In most fuzzy control applications (applying classical fuzzy reasoning), the reasoning method requires a complete fuzzy rule-base, i.e all the possible observations must be covered by the antecedents of the fuzzy rules, which is not always available. Fuzzy control systems based on the Fuzzy Rule Interpolation (FRI) concept play a major role in different platforms, in case if only a sparse fuzzy rule-base is available. This cases the fuzzy model contains only the most relevant rules, without covering all the antecedent universes. The first FRI toolbox being able to handle different FRI methods was developed by Johanyak et. al. in 2006 for the MATLAB environment. The goal of this paper is to introduce some details of the adaptation of the FRI toolbox to support the GNU/OCTAVE programming language. The OCTAVE Fuzzy Rule Interpolation (OCTFRI) Toolbox is an open-source toolbox for OCTAVE programming language, providing a large functionally compatible subset of the MATLAB FRI toolbox as well as many extensions. The OCTFRI Toolbox includes functions that enable the user to evaluate Fuzzy Inference Systems (FISs) from the command line and from OCTAVE scripts, read/write FISs and OBS to/from files, and produce a graphical visualisation of both the membership functions and the FIS outputs. Future work will focus on implementing advanced fuzzy inference techniques and GUI tools.
FRI methods are less popular in the practical application domain. One possible reason is the missing common framework. There are many FRI methods developed independently, having different interpolation concepts and features. One trial for setting up a common FRI framework was the MATLAB FRI Toolbox, developed by Johany\'ak et. al. in 2006. The goals of this paper are divided as follows: firstly, to present a brief introduction of the FRI methods. Secondly, to introduce a brief description of the refreshed and extended version of the original FRI Toolbox. And thirdly, to use different unified numerical benchmark examples to evaluate and analyze the Fuzzy Rule Interpolation Techniques (FRI) (KH, KH Stabilized, MACI, IMUL, CRF, VKK, GM, FRIPOC, LESFRI, and SCALEMOVE), that will be classified and compared based on different features by following the abnormality and linearity conditions .
The goal of this paper is twofold. Once to highlight some basic problematic properties of the KH Fuzzy Rule Interpolation through examples, secondly to set up a brief Benchmark set of Examples, which is suitable for testing other Fuzzy Rule Interpolation (FRI) methods against these ill conditions. Fuzzy Rule Interpolation methods were originally proposed to handle the situation of missing fuzzy rules (sparse rule-bases) and to reduce the decision complexity. Fuzzy Rule Interpolation is an important technique for implementing inference with sparse fuzzy rule-bases. Even if a given observation has no overlap with the antecedent of any rule from the rule-base, FRI may still conclude a conclusion. The first FRI method was the Koczy and Hirota proposed "Linear Interpolation", which was later renamed to "KH Fuzzy Interpolation" by the followers. There are several conditions and criteria have been suggested for unifying the common requirements an FRI methods have to satisfy. One of the most common one is the demand for a convex and normal fuzzy (CNF) conclusion, if all the rule antecedents and consequents are CNF sets. The KH FRI is the one, which cannot fulfill this condition. This paper is focusing on the conditions, where the KH FRI fails the demand for the CNF conclusion. By setting up some CNF rule examples, the paper also defines a Benchmark, in which other FRI methods can be tested if they can produce CNF conclusion where the KH FRI fails.
Default reasoning and interpolation are two important forms of commonsense rule-based reasoning. The former allows us to draw conclusions from incompletely specified states, by making assumptions on normality, whereas the latter allows us to draw conclusions from states that are not explicitly covered by any of the available rules. Although both approaches have received considerable attention in the literature, it is at present not well understood how they can be combined to draw reasonable conclusions from incompletely specified states and incomplete rule bases. In this paper, we introduce an inference system for interpolating default rules, based on a geometric semantics in which normality is related to spatial density and interpolation is related to geometric betweenness. We view default rules and information on the betweenness of natural categories as particular types of constraints on qualitative representations of Gärdenfors conceptual spaces. We propose an axiomatization, extending the well-known System P, and show its soundness and completeness w.r.t. the proposed semantics. Subsequently, we explore how our extension of preferential reasoning can be further refined by adapting two classical approaches for handling the irrelevance problem in default reasoning: rational closure and conditional entailment.
The problcmls of AI effectivent s in manufacturing for Design, Scheduling, Control and Proce -.; Diagnosis are considered. We have developed an effective dialog procedure for a designer. This procedure I ei him to identify file no..xh.'d parameters of a d igned product, i.e., to distinct acceptable paranleters, utm acceptable parameters and paran eters that require additional design sttgly. In lx'x'luling we developed a new intelligent procedure to formulate and find an effective schedule.