International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

An isomorphism f between two continuous Archimedean t-norms T and T′ transforms a T-indistinguishability operator E into a T′-indistinguishability operator f ∘ E and many interesting properties of E are transfered to f ∘ E by f. This paper generalizes this result in order to relate indistinguishability operators with respect to two non isomorphic continuous Archimedean t-norms. This will allow us to transfer definitions and properties from strict to non-strict Archimedean t-norms and vice versa.

In this paper, some new operators for aggregating interval-valued intuitionistic fuzzy information are proposed to deal with multiple attribute decision making problems. Firstly, the C-IFOWA operator and C-IFOWG operator are developed to aggregate all the values in the interval-valued intuitionistic fuzzy numbers. Some of their desirable properties are also studied. Secondly, in order to aggregate a set of interval-valued intuitionistic fuzzy numbers, some new aggregation operators are proposed based on the C-IFOWA operator and C-IFOWG operator. Thirdly, two methods for multiple attribute decision making, in which the attribute values are given in the forms of interval-valued intuitionistic fuzzy numbers are presented. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed methods.

A new metric is proposed on the space of measurable functions in the setting of non-additive measure theory. The convergence induced from the metric can be used to describe the convergence in measure for sequences of measurable functions. Furthermore, the space of measurable functions is complete under the metric.

We present an efficient procedure for factorising probabilistic potentials represented as probability trees. This new procedure is able to detect some regularities that cannot be captured by existing methods. In cases where an exact decomposition is not achievable, we propose a heuristic way to carry out approximate factorisations guided by a parameter called factorisation degree, which is fast to compute. We show how this parameter can be used to control the tradeoff between complexity and accuracy in approximate inference algorithms for Bayesian networks.

In this paper we propose a fuzzy method to detect free paths in real-time using digital stereo images. It is based on looking for linear variations of depth in disparity maps, which are obtained by processing a pair of rectified images from two stereo cameras. By applying least-squares fitting over groups of disparity maps columns to a linear model, free paths are detected by giving a certainty using a fuzzy rule. Experimental results on real outdoor images are also presented.

This paper establishes an axiomatic definition of inclusion measures between Atanassov's intuitionistic fuzzy (A-IF for short) sets. Some kinds of A-IF inclusion measures are constructed by different A-IF operators especially by A-IF implicator, and some new methods for measuring the degree of similarity between A-IF sets are proposed. Moreover, the similarity measure obtained from an A-IF inclusion measure satisfies properties of normal similarity measure. We then define a compatibility measure by a predicates logical idea and construct several functions to measure compatibility for an intuitionistic t-norm.

Human knowledge about monitoring process variables is usually incomplete. To deal with this partial knowledge many types of representation other than the quantitative one are used to describe process variables (qualitative, symbolic interval). Thus, the development of automatic reasoning mechanisms about the process is faced with this problem of multiple data representations. In this paper, a unified principle for reasoning about heterogeneous data is introduced. This principle is based on a simultaneous mapping of data from initially heterogeneous spaces into only one homogeneous space based on a relative measure using appropriate characteristic functions. Once the heterogeneous data are represented in a unified space, a single processing for various analysis purposes can be performed using simple reasoning mechanisms. An application of this principle within a fuzzy logic framework is performed here to demonstrate its effectiveness. We show that simple fuzzy reasoning mechanisms can be used to reason in a unified way about heterogeneous data in three well known machine learning problems.

In this article we introduce the concepts of λ-statistical convergence of order β and strong λp-summability of order β for sequences of fuzzy numbers. Also, we establish some relations between the λ-statistical convergence of order β and strong λp-summability of order β and present some interesting examples to show strictness of some inclusion relations.