readability of the system description and (2) comprehensibility of the system behavior explanations.
The fuzzy modeling methodology named as Highly Interpretable Linguistic Knowledge (HILK) is upgraded. Firstly, a feature selection
procedure based on crisp decision trees is carried out. Secondly, several strong fuzzy partitions are automatically generated
from experimental data for all the selected inputs. For each input, all partitions are compared and the best one according
to data distribution is selected. Thirdly, a set of linguistic rules are defined combining the previously generated linguistic
variables. Then, a linguistic simplification procedure guided by a novel interpretability index is applied to get a more compact
and general set of rules with a minimum loss of accuracy. Finally, partition tuning based on two efficient search strategies
increases the system accuracy while preserving the high interpretability. Results obtained in several benchmark classification
problems are encouraging because they show the ability of the new methodology for generating highly interpretable fuzzy rule-based
classifiers while yielding accuracy comparable to that achieved by other methods like neural networks and C4.5. The best configuration
of HILK will depend on each specific problem under consideration but it is important to remark that HILK is flexible enough
(thanks to the combination of several algorithms in each modeling stage) to be easily adaptable to a wide range of problems.

  • Content Type Journal Article
  • DOI 10.1007/s00500-010-0628-5
  • Authors
    • José M. Alonso, European Centre for Soft Computing (ECSC) 33600 Mieres Asturias Spain
    • Luis Magdalena, European Centre for Soft Computing (ECSC) 33600 Mieres Asturias Spain