Computation of the greatest right and left invariant fuzzy quasi-orders and fuzzy equivalences
| Autor: | Zorana Jančić, Ivana Micić, Stefan Stanimirović |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
0209 industrial biotechnology Fuzzy classification Mathematics::General Mathematics Logic 02 engineering and technology Fuzzy subalgebra Type-2 fuzzy sets and systems Fuzzy logic Defuzzification Algebra 020901 industrial engineering & automation Artificial Intelligence 0202 electrical engineering electronic engineering information engineering Fuzzy set operations Fuzzy number 020201 artificial intelligence & image processing Fuzzy associative matrix ComputingMethodologies_GENERAL Computer Science::Formal Languages and Automata Theory Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 339:99-118 |
| ISSN: | 0165-0114 |
| Popis: | Right invariant fuzzy quasi-orders for fuzzy automata are broadly studied in the recent literature, as they arise as solutions to particular systems of fuzzy relation equations and inequalities. Some of their applications include determinization and state reduction procedures, as well as simulations and bisimulations for fuzzy automata. In this paper we provide a procedure for computing the greatest right invariant fuzzy quasi-order for a given fuzzy automaton over a complete residuated lattice. The proposed procedure terminates in a finite number of steps whenever the underlying structure of the fuzzy automaton is locally finite. When the previous condition is not satisfied, we show that the greatest right invariant fuzzy quasi-order can be obtained by taking the limit value of the convergent array of fuzzy quasi-orders for fuzzy automata over BL-algebras on the real unit interval [ 0 , 1 ] . Analogous procedures for computing the greatest left invariant fuzzy quasi-order, as well as the greatest right and left invariant fuzzy equivalences for a fuzzy automaton are also presented. In addition, the faster algorithm for computing the greatest right invariant equivalence on a nondeterministic automaton is also presented. |
| Databáze: | OpenAIRE |
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