Multiobjective Programming for Type-2 Hierarchical Fuzzy Inference Trees

Abstract

Originally published in:IEEE Transactions on Fuzzy Systems (99), http://doi.org/10.1109/tfuzz.2017.2698399 Rights / License:In Copyright -Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library1063-6706 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract-This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure, i.e., a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure provides a high degree of approximation accuracy. The construction of HFIT takes place in two phases. Firstly, a nondominated sorting based multiobjective genetic programming (MOGP) is applied to obtain a simple tree structure (a low complexity model) with a high accuracy. Secondly, the differential evolution algorithm is applied to optimize the obtained tree's parameters. In the derived tree, each node acquires a different input's combination, where the evolutionary process governs the input's combination. Hence, HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP for the tree's structural optimization that accepts inputs only relevant to the knowledge contained in data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared both theoretically and empirically with recently proposed FISs methods from the literature, such as McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the obtained results, it was found that the HFIT provided less complex and highly accurate models compared to the models produced by the most of other methods. Hence, the proposed HFIT is an efficient and competitive alternative to the other FISs for function approximation and feature selection.

Heuristic design of fuzzy inference systems: A review of three decades of research

“…Automatic HFS formation A majority HFS takes a manual design; whereas, Chen et al (2007) explained the structural optimization of the HFS where hierarchical arrangements of low-dimensional TSK-type FISs were optimized using probabilistic incremental program evolution Salustowicz and Schmidhuber (1997). Ojha et al (2018) proposed a hierarchical fuzzy inference tree approach (HFIT M ) that has an automatic arrangement of FLUs using GP for type-1 and type-2 TSK FISs. HFIT M offered automatic selection of the input variables for each FLUs and that the order of input variables are automatically determined along with the HFS structure's automatic determination.…”

“…For NFS, HFS, and the FISs that have structural representation, the structure simplification is one of the objectives which may indeed indicate to a number of rule reduction, parameter reduction, and rule interaction simplification like the number of MFs reduction. Ojha et al (2018) employed multiobjective genetic programming (MOGA) for the simplification of the model structure while improving accuracy and improving diversity in the rules. These three objectives are conflicting with each other.…”

“…Second, a system will be a deep fuzzy system if it relies on multiple layers of network architecture as described in (Hinton et al, 2012). A multilayer NFS architecture, e.g., by Deng et al (2017) and a multi-stage HFS architecture, e.g., by Ojha et al (2018) may fit this definition. The DFS dimension of FIS research is still an open problem to explore and innovate.…”

Multi-Objective Optimisation of Multi-Output Neural Trees

“…The proposed algorithm MONT is an innovation from the early tree-based learning algorithms such as a flexible neural tree where a tree-like-structure was optimised by using probabilistic incremental program evolution [10] and heterogeneous flexible neural tree (HFNT) [11] where a treelike-structure was optimised by NSGA-II. Similar to these two approaches, in [12], a fuzzy inference system enabled hierarchical tree-based predictors was illustrated. In [13], a tree-based algorithm was evaluated on beta-basis function as a neural node.…”

Fast Training Algorithms for Deep Convolutional Fuzzy Systems with Application to Stock Index Prediction

“…Since then, the hierarchical fuzzy models have been applied to a wide variety of practical problems, such as environmental monitoring [17], educational assessment [18], video deinterlacing [19], price negotiation [20], mobile robots automation [21]- [23], self-nominating in peer-to-peer networks [24], linguistic hierarchy [25], hotel location selection [26], smart structures [27], weapon target assignment [28], image description [29], nutrition evaluation [30], spacecraft control [31], photovoltaic management [32], and wastewater treatment [33]. More recently, the research on the hierarchical fuzzy systems has been advanced along many directions, such as fast implementation [34], adaptive control [35], multiobjective optimization [36], interpretability [37], classification [38], [39] and so on.…”