Fuzzy pharmacology: theory and applications Beth A. Sproule, Claudio A. Naranjo and I. Burhan Türksen Trends in Pharmacological Sciences 2002, 23:412-417 Fuzzy pharmacology is a term coined to represent the application of fuzzy logic and fuzzy set theory to pharmacological problems. Fuzzy logic is the science of reasoning, thinking and inference that recognizes and uses the real world phenomenon that everything is a matter of degree. It is an extension of binary logic that is able to deal with complex systems because it does not require crisp definitions and distinctions for the system components. In pharmacology, fuzzy modeling has been used for the mechanical control of drug delivery in surgical settings, and work has begun evaluating its use in other pharmacokinetic and pharmacodynamic applications. Fuzzy pharmacology is an emerging field that, based on these initial explorations, warrants further investigation.   Predicting outcomes of pharmacotherapy is difficult because of the many sources of pharmacokinetic and pharmacodynamic variation. Several of these sources of variation have been recognized for many years: for example, age, gender, weight, disease state, genetic polymorphisms and concomitant medications [1]. More recently, additional sources have been proposed, including individual variability in drug transporters across biological barriers and in endogenous ligand activity [2]. Thus, modeling to predict outcomes in pharmacology is complex. Traditionally, medical science has used statistical and mathematical approaches for modeling. In general, the pharmacological system is described in mathematical terms, where variables are associated with the outcome of interest in terms of equations with identified parameters (e.g. rate constants). Parameter values are estimated with statistical error values attached to describe variability. Approaches that are conceptually different from this traditional approach have evolved in the field of engineering when confronted with very complex systems. We propose that the approach of fuzzy logic modeling might be particularly suitable for pharmacological problems. What is fuzzy logic? Fuzzy logic is the science of reasoning, thinking and inference that recognizes and uses the real world phenomenon that everything is a matter of degree. In the simplest terms, fuzzy logic theory is an extension of binary logic theory that does not require crisp definitions and distinctions. Instead of assuming everything must be defined crisply into black or white categories (binary view), it is recognized that most things in the world fall somewhere in between black and white, that is, varying shades of gray (fuzzy view). Fuzzy logic is a methodology that captures and uses the concept of fuzziness in a computationally effective manner. This concept was developed >36 years ago when Lofti Zadeh, originally an engineer and systems scientist, expressed the concern that as the complexity of a system increased, the information afforded by traditional mathematical models rapidly declined [3,4] . He felt this was due to the way in which the variables in the system were represented and manipulated in a binary manner: variables (e.g. drug response) would be defined in discrete terms (i.e. poor or good). Using a fuzzy approach the transition between terms can be gradual, and the binary, all or none, options become the extreme ends of a continuum. The fuzzy view of the world was put into operation for computational purposes through the use of fuzzy sets [3]. Fuzzy sets Variables, variable terms, and definitions can be thought of in terms of sets and set theory. In traditional set theory, using a binary view, something either belongs to a set or does not, depending on whether it fits the definition for that set. In other words, it has a degree of membership (µ) to the set either equal to one (µ = 1) or equal to zero (µ = 0). In fuzzy set theory, something can partially belong to a set. A value for a variable might partially belong to a set and have a degree of membership anywhere between zero and one (i.e. 0 µ 1), and thus it can partially belong to several sets with the total membership adding to one ( Box 1). Although often represented as trapezoidal, fuzzy sets can have different shapes including triangular, sigmoidal, bell shaped or irregular [4]. Recently, the concept of Type II fuzzy sets has been introduced, in which the borders of the fuzzy sets are represented as upper and lower boundaries rather than as one line, in order to better express fuzziness [5]. It is fuzzy sets, their definitions and relationships that form the basis of fuzzy system modeling. Fuzziness versus probability It is important to distinguish between the concepts of fuzzy logic and probability. Probability calculus is a tool for estimating the likelihood that something is true or will happen. It is a way of handling and expressing randomness. The concept centers around an all-or-none event – once again, a binary concept – where the event can be defined as an entity having a particular characteristic (i.e. the entity either does or does not have that characteristic). This is very different from fuzziness, which does not try to estimate the likelihood that the entity does or does not have that particular characteristic but rather assesses how much the entity is compatible with the meaning of the word we associated to define that characteristic. For example, an individual patient can have both a partially 'good' response to a medication (i.e. to a degree of 0.7), and a partially 'not good' response (i.e. to a degree of 0.3). This is different from a patient having a 70% probability of having a good response to a medication. In this case, patients will either have a 'good' response (70% of patients) or a 'not good' response (30% of patients). At some point the determination is made whether the response was good or not and the probability estimate is no longer required.   Go to the Full Article > >  As a BioMedNet member you have free full-text access to this article within BioMedNet Reviews for 14 days  You will have full-text access to all articles if your institute subscribes. 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