Fuzzy neural tree in evolutionary computation for architectural design cognition

A novel fuzzy-neural tree (FNT) is presented. Each tree node uses a Gaussian as a fuzzy membership function, so that the approach uniquely is in align with both the probabilistic and possibilistic interpretations of fuzzy membership. It provides a type of logical operation by fuzzy logic (FL) in a neural structure in the form of rule-chaining, yielding a novel concept of weighted fuzzy logical AND and OR operation. The tree can be supplemented both by expert knowledge, as well as data set provisions for model formation. The FNT is described in detail pointing out its various potential utilizations demanding complex modeling and multi-objective optimization therein. One of such demands concerns cognitive computing for design cognition. This is exemplified and its effectiveness is demonstrated by computer experiments in the realm of Architectural design.

[1]  Michael S. Bittermann,et al.  Visual perception in design and robotics , 2007, Integr. Comput. Aided Eng..

[2]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[3]  Didier Dubois,et al.  Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities , 2004, Reliab. Comput..

[4]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[5]  Mustafa Tunay,et al.  Analysis of Possibility Theory for Reasoning under Uncertainty , 2013 .

[6]  D. Dubois,et al.  A Semantics for Possibility Theory Based on Likelihoods , 1997 .

[7]  D. Rajan.  Probability, Random Variables, and Stochastic Processes , 2017 .

[8]  George J. Klir,et al.  Concepts and Fuzzy Logic , 2011 .

[9]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[10]  Pia Veldt Larsen,et al.  In All Likelihood: Statistical Modelling and Inference Using Likelihood , 2003 .

[11]  S. Moral,et al.  On the concept of possibility-probability consistency , 1987 .

[12]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[13]  Michael S. Bittermann,et al.  Generic cognitive computing for cognition , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[14]  D. Dubois,et al.  When upper probabilities are possibility measures , 1992 .

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

[16]  Michael Glykas,et al.  Fuzzy Cognitive Maps , 2010 .

[17]  N. Singpurwalla,et al.  Membership Functions and Probability Measures of Fuzzy Sets , 2004 .

[18]  I. Turksen,et al.  Measurement of Membership Functions: Theoretical and Empirical Work , 2000 .

[19]  D. Dubois,et al.  Unfair coins and necessity measures: Towards a possibilistic interpretation of histograms , 1983 .

[20]  Özer Ciftcioglu,et al.  Fusion of Perceptions in Architectural Design , 2013 .