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

Fuzzy Relative Positioning for On-Line Handwritten Stroke Analysis

http://www.suvisoft.comThis paper deals with the qualitative and robust modelling of the relative positioning of on-line handwritten strokes. We exploit the fuzzy approach to take the imprecision of such relations into account. We first transpose a well-formalized method which proved itself in the domain of image analysis to the on-line case; it aims at evaluating the relation “to be in a given direction” relatively to a reference. Our first contribution is a solution to deal with the particular nature of on-line strokes, which are constituted of non-connected points. Our second and main contribution is a method to learn automatically fuzzy relative position relationships. It aims at evaluating the relation “to be in a given position” relatively to a reference using jointly the direction and the distance. We test the impact of this new fuzzy positioning approach on one possible application: the recognition of handwritten graphic gestures, which requires spatial context information to be discriminated. Whereas the recognition rate is 52.95% without any spatial information, we obtain a maximum of 95.75% when we use learnt relative position relationships

One-class classifiers based on entropic spanning graphs

One-class classifiers offer valuable tools to assess the presence of outliers in data. In this paper, we propose a design methodology for one-class classifiers based on entropic spanning graphs. Our approach takes into account the possibility to process also non-numeric data by means of an embedding procedure. The spanning graph is learned on the embedded input data and the outcoming partition of vertices defines the classifier. The final partition is derived by exploiting a criterion based on mutual information minimization. Here, we compute the mutual information by using a convenient formulation provided in terms of the $\alpha$-Jensen difference. Once training is completed, in order to associate a confidence level with the classifier decision, a graph-based fuzzy model is constructed. The fuzzification process is based only on topological information of the vertices of the entropic spanning graph. As such, the proposed one-class classifier is suitable also for data characterized by complex geometric structures. We provide experiments on well-known benchmarks containing both feature vectors and labeled graphs. In addition, we apply the method to the protein solubility recognition problem by considering several representations for the input samples. Experimental results demonstrate the effectiveness and versatility of the proposed method with respect to other state-of-the-art approaches.Comment: Extended and revised version of the paper "One-Class Classification Through Mutual Information Minimization" presented at the 2016 IEEE IJCNN, Vancouver, Canad

Multicriteria analysis under uncertainty with IANUS - method and empirical results

IANUS is a method for aiding public decision-making that supports efforts towards sustainable development and has a wide range of application. IANUS stands for Integrated Assessment of Decisions uNder Uncertainty for Sustainable Development. This paper introduces the main features of IANUS and illustrates the method using the results of a case study in the Torgau region (eastern Germany). IANUS structures the decision process into four steps: scenario derivation, criteria selection, modeling, evaluation. Its overall aim is to extract the information needed for a sound, responsible decision in a clear, transparent manner. The method is designed for use in conflict situations where environmental and socioeconomic effects need to be considered and so an interdisciplinary approach is required. Special emphasis is placed on a broad perception and consideration of uncertainty. Three types of uncertainty are explicitly taken into account by IANUS: development uncertainty (uncertainty about the social, economic and other developments that affect the consequences of decision), model uncertainty (uncertainty associated with the prediction of the effects of decisions), and weight uncertainty (uncertainty about the appropriate weighting of the criteria). The backbone of IANUS is a multicriteria method with the ability to process uncertain information. In the case study the multicriteria method PROMETHEE is used. Since PROMETHEE in its basic versions is not able to process uncertain information an extension of this method is developed here and described in detail. --

A Model for Evaluating Soil Vulnerability to Erosion Using Remote Sensing Data and A Fuzzy Logic System

Soil vulnerability is the capacity of one or more of the ecological functions of the soil system to be harmed. It is a complex concept which requires the identification of multiple environmental factors and land management at different temporal and space scales. The employment of geospatial information with good update capabilities could be a satisfactory tool to assess potential soil vulnerability changes in large areas. This chapter presents the application of two land degradation case studies which is simple, synoptic, and suitable for continuous monitoring model based on the fuzzy logic. The model combines topography and vegetation status information to assess soil vulnerability to land degradation. Topographic parameters were obtained from digital elevation models (DEM), and vegetation status information was derived from the computation of the normalized difference vegetation index (NDVI) satellite images. This spectral index provides relevance and is updated for each scene, evidences about the biomass and soil productivity, and vegetation density cover or vegetation stress (e.g., forest fires, droughts). Modeled output maps are suitable for temporal change analysis, which allows the identification of the effect of land management practices, soil and vegetation regeneration, or climate effects