From Numeric Models to Granular System Modeling

Abstract In the era of advanced methodologies and practices of system modeling, we are faced with ever growing challenges of building models of complex systems that are in full rapport with reality. These challenges are multifaceted. Human centricity becomes of paramount relevance in system modeling and because of this models need to be customized and easily interpretable. More and more visibly, experimental data and knowledge of varying quality being directly acquired from experts have to be efficiently utilized in the construction of models. The quality of data and ensuing quality of models have to be prudently quantified. There are ongoing and even exacerbated challenges to build intelligent systems, modeling multifaceted phenomena, and deliver efficient models that help users describe and understand systems and support processes of decision-making. We have to become fully cognizant that processing and modeling has to be realized with the use of entities endowed with well-defined semantics, namely information granules. Human do not perceive reality and reason in terms of numbers but rather utilize more abstract constructs (information granules), which are helpful in setting up a certain cognitive perspective and ignore irrelevant details when dealing with the complexity of the systems.

[1]  Anne Laurent,et al.  Extracting compact and information lossless sets of fuzzy association rules , 2011, Fuzzy Sets Syst..

[2]  Serge Guillaume,et al.  Linguistic knowledge base simplification regarding accuracy and interpretability , 2006 .

[3]  Witold Pedrycz,et al.  Granular Computing: Analysis and Design of Intelligent Systems , 2013 .

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

[5]  Francisco Herrera,et al.  A Fast and Scalable Multiobjective Genetic Fuzzy System for Linguistic Fuzzy Modeling in High-Dimensional Regression Problems , 2011, IEEE Transactions on Fuzzy Systems.

[6]  Frank Chung-Hoon Rhee,et al.  Uncertain Fuzzy Clustering: Interval Type-2 Fuzzy Approach to $C$-Means , 2007, IEEE Transactions on Fuzzy Systems.

[7]  James C. Bezdek,et al.  Modified Objective Function Algorithms , 1981 .

[8]  Witold Pedrycz,et al.  Shadowed sets: representing and processing fuzzy sets , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

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

[11]  Lotfi A. Zadeh,et al.  A Note on Z-numbers , 2011, Inf. Sci..

[12]  Andrzej Bargiela,et al.  An Optimization of Allocation of Information Granularity in the Interpretation of Data Structures: Toward Granular Fuzzy Clustering , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Witold Pedrycz,et al.  Fuzzy Systems Engineering - Toward Human-Centric Computing , 2007 .

[14]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[15]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[16]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[17]  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..

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

[19]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..