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Axioms
Special Issues
Axiomatic Approach to Monotone Measures and Integrals
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Axiomatic Approach to Monotone Measures and Integrals

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 March 2013) | Viewed by 12069

Special Issue Editor

Prof. Dr. Radko Mesiar

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinskeho 11, 81005 Bratislava, Slovakia
Interests: non-additive measure and integral theory; uncertainty modelling; fuzzy sets and fuzzy logic; multicriteria decision support; copulas; triangular norms; aggregation operators and related operators; intelligent computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

monotone measures and integrals generalizing the classical additive approach occur frequently in many diverse fields of mathematical but also economical and engineering sciences, in several kinds of decisions procedures when considering interaction, etc. The standard development of the theory goes from constructive proposal to final axiomatization - see, e.g., the case of Riemann, Lebesgue or Choquet integrals. Recently, several new approaches to measures and integrals (mostly dealing with real-valued set functions as measures and real-vaalued functions as integrands) appeared, mostly aiming to find appropriate models for advanced multi-criteria decision aid. Obviously, new proposals are also beyond the above mentioned framework. Special Issue of Axioms "Axiomatic Approach to Monotone Measures and Integrals" aims to collect axiomatization of these new types of monotone measures and integrals, as well as related survey papers.

Prof. Dr. Radko Mesiar
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • capacity
  • convergence theorems
  • Dempster-Shafer theory
  • interaction index
  • integral
  • integral inequalities
  • measures of information
  • monotone measure
  • possibility theory
  • signed measure
  • states on algebraic structures

Published Papers (2 papers)

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Research

241 KiB  
Article
Discrete Integrals Based on Comonotonic Modularity
by Miguel Couceiro and Jean-Luc Marichal
Axioms 2013, 2(3), 390-403; https://doi.org/10.3390/axioms2030390 - 23 Jul 2013
Cited by 3 | Viewed by 4703
Abstract
It is known that several discrete integrals, including the Choquet and Sugeno integrals, as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of [...] Read more.
It is known that several discrete integrals, including the Choquet and Sugeno integrals, as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals, as well as natural extensions of Sugeno integrals. Full article
(This article belongs to the Special Issue Axiomatic Approach to Monotone Measures and Integrals)
252 KiB  
Article
Using the Choquet Integral in the Fuzzy Reasoning Method of Fuzzy Rule-Based Classification Systems
by Edurne Barrenechea, Humberto Bustince, Javier Fernandez, Daniel Paternain and José Antonio Sanz
Axioms 2013, 2(2), 208-223; https://doi.org/10.3390/axioms2020208 - 23 Apr 2013
Cited by 55 | Viewed by 6944
Abstract
In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy [...] Read more.
In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the new method with the same fuzzy measure for all the classes. However, the relationship among the set of rules of each class can be different and therefore the best fuzzy measure can change depending on the class. Consequently, we propose a learning method by means of a genetic algorithm in which the most suitable fuzzy measure for each class is computed. From the obtained results it is shown that our new proposal allows the performance of the classical fuzzy reasoning methods of the winning rule and additive combination to be enhanced whenever the fuzzy measure is appropriate for the tackled problem. Full article
(This article belongs to the Special Issue Axiomatic Approach to Monotone Measures and Integrals)
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