A prototype-based rule inference system incorporating linear functions

doi:10.1016/j.fss.2010.05.002

Fuzzy Sets and Systems

Volume 161, Issue 21, 1 November 2010, Pages 2831-2853

https://doi.org/10.1016/j.fss.2010.05.002 Get rights and content

Abstract

A calculus of appropriateness measures of linguistic expressions is proposed, which is based on the prototype theory and random set theory interpretation of vague concepts. A prototype-based rule inference system is then introduced to incorporate linguistic labels in the rule antecedents and linear functions in the consequents of rules. And a rule learning algorithm is developed by combining a new clustering algorithm and a conjugate gradient algorithm. The proposed prototype-based inference system is then applied to a number of benchmark prediction problems including a nonlinear two-dimensional surface, the Mackey–Glass time series and the sunspot time-series. Results suggest that the proposed model is very robust and can perform well in high-dimensional noisy data.

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Cited by (12)

Anchor concept: A conceptual model with an expandable boundary
2016, Knowledge-Based Systems
Citation Excerpt :
Gardenfors [10] has introduced the conceptual spaces theory, concepts are described as convex regions of a conceptual space, which provides a natural relationship to prototype theory. Lawry [11–13] and Tang [14,15] have introduced another prototype theory approach for vague concepts modeling, in order to define boundaries for labels and measure the vagueness of concept, uncertain thresholds is adopted on the distance between objects and prototypes, which provides a relationship between the epistemic view of vagueness and prototype theory. These works focus on measure of conceptual distance (or similarity), which is an important fundamental aspect of prototype theory approach.
The existing conceptual modeling theories show the deficiencies in the research concerning the structure and formation mechanism of the concept. The deficiencies include two aspects, namely, the weak capability for treating the extension variability of the concept induced by the failure in defining the expandable boundary of the structure and the weak capability for handling the contradictory information caused by the utilization of the deterministic parameters or classical logic. In this paper, the “anchor concept” formal model is constructed based on the “prototype” and “family resemblance” principles in the prototype category theory. The modeling idea was explained as follows: a semantic boundary of the anchor concept is first constructed, the expansion of the boundary concludes as the interactions of “characteristic granules”. The interference mechanism in the formation process of the concept is then studied to solve the divergence induced by contradictory information. The results obtained provide a theoretical basis and a reference for further exploring the dynamic construction of the conceptual system with contradictory information.
A bipolar model of vague concepts based on random set and prototype theory
2012, International Journal of Approximate Reasoning
We argue that vagueness is a multi-faceted phenomenon requiring a framework for concept representation incorporating aspects of typicality, semantic uncertainty and indeterminism. In this paper we propose a bipolar model for vague concepts within the framework of prototype theory where concepts are represented by prototypical regions of an underlying conceptual space, and in which the appropriateness of a concept label to describe a given instance is determined on the basis of both a lower and an upper threshold on the distance from the defining prototype. Essentially, the label is absolutely appropriate as a description, providing that the distance to the prototype is less than the lower threshold, and not absolutely inappropriate if it is less than the upper threshold. Hence, in effect a concept is defined by lower and upper neighbourhoods of the prototype within the conceptual space, and the borderline region between the neighbourhoods identifies those elements of the space for which the concept label is neither absolutely appropriate nor absolutely inappropriate to describe. Semantic uncertainty is then represented by a joint probability density function on the lower and upper thresholds so that the lower and upper neighbourhoods correspond to nested random sets. This naturally results in lower and upper appropriateness measures quantifying the belief that a concept label is absolutely appropriate and not absolutely inappropriate to describe a given element of the space. These measures can then be related to the random set interpretation of fuzzy sets and in particular to lower and upper membership functions in interval fuzzy set theory.
Signatures: Definitions, operators and applications to fuzzy modelling
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This paper presents a new framework for the symbolic representation of data which is referred to as signatures. The definitions of signatures and of signature trees are first given. Original operators on signatures are next presented, i.e., contraction, extension, pruning, addition, multiplication, and grafting. Attractive applications of signatures related to the modelling of fuzzy inference systems are suggested and discussed. An example is included to accompany the theoretical results.
LVQ algorithm with instance weighting for generation of prototype-based rules
2011, Neural Networks
Citation Excerpt :
Despite these arguments prototype-based rules are still much less popular than other forms of rules. The use of prototype-based rule systems with linear functions for control (Tang & Lawry, 2010) may use linguistic labels but it is simply a basis set expansion technique that does not lead to comprehensible description of data. Similarity-Based Methods offer a rich framework (Duch, 2000; Duch, Adamczak, & Diercksen, 2000) for construction of such methods.
Crisp and fuzzy-logic rules are used for comprehensible representation of data, but rules based on similarity to prototypes are equally useful and much less known. Similarity-based methods belong to the most accurate data mining approaches. A large group of such methods is based on instance selection and optimization, with the Learning Vector Quantization (LVQ) algorithm being a prominent example. Accuracy of LVQ depends highly on proper initialization of prototypes and the optimization mechanism. This paper introduces prototype initialization based on context dependent clustering and modification of the LVQ cost function that utilizes additional information about class-dependent distribution of training vectors. This approach is illustrated on several benchmark datasets, finding simple and accurate models of data in the form of prototype-based rules.
Multi-source information fusion model in rule-based Gaussian-shaped fuzzy control inference system incorporating Gaussian density function
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On the development of signatures for Artificial Intelligence applications
2014, IEEE International Conference on Fuzzy Systems

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A prototype-based rule inference system incorporating linear functions

Abstract

Inf. Sci.

Inf. Sci.

Inf. Sci.

Int. J. Man–Machine Stud.

Fuzzy Sets and Systems

Int. J. Approx. Reasoning

Artif. Intell.

Int. J. Approx. Reasoning

Int. J. Approx. Reasoning

Inf. Sci.

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Artif. Intell.

Cogn. Psychol.

Inf. Sci.

Inf. Sci.

Fuzzy logic=computing with words

IEEE Trans. Fuzzy Syst.

From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions

IEEE Trans. Circuits Syst. I