100 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 15, NO. 1, JANUARY 2011 Intuitionistic Fuzzy Cognitive Maps for Medical Decision Making Dimitris K. Iakovidis, Member, IEEE, and Elpiniki Papageorgiou Abstract—Medical decision making can be regarded as a pro- cess, combining both analytical cognition and intuition. It involves reasoning within complex causal models of multiple concepts, usu- ally described by uncertain, imprecise, and/or incomplete informa- tion. Aiming to model medical decision making, we propose a novel approach based on cognitive maps and intuitionistic fuzzy logic. The new model, called intuitionistic fuzzy cognitive map (iFCM), extends the existing fuzzy cognitive map (FCM) by considering the expert’s hesitancy in the determination of the causal relations between the concepts of a domain. Furthermore, a modification in the formulation of the new model makes it even less sensitive than the original model to missing input data. To validate its effective- ness, an iFCM with 34 concepts representing fuzzy, linguistically expressed patient-specific data, symptoms, and multimodal mea- surements was constructed for pneumonia severity assessment. The results obtained reveal its comparative advantage over the respec- tive FCM model by providing decisions that match better with the ones made by the experts. The generality of the proposed approach suggests its suitability for a variety of medical decision-making tasks. Index Terms—Fuzzy cognitive maps (FCM), fuzzy logic, intu- itionistic fuzzy sets (IFSs), medical decision support. I. INTRODUCTION T HE modeling of medical decision making has been among the leading research objectives for decades [1], [2]. Pi- oneering modeling approaches based on Bayesian logic have appeared since the late 1950s [3]. Later on, fuzzy logic has been considered mainly as a means to model the inherent un- certainty present in real-world medical decision making, with the approaches of Zadeh [4], Sanchez [5], and Adlassnig [6] to be among the most recognized ones. More recently, signif- icant results have been obtained in modeling medical decision making by an alternative fuzzy logic-based approach known as fuzzy cognitive map (FCM) [6]–[10], whereas the application of generalizations of the conventional fuzzy sets, such as the intuitionistic fuzzy sets (IFSs) [11], have already provided indi- cations for their applicability in the medical domain [12]–[16]. FCMs are simple, yet powerful tools for modeling and sim- ulation of dynamic systems, based on domain-specific knowl- Manuscript received April 29, 2010; revised August 4, 2010; accepted October 25, 2010. Date of publication November 18, 2010; date of current version January 4, 2011. This work was realized in the context of the DebugIT Project which is supported in part by the EC FP7 under Grant Agreement FP7- 217139. The authors are with the Department of Informatics and Computer Tech- nology, Technological Educational Institute of Lamia, Lamia 35100, Greece (e-mail: dimitris.iakovidis@ieee.org; epapageorgiou@teilam.gr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TITB.2010.2093603 edge and experience. Its components include concepts that can be causally interrelated and can represent uncertain and im- precise knowledge through fuzzy logic. They present a num- ber of advantages over conventional fuzzy approaches to rea- soning. These include handling of incomplete even conflicting information, easy construction and parameterization, and they allow users to rapidly compare their mental models with re- ality [6]–[10]. Medical decision-making models that have been based on FCMs include models for radiotherapy treatment plan- ning [17], brain tumor characterization [18], management of uri- nary tract infections [19], and for prediction of pneumonia [20]. IFSs are generalized fuzzy sets in the sense that their elements are characterized not only by a membership value, indicating the degree of belongingness to that set, but also by a nonmembership value. The nonmembership value indicates the degree to which an element does not belong to that set, whereas it needs not necessarily be symmetric to the membership value. The main advantage of the IFSs is that they are able to consider a degree of hesitancy in the belongingness of an element to a set. The applications of IFSs in decision making are still very limited. In the spirit of the Sanchez’s approach, an example application of the IFSs for medical decision making has been demonstrated in [12], whereas in [13] a method based on distances between IFSs has been proposed as an alternative for the same purpose. In [14], the approach proposed in [13] was further extended by considering a symmetric discrimination information measure. Recent applications of IFSs in biomedicine include bacteria classification [15] and medical image segmentation [16]. In this paper, we propose the intuitionistic fuzzy cognitive map (iFCM) as an extension of the original FCM model, aiming to exploit the advantages of both FCMs and IFSs. In the context of IFSs, a factor of hesitancy is introduced in the definition of the cause–effect relations among the concepts of the FCM, thus pro- viding an additional cue regarding the experts’ knowledge and way of thinking. A preliminary version of the proposed model has been presented in [21]. In that work, the iFCM outperformed the original FCM in two indicative scenarios for pneumonia risk assessment using only 12 concepts. In this paper, we evaluate the effectiveness of the proposed model on an extended dataset using the 34-concept approach presented in [20]. This prelimi- nary approach was based on the original FCM model, whereas in our study it is based on the iFCM model, which is compared with FCM in more patient cases. Furthermore, the iFCM used in [21] has been reformulated so that its decisions are even less affected by missing input data. The rest of this paper consists of four sections. Section II describes the proposed iFCM model while providing a neces- sary background on FCMs and IFSs. Section III describes the 1089-7771/$26.00 © 2011 IEEE