Abstract
Various fuzzy inference systems that operate on the basis of polynomial consequents of fuzzy rules. As well as inference methods for such systems, in particular, Takagi-Sugeno fuzzy inference systems, their differences from other popular fuzzy systems, such as Mamdani systems, etc., are considered. The attention is focused on the features of the functioning of such systems both in the construction of elementary fuzzy systems. The Systems for which the calculation of the general logical conclusion involves intermediate levels of logical inference with many hierarchically interconnected blocks of fuzzy rules. Fuzzy sets of type 2 are considered, the membership index of which is a fuzzy term of the first type. This allows you to take into account the secondary fuzziness of linguistic concepts in the design of intelligent systems based on fuzzy inference. Fuzzy systems of the second type based on Takagi-Sugeno systems and the iterative Karnik-Mendel algorithm are considered to obtain a logical conclusion for fuzzy systems with the interval membership functions of the second type in the antecedents of fuzzy rules. The proposed procedure for lowering the order of fuzzy rules for higher-order Takagi-Sugeno fuzzy systems is described and justified. A fuzzy inference method for higher-order fuzzy systems based on the partition of a set of input variables is proposed. It is proposed to build a separate block of fuzzy rules for each of the input subspaces in the presence of a common polynomial. Which is a higher-order consequent, that reduces the total number of fuzzy rules in blocks.
Highlights
Since the creation of the Lotfie Zadeh apparatus of fuzzy logic [1], it has become possible to operate with qualitative quantities that are linguistic in nature [2]
Fuzzy logical inference (FLI) is often used in the development of intelligent systems that operate on the basis of predicate rule blocks
In the research we looked in various types of fuzzy inference systems operating on the basis of fuzzy rules with polynomial consequents, in particular Takagi-Sugeno systems
Summary
Since the creation of the Lotfie Zadeh apparatus of fuzzy logic [1], it has become possible to operate with qualitative (categorical) quantities that are linguistic in nature [2]. Fuzzy logical inference (FLI) is often used in the development of intelligent systems that operate on the basis of predicate rule blocks. Take into account the fuzzy (vague) nature of the quantities being operated, often arising when using linguistic variables [2, 4, 5]. When constructing fuzzy systems [6], an expert in the problem area plays an important role. The knowledge and experience of whom are used primarily in constructing blocks of fuzzy rules, due to insufficient knowledge in solving a narrow circle of expert and intellectual problems [7–8]. Expert tasks [9], clustering problems [10-11], selection, optimization, decision making, pattern recognition [7, 12-15], etc.
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