Novel fuzzy inference system (FIS) analysis and design based on lattice theory. Part I: Working principles

摘要: This work substantiates novel perspectives and tools for analysis design of fuzzy inference systems (FIS). It is shown rigorously that the cardinality set F numbers equals ℵ1, hence a FIS can implement “in principle” ℵ2 functions, where ℵ1 R real numbers; furthermore, endowed with capacity local generalization. A formulation in context lattice theory introduces tunable metric distance d K between numbers. Implied advantages include: (1) an alleviation curse-of-dimensionality problem, regarding number rules, (2) to cope heterogeneous data including (fuzzy) intervals (3) introduce systematically useful non-linearities. Extensive evidence from literature appears corroborate proposed perspectives. Computational experiments demonstrate utility tools. real-world industrial application also described.