The Fuzziness in Molecular, Supramolecular, and Systems Chemistry

Fuzzy Logic is a good model for the human ability to compute words. It is based on the theory of fuzzy set. A fuzzy set is different from a classical set because it breaks the Law of the Excluded Middle. In fact, an item may belong to a fuzzy set and its complement at the same time and with the same or different degree of membership. The degree of membership of an item in a fuzzy set can be any real number included between 0 and 1. This property enables us to deal with all those statements of which truths are a matter of degree. Fuzzy logic plays a relevant role in the field of Artificial Intelligence because it enables decision-making in complex situations, where there are many intertwined variables involved. Traditionally, fuzzy logic is implemented through software on a computer or, even better, through analog electronic circuits. Recently, the idea of using molecules and chemical reactions to process fuzzy logic has been promoted. In fact, the molecular word is fuzzy in its essence. The overlapping of quantum states, on the one hand, and the conformational heterogeneity of large molecules, on the other, enable context-specific functions to emerge in response to changing environmental conditions. Moreover, analog input–output relationships, involving not only electrical but also other physical and chemical variables can be exploited to build fuzzy logic systems. The development of “fuzzy chemical systems” is tracing a new path in the field of artificial intelligence. This new path shows that artificially intelligent systems can be implemented not only through software and electronic circuits but also through solutions of properly chosen chemical compounds. The design of chemical artificial intelligent systems and chemical robots promises to have a significant impact on science, medicine, economy, security, and wellbeing. Therefore, it is my great pleasure to announce a Special Issue of Molecules entitled “The Fuzziness in Molecular, Supramolecular, and Systems Chemistry.” All researchers who experience the Fuzziness of the molecular world or use Fuzzy logic to understand Chemical Complex Systems will be interested in this book

Fuzzy Logic in Clinical Practice Decision Support Systems

Computerized clinical guidelines can provide significant benefits to health outcomes and costs, however, their effective implementation presents significant problems. Vagueness and ambiguity inherent in natural (textual) clinical guidelines is not readily amenable to formulating automated alerts or advice. Fuzzy logic allows us to formalize the treatment of vagueness in a decision support architecture. This paper discusses sources of fuzziness in clinical practice guidelines. We consider how fuzzy logic can be applied and give a set of heuristics for the clinical guideline knowledge engineer for addressing uncertainty in practice guidelines. We describe the specific applicability of fuzzy logic to the decision support behavior of Care Plan On-Line, an intranet-based chronic care planning system for General Practitioners

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they are also used in many other fields ranging from economics, management, agricultural sciences, engineering or informatics to medicine. This paper focuses on the use of MCs for the design of non-life bonus-malus systems (BMSs). It proposes quantifying the uncertainty of transition probabilities in BMSs by using fuzzy numbers (FNs). To do so, Fuzzy MCs (FMCs) as defined by Buckley and Eslami in 2002 are used, thus giving rise to the concept of Fuzzy BMSs (FBMSs). More concretely, we describe in detail the common BMS where the number of claims follows a Poisson distribution under the hypothesis that its characteristic parameter is not a real but a triangular FN (TFN). Moreover, we reflect on how to fit that parameter by using several fuzzy data analysis tools and discuss the goodness of triangular approximates to fuzzy transition probabilities, the fuzzy stationary state, and the fuzzy mean asymptotic premium. The use of FMCs in a BMS allows obtaining not only point estimates of all these variables, but also a structured set of their possible values whose reliability is given by means of a possibility measure. Although our analysis is circumscribed to non-life insurance, all of its findings can easily be extended to any of the abovementioned fields with slight modifications.University of Barcelon