The aim of the paper is to summarize and interpret some ideas regarding effective processing of vague data. The main contribution of the submitted approach consists in respecting the fact that vague data can be decomposed into two parts. The numerical one, describing the quantitative value of such data, and the semantic one characterizing the qualitative structure of the vagueness included into them. This partition of vague verbal data leads to a significant simplification of their practical processing,...

Information quality is crucial to any information fusion system as combining unreliable or partially credible pieces of information may lead to erroneous results. In this paper, Dempster-Shafer theory of evidence is being used as a framework for representing and combining uncertain pieces of information. We propose a method of dynamic estimation of evidence discounting rates based on the credibility of pieces of information. The credibility of a piece of information Cre(In) is evaluated through...

We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system $\mathscr{H}$ is star-like with centre $X$ if and only if every two compositional expressions with “base scheme” $\mathscr{H}$ and “key” $X$ are equivalent. This result is stronger than Jiroušek’s result which states that, if $\mathscr{H}$ is star-like with centre $X$, then every two generating sequences with base scheme $\mathscr{H}$ and key $X$ are equivalent. Then, we focus on canonical expressions, by which we mean compositional expressions $\theta$ such that the sequence of the sets featured in...

This paper deals with many valued case of modus ponens. Cases with implicative and with clausal rules are studied. Many valued modus ponens via discrete connectives is studied with implicative rules as well as with clausal rules. Some properties of discrete modus ponens operator are given.

We propose a new additive decomposition of probability tables – tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one- dimensional tables. Entries in tables are allowed to be any real number, i. e. they can be also negative numbers. The possibility of having...

The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being...

Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired...

This paper aims to develop an analysis of how ignorance affects the reasoning activity and is related to the concept of uncertainty. With reference to a simple inferential reasoning step, involving a single piece of relational knowledge, we identify four types of ignorance and show how they give rise to different types of uncertainty. We then introduce the concept of reasoning attitude, as a basic choice about how reasoning should be carried out in presence of ignorance. We identify two general...

A fuzzy system has been developed to ponder update decisions both for the trajectories and shapes estimated for targets. It is embedded in an A-SMGCS Surveillance function for airport surface, based on video data processing, in charge of the automatic detection, identification and tracking of all interesting targets (aircraft and relevant ground vehicles). The tracking system captures a sequence of images, preprocesses them to extract the moving regions (blobs), and associates the blobs to tracks...

The paper introduces a general axiomatic notion of approximation mapping, a mapping that associates to each crisp proposition p a fuzzy set representing approximately p. It is shown how it can be obtained through fuzzy relations, which are at least reflexive. We study the corresponding multi-modal systems depending on the properties satisfied by the approximate relation. Finally, we show some equivalences between possibilistic logical consequences and global/local logical consequences in the multi-modal...

Fuzzy data mining by means of the fuzzy decision tree method enables the construction of a set of fuzzy rules. Such a rule set can be associated with a database as a knowledge base that can be used to help answering frequent queries. In this paper, a study is done that enables us to show that classification by means of a fuzzy decision tree is equivalent to the generalized modus ponens. Moreover, it is shown that the decision taken by means of a fuzzy decision tree is more stable when observation...

We have shown a model of fuzzy neural network that is able to infer the relations associated to the transitions of a fuzzy automaton from a fuzzy examples set. Neural network is trained by a backpropagation of error based in a smooth derivative [1]. Once network has been trained the fuzzy relations associated to the transitions of the automaton are found encoded in the weights.

In this paper, the method of least squares is applied to the fuzzy inference rules. We begin studying the conditions in which from a fuzzy set we can build another through the method of least squares. Then we apply this technique in order to evaluate the conclusions of the generalized modus ponens. We present different theorems and examples that demonstrate the fundamental advantages of the method studied.

The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive fuzzy...

A flexible query model is presented for semi-structured information stored in well-formed XML documents, modeled as XML fuzzy graphs by computing estimates of the importance of the information associated to XML elements and attributes. The notion of fuzzy graph closure with threshold is then used to obtain a fuzzy extension of the XML fuzzy graphs’ topological structure. Weights associated to closure arcs are computed as a conjunction of the importance values of the underlying arcs in the original...

In this paper, we generalize the noisy-or model. The generalizations are three-fold. First, we allow parents to be multivalued ordinal variables. Second, parents can have both positive and negative influences on their common child. Third, we describe how the suggested generalization can be extended to multivalued child variables. The major advantage of our generalizations is that they require only one parameter per parent. We suggest a model learning method and report results of experiments on the...

The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet $(p,i,j)$, which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.