From Fuzzy Cognitive Maps to Granular Cognitive Maps

Fuzzy cognitive maps (FCMs) form a class of graph-oriented fuzzy models describing causal relationships among concepts. In this study, we augment these models by introducing their generalization coming in the form of granular FCMs. In contrast with FCMs, in the granular FCMs, the connections between the nodes (states) are described in the form of information granules, especially intervals and fuzzy sets. Key scenarios in which granular models (and granular FCMs) arise are presented in order to offer a compelling rationale behind the formation of such models. In the context of system modeling, we show that information granularity emerges as an important design asset. We discuss detailed schemes of allocation of information granularity and quantify a performance of the resulting granular FCM in terms of a coverage criterion. For illustrative purposes, the detailed studies are completed for granular FCMs with interval-valued connections.

[1]  Witold Pedrycz,et al.  Knowledge transfer in system modeling and its realization through an optimal allocation of information granularity , 2012, Appl. Soft Comput..

[2]  Bart Kosko,et al.  Fuzzy Cognitive Maps , 1986, Int. J. Man Mach. Stud..

[3]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[4]  Jose L. Salmeron,et al.  A Review of Fuzzy Cognitive Maps Research During the Last Decade , 2013, IEEE Transactions on Fuzzy Systems.

[5]  Andrzej Bargiela,et al.  Toward a Theory of Granular Computing for Human-Centered Information Processing , 2008, IEEE Transactions on Fuzzy Systems.

[6]  Witold Pedrycz,et al.  The design of cognitive maps: A study in synergy of granular computing and evolutionary optimization , 2010, Expert Syst. Appl..

[7]  Chunyan Miao,et al.  An Extension to Fuzzy Cognitive Maps for Classification and Prediction , 2011, IEEE Transactions on Fuzzy Systems.

[8]  Chrysostomos D. Stylios,et al.  Active Hebbian learning algorithm to train fuzzy cognitive maps , 2004, Int. J. Approx. Reason..

[9]  Witold Pedrycz,et al.  Allocation of information granularity in optimization and decision-making models: Towards building the foundations of Granular Computing , 2014, Eur. J. Oper. Res..

[10]  Elpiniki I. Papageorgiou,et al.  Fuzzy cognitive map ensemble learning paradigm to solve classification problems: Application to autism identification , 2012, Appl. Soft Comput..

[11]  Kaoru Hirota,et al.  Concepts of probabilistic sets , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[12]  Witold Pedrycz,et al.  Learning fuzzy cognitive maps with required precision using genetic algorithm approach , 2004 .

[13]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[14]  Witold Pedrycz,et al.  Knowledge-based clustering - from data to information granules , 2007 .

[15]  João Paulo Carvalho,et al.  On the semantics and the use of fuzzy cognitive maps and dynamic cognitive maps in social sciences , 2013, Fuzzy Sets Syst..

[16]  Witold Pedrycz,et al.  Genetic learning of fuzzy cognitive maps , 2005, Fuzzy Sets Syst..

[17]  Dimitrios K. Iakovidis,et al.  Intuitionistic Fuzzy Cognitive Maps , 2013, IEEE Transactions on Fuzzy Systems.

[18]  R. Axelrod.  Structure of decision : the cognitive maps of political elites , 2015 .

[19]  Andrzej Bargiela,et al.  Granular mappings , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[20]  Witold Pedrycz,et al.  Granular computing: an introduction , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[21]  José Aguilar,et al.  Different dynamic causal relationship approaches for cognitive maps , 2013, Appl. Soft Comput..

[22]  Elpiniki I. Papageorgiou,et al.  Application of Evolutionary Fuzzy Cognitive Maps for Prediction of Pulmonary Infections , 2012, IEEE Transactions on Information Technology in Biomedicine.

[23]  Witold Pedrycz,et al.  Numerical and Linguistic Prediction of Time Series With the Use of Fuzzy Cognitive Maps , 2008, IEEE Transactions on Fuzzy Systems.

[24]  Jeffrey S. Kargel,et al.  Autonomous real-time landing site selection for Venus and Titan using Evolutionary Fuzzy Cognitive Maps , 2012, Appl. Soft Comput..

[25]  Chunyan Miao,et al.  Dynamical cognitive network - an extension of fuzzy cognitive map , 2001, IEEE Trans. Fuzzy Syst..

[26]  Elpiniki I. Papageorgiou,et al.  Multi-step prediction of pulmonary infection with the use of evolutionary fuzzy cognitive maps , 2012, Neurocomputing.

[27]  Witold Pedrycz,et al.  Distributed fuzzy system modeling , 1995, IEEE Trans. Syst. Man Cybern..

[28]  John B. Bowles,et al.  Using Fuzzy Cognitive Maps as a System Model for Failure Modes and Effects Analysis , 1996, Inf. Sci..

[29]  Yiannis S. Boutalis,et al.  Fuzzy Cognitive Maps for Pattern Recognition Applications , 2008, Int. J. Pattern Recognit. Artif. Intell..

[30]  Giovanni Acampora,et al.  On the Temporal Granularity in Fuzzy Cognitive Maps , 2011, IEEE Transactions on Fuzzy Systems.