Fuzzy rule base interpolation based on semantic revision

Attribute-Weighted Fuzzy Interpolative Reasoning

“…Characteristics [Hsiao et al, 1998] Exploiting slopes of fuzzy sets to obtain valid conclusions [Wu et al, 1996] Using similarity transfers to guarantee valid interpolation [Baranyi et al, 1995, Baranyi and Kóczy, 1996a, Baranyi et al, 2004, Baranyi et al, 1998 Adopting generalised concept for interpolation and extrapolation [Kawaguchi and Miyakoshi, 2000a, Kawaguchi and Miyakoshi, 2000b, Kawaguchi and Miyakoshi, 2001, Kawaguchi et al, 1997 Performing B-spline based interpolation , Chen and Shen, 2017, Huang and Shen, 2006, Huang and Shen, 2008, Li et al, 2019a, Li et al, 2018c, Naik et al, 2017b,Yang et al, 2017 Running FRI with scale and move transformation (T-FRI) Apart from the two major groups of FRI methods to conduct fuzzy interpolative reasoning as outlined above, there are alternative FRI techniques, as summarised in Table 2.5. This shows the diversity of this interesting research area.…”

“…Bearing significant similarity with the intermediate rule based FRI methods as outlined above is another approach, which is herein referred to as generalised function-based for convenience. Example methods falling within this family include those reported by [Baranyi et al, 1995, Baranyi and Kóczy, 1996a, Baranyi et al, 2004, Baranyi et al, 1998. Unlike the α-cut based interpolation algorithms, given an unmatched observation, this approach infers the conclusion based on the interpolation of fuzzy relations instead of using α-cut distances.…”

Bio-inspired computing tools and applications: position paper

“…There have been a number extensions, we survey some different approaches: the use of a spatial geometric representation allows us to avoid the requirements of convex or normal fuzzy sets, and guarantees interpretable conclusions in all cases [26] (see Fig. 7); an extension on the latter technique using the interpolation of the semantics of the rules and their interrelationships to guarantee the direct interpretability of the conclusions and piecewise linearity for triangular membership functions [27]; finally, returning to modified a-cut interpolation (MACI) methods which retain the low computational complexity of the original KH method, firstly retaining vector description of the fuzzy sets as characteristic points, coordinate transformation, and considering the fuzziness flanking information in the input spaces at the conclusion leads to efficient interpolation of fuzzy rules for multidimensional input variables [28]; and a generalization of characteristic points for different a-cut levels with normalization and aggregation functions leads to always acceptable conclusions [29].…”

Towards Dynamic Fuzzy Rule Interpolation via Density-Based Rule Promotion from Interpolated Outcomes

“…The first approach is centred on the utilisation of α-cuts, whereby the α-cut of an interpolated consequent is calculated from the α-cuts of its antecedents, as outlined by the resolution principle [6][7][8][9]. The second methodology employs the concept of similarity of fuzzy value and analogical reasoning [10][11][12][13][14][15][16][17]. Specifically, within this latter category, an FRI algorithm generates intermediate fuzzy rules based on the principle of similarity.…”