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A characterization for residuated implications on the set of all the closed intervals in J[0,1]. Application to the L-fuzzy concept theory.

Cristina Alcalde, Ana Burusco, Ramón Fuentes-González (2005)

Mathware and Soft Computing

In this paper, a new characterization for the interval-valued residuated fuzzy implication operators is presented, with which it is possible to use them in a simple and efficient way, since the calculation of the values of an intervalvalued implication applicated to two intervals is reduced to the study of a fuzzy implication applicated to the extremes of these intervals. This result is very important in order to extract knowledge from an L-fuzzy context with incomplete information. Finally, some...

A classical decision theoretic perspective on worst-case analysis

Moshe Sniedovich (2011)

Applications of Mathematics

We examine worst-case analysis from the standpoint of classical Decision Theory. We elucidate how this analysis is expressed in the framework of Wald's famous Maximin paradigm for decision-making under strict uncertainty. We illustrate the subtlety required in modeling this paradigm by showing that information-gap's robustness model is in fact a Maximin model in disguise.

A comparison of evidential networks and compositional models

Jiřina Vejnarová (2014)

Kybernetika

Several counterparts of Bayesian networks based on different paradigms have been proposed in evidence theory. Nevertheless, none of them is completely satisfactory. In this paper we will present a new one, based on a recently introduced concept of conditional independence. We define a conditioning rule for variables, and the relationship between conditional independence and irrelevance is studied with the aim of constructing a Bayesian-network-like model. Then, through a simple example, we will...

A context-based approach to linguistic hedges

Martine De Cock, Etienne Kerre (2002)

International Journal of Applied Mathematics and Computer Science

We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones proposed that are suitable to perform this representation task for a lattice L different from the unit interval....

A discussion on aggregation operators

Daniel Gómez, Montero, Javier (2004)

Kybernetika

It has been lately made very clear that aggregation processes can not be based upon a unique binary operator. Global aggregation operators have been therefore introduced as families of aggregation operators { T n } n , being each one of these T n the n -ary operator actually amalgamating information whenever the number of items to be aggregated is n . Of course, some mathematical restrictions can be introduced, in order to assure an appropriate meaning, consistency and key mathematical capabilities. In this...

A general approach to decomposable bi-capacities

Susanne Saminger, Radko Mesiar (2003)

Kybernetika

We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and k -additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.

A multi-granular linguistic model to evaluate the suitability of installing an ERP system.

Pedro José Sánchez, Luis G. Pérez, Francisco Mata, Antonio Gabriel López-Herrera (2005)

Mathware and Soft Computing

The use of Enterprise Resource Planning (ERP) has shown clearly useful and economically profitable in most very large organizations which manage a great deal of data in their information systems. Nevertheless, the decision of installing an ERP system is not easy and it depends on the size, future profits and other features of the companies. The assessments of the parameters (features, aspects) used to evaluate the suitability of the ERP may be vague and imprecise because they are usually perceptions...

A new definition of the fuzzy set

Andrzej Piegat (2005)

International Journal of Applied Mathematics and Computer Science

The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.

A nonstandard modification of Dempster combination rule

Ivan Kramosil (2002)

Kybernetika

It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like...

Aggregation, Non-Contradiction and Excluded-Middle.

Ana Pradera, Enric Trillas (2006)

Mathware and Soft Computing

This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying them w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.

Aggregations preserving classes of fuzzy relations

Józef Drewniak, Urszula Dudziak (2005)

Kybernetika

We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special...

Alternative definitions of conditional possibilistic measures

Ivan Kramosil (1998)

Kybernetika

The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning...

An architecture for making judgments using computing with words

Jerry Mendel (2002)

International Journal of Applied Mathematics and Computer Science

Our thesis is that computing with words needs to account for the uncertainties associated with the meanings of words, and that these uncertainties require using type-2 fuzzy sets. Doing this leads to a proposed architecture for making it judgments by means of computing with words, i.e., to a perceptual computer-the Per-C. The Per-C includes an encoder, a type-2 rule-based fuzzy logic system, and a decoder. It lets all human-computer interactions be performed using words. In this paper, a quantitative...

An ILP model for a monotone graded classification problem

Peter Vojtáš, Tomáš Horváth, Stanislav Krajči, Rastislav Lencses (2004)

Kybernetika

Motivation for this paper are classification problems in which data can not be clearly divided into positive and negative examples, especially data in which there is a monotone hierarchy (degree, preference) of more or less positive (negative) examples. We present a new formulation of a fuzzy inductive logic programming task in the framework of fuzzy logic in narrow sense. Our construction is based on a syntactical equivalence of fuzzy logic programs FLP and a restricted class of generalised annotated...

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