FCM-Based Modeling of LMS Users' Quality of Interaction

Part III is concluded with this chapter that proposes a Fuzzy Cognitive Map (FCM)-based modeling of the Quality of Interaction (QoI) of the Learning Management System (LMS) users within a blended (b)-learning context, namely FCM-QoI model. Two training/testing scenarios were conducted and explored here, i.e., time-dependent and time-independent, using as pre-validated QoI data the ones presented in chapter 13. Moreover, a FCM-Viewer application that facilitates the visualization of the FCM-QoI model structure is also presented. The experimental results show that the proposed FCM-QoI model can provide concepts interconnection and causal dependencies representation of LMS users' interaction behavior. With this chapter, the circle around the basic fuzzy logic topics discussed in Part II, i.e., FIS, ANFIS, IFIS and FCM, injected into the educational context is fulfilled. Based on the models discussed so far, prospective hybrid modeling approaches are envisioned in the final section of the book (Part IV) that follows.

Modal operators on bounded commutative residuated ℓ-monoids

Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROVÁ,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.