Lattice-valued finite state machines and lattice-valued transformation semigroups

Authors:
M. GóMez;I. Lizasoain;C. Moreno
Affiliations:
Departamento de Matemáticas, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain;Departamento de Matemáticas, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain;Departamento de Matemáticas, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain
Venue:
Fuzzy Sets and Systems
Year:
2012

Citing 11
Cited 0

Interval valued intuitionistic fuzzy sets

Fuzzy Sets and Systems
Determinism and fuzzy automata

Information Sciences—Informatics and Computer Science: An International Journal
On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision

Information Sciences: an International Journal
A representation of t-norms in interval-valued L-fuzzy set theory

Fuzzy Sets and Systems
Generation of interval-valued fuzzy and atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from Kα operators: Laws for conjunctions and disjunctions, amplitude

International Journal of Intelligent Systems
Interval-valued fuzzy sets constructed from matrices: Application to edge detection

Fuzzy Sets and Systems
Intuitionistic fuzzy transformation semigroups

Information Sciences: an International Journal
Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids

Fuzzy Sets and Systems
Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued “intuitionistic” sets, “intuitionistic” fuzzy sets and topologies

Fuzzy Sets and Systems
A class of aggregation functions encompassing two-dimensional OWA operators

Information Sciences: an International Journal
Finite automata theory with membership values in lattices

Information Sciences: an International Journal

Quantified Score

Hi-index	0.20

Visualization

Abstract

This paper provides a generalization of known results about fuzzy finite state machines, fuzzy transformation semigroups and their relationship by broading the truth values domain from the interval [0,1] to a complete lattice endowed with a t-norm and a t-conorm. So, we deal with the concepts of L-fuzzy finite state machines and L-fuzzy transformation semigroups and we prove that the cited generalization is possible if and only if the t-norm and the t-conorm satisfy a distributive property. If we consider the complete lattice of the closed intervals inside the original lattice L, we give methods to obtain an interval lattice-valued finite state machine and an interval lattice-valued transformation semigroup from two L-fuzzy finite state machines or two L-fuzzy transformation semigroups, respectively. Conversely, we show two different ways to build a faithful L-fuzzy transformation semigroup from an interval lattice-valued state machine. In fact, both methods give the same result.