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Proceedings ArticleDOI

A general interpolation technique in fuzzy rule bases with arbitrary membership functions

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TLDR
A general multidimensional fuzzy rule interpolation method, compared to the existing interpolation methods, that can be applied to arbitrary type of fuzzy sets, and does not require convex and normal sets in the rules.
Abstract
Presents a general multidimensional fuzzy rule interpolation method. This method, compared to the existing interpolation methods, can be applied to arbitrary type of fuzzy sets, and does not require convex and normal sets in the rules. Another important difference is the new method gives an interpretable conclusion in every case, unlike the previously published methods. As a matter of course, to apply arbitrary type of sets, the general method makes calculation necessary for "every point" of the sets. A special method, based on the theory of the general method, is introduced for application in practice, which needs low computational capacity. The specialised method uses three of the most wide spread set types in practice: the crisp, the triangular, and the trapezoidal fuzzy sets. The difference between the new and the former methods is pointed out by examples and the results of different formal methods.

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TL;DR: The present work characterizes membership functions by the conditions of sum normalization (SN), nonnegativeness (NN), and normality (NO).
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Fuzzy interpolative reasoning via scale and move transformations

TL;DR: This paper presents an interpolative reasoning method by means of scale and move transformations that can be used to interpolate fuzzy rules involving complex polygon, Gaussian or other bell-shaped fuzzy membership functions.
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Fuzzy Interpolation and Extrapolation: A Practical Approach

TL;DR: The work of Huang and Shen is extended, and the result enables both interpolation and extrapolation which involve multiple fuzzy rules, with each rule consisting of multiple antecedents.
References
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Journal ArticleDOI

Outline of a New Approach to the Analysis of Complex Systems and Decision Processes

TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Journal ArticleDOI

An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller

TL;DR: Fuzzy logic is used to convert heuristic control rules stated by a human operator into an automatic control strategy, and the control strategy set up linguistically proved to be far better than expected in its own right.
Journal ArticleDOI

Ordering, distance and closeness of fuzzy sets

TL;DR: The fuzzy distance of two C NF sets can be defined, and by this distance, closeness and similarity of CNF sets, as well.
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A proposal on approximate reasoning based on revision principle and fixed value law

TL;DR: According to the fixed value law, it will become possible to deduce Q' from Q by shifting the membership function, and a set of linear revising formulas will be given.
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