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 Rules from Ant-Inspired Computation

Centre for Intelligent Systems and their ApplicationsThis research identifies and investigates major issues in inducing accurate and comprehensible fuzzy rules from datasets.A review of the current literature on fuzzy rulebase induction uncovers two significant issues: A. There is a tradeoff between inducing accurate fuzzy rules and inducing comprehensible fuzzy rules; and, B. A common strategy for the induction of fuzzy rulebases, that of iterative rule learning where the rules are generated one by one and independently of each other, may not be an optimal one.FRANTIC, a system that provides a framework for exploring the claims above is developed. At the core lies a mechanism for creating individual fuzzy rules. This is based on a significantly modified social insect-inspired heuristic for combinatorial optimisation -- Ant Colony Optimisation. The rule discovery mechanism is utilised in two very different strategies for the induction of a complete fuzzy rulebase: 1. The first follows the common iterative rule learning approach for the induction of crisp and fuzzy rules; 2. The second has been designed during this research explicitly for the induction of a fuzzy rulebase, and generates all rules in parallel.Both strategies have been tested on a number of classification problems, including medical diagnosis and industrial plant fault detection, and compared against other crisp or fuzzy induction algorithms that use more well-established approaches. The results challenge statement A above, by presenting evidence to show that one criterion need not be met at the expense of the other. This research also uncovers the cost that is paid -- that of computational expenditure -- and makes concrete suggestions on how this may be resolved.With regards to statement B, until now little or no evidence has been put forward to support or disprove the claim. The results of this research indicate that definite advantages are offered by the second simultaneous strategy, that are not offered by the iterative one. These benefits include improved accuracy over a wide range of values for several key system parameters. However, both approaches also fare well when compared to other learning algorithms. This latter fact is due to the rule discovery mechanism itself -- the adapted Ant Colony Optimisation algorithm -- which affords several additional advantages. These include a simple mechanism within the rule construction process that enables it to cope with datasets that have an imbalanced distribution between the classes, and another for controlling the amount of fit to the training data.In addition, several system parameters have been designed to be semi-autonomous so as to avoid unnecessary user intervention, and in future work the social insect metaphor may be exploited and extended further to enable it to deal with industrial-strength data mining issues involving large volumes of data, and distributed and/or heterogeneous databases