Special Issue "Axiomatic Approach to Monotone Measures and Integrals"

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

Deadline for manuscript submissions: closed (30 March 2013)

Special Issue Editor

Guest Editor
Prof. Dr. Radko Mesiar (Website)

Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinskeho 11, 81368 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 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

Submission

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. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as 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 refereed through a 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 quarterly journal published by MDPI.

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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

Open AccessArticle Discrete Integrals Based on Comonotonic Modularity
Axioms 2013, 2(3), 390-403; doi:10.3390/axioms2030390
Received: 16 April 2013 / Revised: 31 May 2013 / Accepted: 19 June 2013 / Published: 23 July 2013
PDF Full-text (241 KB) | HTML Full-text | XML Full-text
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 [...] 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)
Open AccessArticle Using the Choquet Integral in the Fuzzy Reasoning Method of Fuzzy Rule-Based Classification Systems
Axioms 2013, 2(2), 208-223; doi:10.3390/axioms2020208
Received: 25 February 2013 / Revised: 21 March 2013 / Accepted: 3 April 2013 / Published: 23 April 2013
Cited by 6 | PDF Full-text (252 KB) | HTML Full-text | XML Full-text
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 [...] 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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