Lattice Generalizations of the Concept of Fuzzy Numbers and Zadeh's Extension Principle

  title={Lattice Generalizations of the Concept of Fuzzy Numbers and Zadeh's Extension Principle},
  author={Dmitry Maximov},
  • D. Maximov
  • Published 12 August 2022
  • Computer Science
  • ArXiv
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh’s extension principle for determining the degree of membership of a function of fuzzy numbers is corrected for this generalization. An analogue of the concept of mean value is also suggested. The use of partially ordered values in cognitive maps with comparison of… 



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