The legacy of 50 years of fuzzy sets: A discussion

International audienceThis note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L.A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline members, a plausibility distribution, or a preference profile. It also questions the motivations for some existing generalized fuzzy sets. This note clearly reflects the shared personal views of its authors

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

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

Investigation on soft computing techniques for airport environment evaluation systems

Spatial and temporal information exist widely in engineering fields, especially in airport environmental management systems. Airport environment is influenced by many different factors and uncertainty is a significant part of the system. Decision support considering this kind of spatial and temporal information and uncertainty is crucial for airport environment related engineering planning and operation. Geographical information systems and computer aided design are two powerful tools in supporting spatial and temporal information systems. However, the present geographical information systems and computer aided design software are still too general in considering the special features in airport environment, especially for uncertainty. In this thesis, a series of parameters and methods for neural network-based knowledge discovery and training improvement are put forward, such as the relative strength of effect, dynamic state space search strategy and compound architecture. [Continues.

Updated discussions on ‘Hybrid multiple criteria decisionmaking methods: a review of applications for sustainability issues’

A recent review discussed a variety of hybrid multiple criteria decision-making (H.M.C.D.M.) methods on the subject of sustainability issues. Some soft computing techniques, such as the fuzzy set, have contributed significantly to H.M.C.D.M. studies, emulating the imprecise or uncertain judgments of experts/decision makers in a complex environment. Nevertheless, a new rising trend in H.M.C.D.M., known as multiple rule-based decision-making (M.R.D.M.), which has the advantage of revealing understandable knowledge for supporting systematic improvements based on influential network relation maps (I.N.R.M.), was not discussed in the review. This study therefore attempts to extend the review by introducing recent developments and the associated work on M.R.D.M. for solving practical problems, updating the discussion