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Machine Learning via rough mereology

Lech T. Polkowski

TL;DR

This note expands RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas of ML and AI which provides a measurable degree of uncertainty to those areas.

Abstract

Rough sets (RS)proved a thriving realm with successes inn many fields of ML and AI. In this note, we expand RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas.

Machine Learning via rough mereology

TL;DR

This note expands RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas of ML and AI which provides a measurable degree of uncertainty to those areas.

Abstract

Rough sets (RS)proved a thriving realm with successes inn many fields of ML and AI. In this note, we expand RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas.

Paper Structure

This paper contains 8 sections, 20 theorems, 12 equations, 1 figure.

Table of Contents

  1. Rough Sets
  2. Mereology
  3. Rough Mereology and rough subsets
  4. Granular computing
  5. Granular deciders
  6. Intensional logic for information/decision systems
  7. Synthesis of compound entities
  8. Spatial reasoning and robotics

Key Result

Theorem 1

The following are properties of the predicate $subst$.

Figures (1)

  • Figure 1: The cross formation navigating obstacles. Courtesy PJIIT Publishers

Theorems & Definitions (55)

  • Definition 1: Axiom schemes for part predicate
  • Definition 2: The subset predicate
  • Theorem 1
  • Definition 3: The predicate of Overlap
  • Definition 4: Axiom scheme (A4)
  • Definition 5: Class
  • Definition 6: Topological predicates
  • Definition 7: The Tarski algebra
  • Definition 8: The mereological implication
  • Theorem 2: Mereological implication
  • ...and 45 more