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Should we say that the logical framework here is Set-Fmla on the basis of what ends up being proved, or that it is Fmla, on the basis of what the premisses and conclusions of the rules involved are?
The initial apexes (center points) of the membership functions based on C-Means algorithm are tuned with the aid of the genetic algorithm (GA), while the tuned apexes are also used to adjust the points of the consequent polynomials (conclusions) of the rules.
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The conclusion of the rule is about the partial correctness of the program α1;α2 (i.e., α1 sequentially composed with α2), that follows from the two assumptions.
If a 'true-branch' leads to a terminal node t, and the condition of t is not fulfilled then the conclusion of the rule in the parent node of t is taken.
As is standard in proof theory, the way to read these rules of inference is that above the horizontal rule — are the the premises of the rule (which are equations) and the equation below the horizontal rule is the conclusion of the rule of inference.
This classification concerns the form of the conclusion part of the rules that can be either constant or formed by some linear functions.
The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, modified quadratic, and cubic.
Moreover, the weighted Least Square (WLS) learning is exploited to estimate the coefficients of the polynomial forming the conclusion part of the rules.
information granules built in the reduced input space and a collection of local linear models forming the conclusion parts of the rules.
Hence, some conclusions of the default rule no longer apply.
Through assigning soundly information granularity to the related parameters of the antecedents and the conclusions of fuzzy rules of the original Sugeno-type model (i.e. granulate these parameters in the way of optimal allocation of information granularity becomes realized), the original Sugeno-type model is extended to its granular counterpart (granular model).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com