Skip to main content
Erschienen in: International Journal of Machine Learning and Cybernetics 4/2013

01.08.2013 | Original Article

Implication operators on the set of -irreducible element in the linguistic truth-valued intuitionistic fuzzy lattice

verfasst von: Li Zou, Xin Liu, Zheng Pei, Degen Huang

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 4/2013

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We construct a kind of linguistic truth-valued intuitionistic fuzzy lattice based on linguistic truth-valued lattice implication algebras to deal with linguistic truth values. We get some properties of implication operators on the set of ∨-irreducible elements. And furthermore the implication operators on the linguistic truth-valued intuitionistic fuzzy lattice are discussed. The proposed system can better express both comparable and incomparable information. Also it can deal with both positive and negative evidences which are represented by linguistic truth values at the same time during the information processing system.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Weitere Produktempfehlungen anzeigen
Literatur
2.
Zurück zum Zitat Atanassov KT (2005) Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, H. Prade’s paper “Terminological difficulties in fuzzy set theory: the case of ‘Intuitionistic Fuzzy Sets’”. Fuzzy Sets Syst 156:496–499 Atanassov KT (2005) Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, H. Prade’s paper “Terminological difficulties in fuzzy set theory: the case of ‘Intuitionistic Fuzzy Sets’”. Fuzzy Sets Syst 156:496–499
3.
Zurück zum Zitat Deschrijver G, Kerre EE (2007) On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Inf Sci 177:1860–1866 Deschrijver G, Kerre EE (2007) On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Inf Sci 177:1860–1866
4.
Zurück zum Zitat Espinilla M, Liu J, Martinez L (2011) An extended hierarchical linguistic model for decision-making problems. Comput Intell 27(3):489–512MathSciNetMATHCrossRef Espinilla M, Liu J, Martinez L (2011) An extended hierarchical linguistic model for decision-making problems. Comput Intell 27(3):489–512MathSciNetMATHCrossRef
5.
Zurück zum Zitat Herrera F, Martinez L (2001) The 2-tuple fuzzy linguistic computational model, advantages of its linguistic description, accuracy and consistency. Int J Uncertain Fuzziness Knowl-Based Syst 9:33–48MathSciNetMATHCrossRef Herrera F, Martinez L (2001) The 2-tuple fuzzy linguistic computational model, advantages of its linguistic description, accuracy and consistency. Int J Uncertain Fuzziness Knowl-Based Syst 9:33–48MathSciNetMATHCrossRef
6.
Zurück zum Zitat Herrera F, Lopez E, Mendana C, Rodriguez MA (2001) A linguistic decision model for personnel management solved with a linguistic biojective genetic algorithm. Fuzzy Sets Syst 118:47–64MathSciNetCrossRef Herrera F, Lopez E, Mendana C, Rodriguez MA (2001) A linguistic decision model for personnel management solved with a linguistic biojective genetic algorithm. Fuzzy Sets Syst 118:47–64MathSciNetCrossRef
7.
Zurück zum Zitat Herrera F, Alonso S, Chiclana F, Herrera-Viedma E (2009) Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim Decis Making 8(4):337–364MathSciNetCrossRef Herrera F, Alonso S, Chiclana F, Herrera-Viedma E (2009) Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim Decis Making 8(4):337–364MathSciNetCrossRef
8.
Zurück zum Zitat Ho NC (2007) A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges. Fuzzy Sets Syst 158:436–451MATHCrossRef Ho NC (2007) A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges. Fuzzy Sets Syst 158:436–451MATHCrossRef
9.
Zurück zum Zitat Huynh VN, Ho TB, Nakamori Y (2002) A parametric representation of linguistic hedges in Zadeh’s fuzzy logic. Int J Approx Reason 30:203–223MathSciNetMATHCrossRef Huynh VN, Ho TB, Nakamori Y (2002) A parametric representation of linguistic hedges in Zadeh’s fuzzy logic. Int J Approx Reason 30:203–223MathSciNetMATHCrossRef
10.
Zurück zum Zitat Liu BD (2004) Uncertainty theory: an introduction to its axiomatic foundations. Springer, Berlin Liu BD (2004) Uncertainty theory: an introduction to its axiomatic foundations. Springer, Berlin
11.
Zurück zum Zitat Liu BD (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin Liu BD (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
12.
Zurück zum Zitat Mahapatra GS, Mandal TK, Samanta GP (2011) A production inventory model with fuzzy coefficients using parametric geometric programming approach. Int J Mach Learn Cyber 2(2):99–105CrossRef Mahapatra GS, Mandal TK, Samanta GP (2011) A production inventory model with fuzzy coefficients using parametric geometric programming approach. Int J Mach Learn Cyber 2(2):99–105CrossRef
13.
Zurück zum Zitat Martinez L, Ruan D, Herrera F (2010) Computing with words in decision support systems: an overview on models and applications. Int J Comput Intell Syst 3(4):382–395 Martinez L, Ruan D, Herrera F (2010) Computing with words in decision support systems: an overview on models and applications. Int J Comput Intell Syst 3(4):382–395
14.
