ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 0903.0959
73
4
v1v2 (latest)

Convergence, Strong Law of Large Numbers, and Measurement Theory in the Language of Fuzzy Variables

5 March 2009
A. Bzowski
M. Urbański
ArXiv (abs)PDFHTML
Abstract

In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with convergence of their fuzzy distributions. In this context we prove a general formulation of the Strong Law of Large Numbers for fuzzy sets and fuzzy variables with Archimedean t-norms. Next we dispute a structure of fuzzy logics and postulate a new definition of necessity measures. Finally, we prove fuzzy version of the Glivenko-Cantelli theorem and use it for a construction of a complete fuzzy measure theory.

View on arXiv
Comments on this paper