On additions of interactive fuzzy numbers

In this paper we will summarize some properties of the extended addition operator on fuzzy numbers, where the interactivity relation between fuzzy numbers is given by their joint possibility distributio

A possibilistic approach to latent structure analysis for symmetric fuzzy data.

In many situations the available amount of data is huge and can be intractable. When the data set is single valued, latent structure models are recognized techniques, which provide a useful compression of the information. This is done by considering a regression model between observed and unobserved (latent) fuzzy variables. In this paper, an extension of latent structure analysis to deal with fuzzy data is proposed. Our extension follows the possibilistic approach, widely used both in the cluster and regression frameworks. In this case, the possibilistic approach involves the formulation of a latent structure analysis for fuzzy data by optimization. Specifically, a non-linear programming problem in which the fuzziness of the model is minimized is introduced. In order to show how our model works, the results of two applications are given.Latent structure analysis, symmetric fuzzy data set, possibilistic approach.

Exploration of Subjective Color Perceptual-Ability by EEG-Induced Type-2 Fuzzy Classifiers

Perceptual-ability informally refers to the ability of a person to recognize a stimulus. This paper deals with color perceptual-ability measurement of subjects using brain response to basic color (red, green and blue) stimuli. It also attempts to determine subjective ability to recognize the base colors in presence of noise tolerance of the base colors, referred to as recognition tolerance. Because of intra- and inter-session variations in subjective brain signal features for a given color stimulus, there exists uncertainty in perceptual-ability. In addition, small variations in the color stimulus result in wide variations in brain signal features, introducing uncertainty in perceptual-ability of the subject. Type-2 fuzzy logic has been employed to handle the uncertainty in color perceptual-ability measurements due to a) variations in brain signal features for a given color, and b) the presence of colored noise on the base colors. Because of limited power of uncertainty management of interval type-2 fuzzy sets and high computational overhead of its general type-2 counterpart, we developed a semi-general type-2 fuzzy classifier to recognize the base color. It is important to note that the proposed technique transforms a vertical slice based general type-2 fuzzy set into an equivalent interval type-2 counterpart to reduce the computational overhead, without losing the contributions of the secondary memberships. The proposed semi-general type-2 fuzzy sets induced classifier yields superior performance in classification accuracy with respect to existing type-1, type-2 and other well-known classifiers. The brain-understanding of a perceived base or noisy base colors is also obtained by exact low resolution electromagnetic topographic analysis (e-LORETA) software. This is used as the reference for our experimental results of the semi-general type-2 classifier in color perceptual-ability detection. Statistical tests undertaken confirm the superiority of the proposed classifier over its competitors. The proposed technique is expected to have interesting applications in identifying people with excellent color perceptual-ability for chemical, pharmaceutical and textile industries

The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times

Three-valued logics, uncertainty management and rough sets

This paper is a survey of the connections between three-valued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such translations may provide mathematically elegant algebraic settings for rough sets, the interpretability of these connectives in terms of an original set approximated via an equivalence relation is very limited, thus casting doubts on the practical relevance of truth-functional logical renderings of rough sets

The approximation of left-continuous t-norms

Abstract A discrete t-norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t-norms. We show that any left-continuous t-norm can, in a natural sense, be approximated by a discrete t-norm with an arbitrary precision