# zbMATH — the first resource for mathematics

Information cells and information cell mixture models for concept modelling. (English) Zbl 1259.68118
Summary: By combining the prototype theory and random set theory interpretations of vague concepts, a novel structure named information cell and a combined structure named information cell mixture model are proposed to represent the semantics of vague concepts. An information cell $$L_i$$ on the domain $$\Omega$$ has a transparent cognitive structure ‘$$L_i =\text{about} P_i$$’ which is mathematically formalized by a 3-tuple $$\langle P_i ,d_i ,\delta_i \rangle$$; comprising a prototype set $$P_i$$ ($$\subseteq \Omega$$), a distance function $$d_i$$ on $$\Omega$$ and a density function $$\delta_i$$ on $$[0,+\infty)$$. An information cell mixture model on domain $$\Omega$$ is actually a set of weighted information cells $$L_i$$s. A positive neighborhood function of the information cell mixture model is introduced in this paper to reflect the belief distribution of positive neighbors of the underlying concept. An information cellularization algorithm is also proposed to learn the information cell mixture model from a training data set, which is a direct application of the $$k$$-means and EM algorithms. Information cell mixture models provide some tools for information coarsening and concept modelling, and have potential applications in uncertain reasoning and classification.
##### MSC:
 68Q55 Semantics in the theory of computing
LFOIL
Full Text:
##### References:
 [1] Dubois, D., & Prade, H. (1988). An introduction to possibilistic and fuzzy logics. In P. Smets, E. H. Mamdani, D. Dubois, & H. Prade (Eds.), Non-standard logics for automated reasoning (pp. 287–326). San Diego: Academic Press. [2] Dubois, D., & Prade, H. (1997). The three semantics of fuzzy sets. Fuzzy Sets and Systems, 90, 141–150. · Zbl 0919.04006 · doi:10.1016/S0165-0114(97)00080-8 [3] Goodman, I. R. (1982). Fuzzy sets as equivalence classes of random sets. In R. Yager (Ed.), Fuzzy set and possibility theory (pp. 327–342). [4] Goodman, I., & Nguyen, H. (1985). Uncertainty model for knowledge based systems. Amsterdam: North Holland. · Zbl 0576.94001 [5] Lawry, J. (2004). A framework for linguistic modelling. Artificial Intelligence, 155, 1–39. · Zbl 1085.68695 · doi:10.1016/j.artint.2003.10.001 [6] Lawry, J. (2006). Modelling and reasoning with vague concepts. Berlin: Springer. · Zbl 1092.68095 [7] Lawry, J. (2008). Appropriateness measures: an uncertainty model for vague concepts. Synthese, 161, 255–269. · Zbl 1140.68066 · doi:10.1007/s11229-007-9158-9 [8] Lawry, J., & Tang, Y. (2008). Relating prototype theory and label semantics. In D. Dubois, M. A. Lubiano, H. Prade, M. A. Gil, P. Grzegorzewski, & O. Hryniewicz (Eds.), Soft methods for handling variability and imprecision (pp. 35–42). [9] Lawry, J., & Tang, Y. (2009). Uncertainty modelling for vague concepts: a prototype theory approach. Artificial Intelligence, 173(18), 1539–1558. · Zbl 1185.68710 · doi:10.1016/j.artint.2009.07.006 [10] Lawry, J., Hall, J., & Bovey, R. (2004). Fusion of expert and learnt knowledge in a framework of fuzzy labels. International Journal of Approximate Reasoning, 36, 151–198. · doi:10.1016/j.ijar.2003.10.005 [11] Nguyen, H. (1984). On modeling of linguistic information using random sets. Information Sciences, 34, 265–274. · Zbl 0557.68066 · doi:10.1016/0020-0255(84)90052-5 [12] Qin, Z., & Lawry, J. (2005). Decision tree learning with fuzzy labels. Information Sciences, 172(1–2), 91–129. · Zbl 1087.68094 · doi:10.1016/j.ins.2004.12.005 [13] Qin, Z., & Lawry, J. (2008). LFOIL: Linguistic rule induction in the label semantics framework. Fuzzy Sets and Systems, 159(4), 435–448. · Zbl 1176.68164 · doi:10.1016/j.fss.2007.10.008 [14] Sotirov, G., & Krasteva, E. (1994). An approach to group decision making under uncertainty with application to project selection. Annals of Operations Research, 51(3), 115–126. · Zbl 0812.90085 · doi:10.1007/BF02032480 [15] Tang, Y. (2008). A collective decision model involving vague concepts and linguistic expressions. IEEE Transactions on Systems, Man, and Cybernetics, Part B, Cybernetics, 38(2), 421–428. · doi:10.1109/TSMCB.2007.913125 [16] Tang, Y., & Lawry, J. (2009). Linguistic modelling and information coarsening based on prototype theory and label semantics. International Journal of Approximate Reasoning, 50(8), 1177–1198. · Zbl 1191.68699 · doi:10.1016/j.ijar.2009.01.004 [17] Tang, Y., & Lawry, J. (2010). A prototype-based rule inference system incorporating linear functions. Fuzzy Sets and Systems, 161(21), 2831–2853. · Zbl 1207.68392 · doi:10.1016/j.fss.2010.05.002 [18] Tang, Y., & Zheng, J. (2006). Linguistic modelling based on semantic similarity relation among linguistic labels. Fuzzy Sets and Systems, 157(12), 1662–1673. · Zbl 1101.68886 · doi:10.1016/j.fss.2006.02.014 [19] Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.