Zurück zum Zitat Nguyen CH, Huynh VN (2002) An algebraic approach to linguistic hedges in Zadeh’s fuzzy logic. Fuzzy Set Syst 129:229–254MATHCrossRef Nguyen CH, Huynh VN (2002) An algebraic approach to linguistic hedges in Zadeh’s fuzzy logic. Fuzzy Set Syst 129:229–254MATHCrossRef
15.
Zurück zum Zitat Pei Z (2007) The algebraic properties of linguistic value “Truth” and its reasoning. Lecture notes in artificial intelligence, vol 4529 (IFSA2007). Springer, Berlin, pp 436–444 Pei Z (2007) The algebraic properties of linguistic value “Truth” and its reasoning. Lecture notes in artificial intelligence, vol 4529 (IFSA2007). Springer, Berlin, pp 436–444
16.
Zurück zum Zitat Pei Z (2009) Fuzzy risk analysis based on linguistic information fusion. ICIC Exp Lett 3(3):325–330 Pei Z (2009) Fuzzy risk analysis based on linguistic information fusion. ICIC Exp Lett 3(3):325–330
17.
Zurück zum Zitat Pei Z, Ruan D, Liu J, Xu Y (2009) Linguistic values based intelligent information processing: theory, methods, and application. Atlantis computational intelligence systems, vol 1. Atlantis Press/World Scientific, Singapore Pei Z, Ruan D, Liu J, Xu Y (2009) Linguistic values based intelligent information processing: theory, methods, and application. Atlantis computational intelligence systems, vol 1. Atlantis Press/World Scientific, Singapore
18.
Zurück zum Zitat Pei Z, Xu Y, Ruan D, Qin K (2009) Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations. Inf Sci 179:2325–2332MATHCrossRef Pei Z, Xu Y, Ruan D, Qin K (2009) Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations. Inf Sci 179:2325–2332MATHCrossRef
19.
Zurück zum Zitat Soni H, Shah NH (2011) Optimal policy for fuzzy expected value production inventory model with imprecise production preparation-time. Int J Mach Learn Cyber 2(4):219–224MathSciNetCrossRef Soni H, Shah NH (2011) Optimal policy for fuzzy expected value production inventory model with imprecise production preparation-time. Int J Mach Learn Cyber 2(4):219–224MathSciNetCrossRef
20.
21.
Zurück zum Zitat Wang LJ (2011) An improved multiple fuzzy NNC system based on mutual information and fuzzy integral. Int J Mach Learn Cyber 2(1):25–36CrossRef Wang LJ (2011) An improved multiple fuzzy NNC system based on mutual information and fuzzy integral. Int J Mach Learn Cyber 2(1):25–36CrossRef
22.
Zurück zum Zitat Wang XZ, Dong CR (2009) Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567CrossRef Wang XZ, Dong CR (2009) Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567CrossRef
23.
Zurück zum Zitat Wang DG, Song WY, Li HX (2008) Unified forms of fuzzy similarity inference method for fuzzy reasoning and fuzzy systems. Int J Innov Comput Inf Control 4(10):2285–2294 Wang DG, Song WY, Li HX (2008) Unified forms of fuzzy similarity inference method for fuzzy reasoning and fuzzy systems. Int J Innov Comput Inf Control 4(10):2285–2294
24.
Zurück zum Zitat Wang XZ, He YL, Dong LC, Zhao HY (2011) Particle swarm optimization for determining fuzzy measures from data. Inf Sci 181(19):4230–4252MATHCrossRef Wang XZ, He YL, Dong LC, Zhao HY (2011) Particle swarm optimization for determining fuzzy measures from data. Inf Sci 181(19):4230–4252MATHCrossRef
25.
Zurück zum Zitat Wu J, Wang ST, Fu-lai C (2011) Positive and negative fuzzy rule system, extreme learning machine and image classification. Int J Mach Learn Cyber 2(4):261–271CrossRef Wu J, Wang ST, Fu-lai C (2011) Positive and negative fuzzy rule system, extreme learning machine and image classification. Int J Mach Learn Cyber 2(4):261–271CrossRef
26.
Zurück zum Zitat Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(11):1179–1187 Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(11):1179–1187
27.
Zurück zum Zitat Xu Y, Ruan D, Kerre EE, Liu J (2000) α-Resolution principle based on lattice-valued propositional logic LP(X). Inf Sci 130:195–223MathSciNetMATHCrossRef Xu Y, Ruan D, Kerre EE, Liu J (2000) α-Resolution principle based on lattice-valued propositional logic LP(X). Inf Sci 130:195–223MathSciNetMATHCrossRef
28.
Zurück zum Zitat Xu Y, Ruan D, Kerre EE, Liu J (2001) α-Resolution principle based on first-order lattice-valued propositional logic LF(X). Inf Sci 132:195–223MathSciNetCrossRef Xu Y, Ruan D, Kerre EE, Liu J (2001) α-Resolution principle based on first-order lattice-valued propositional logic LF(X). Inf Sci 132:195–223MathSciNetCrossRef
29.
Zurück zum Zitat Xu Y, Liu J, Ruan D, Lee TT (2006) On the consistency of rule bases based on lattice-valued first-order logic LF(X). Int J Intell Syst 21:399–424MATHCrossRef Xu Y, Liu J, Ruan D, Lee TT (2006) On the consistency of rule bases based on lattice-valued first-order logic LF(X). Int J Intell Syst 21:399–424MATHCrossRef
31.
Zurück zum Zitat Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning. Parts 1, 2, 3. Inf Sci 8:301–357; 9:43–80 (1975) Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning. Parts 1, 2, 3. Inf Sci 8:301–357; 9:43–80 (1975)
32.
Zurück zum Zitat Zou L, Ruan D, Pei Z, Xu Y (2008) A linguistic truth-valued reasoning approach in decision making with incomparable information. J Intell Fuzzy Syst 19(4–5):335–343MATH Zou L, Ruan D, Pei Z, Xu Y (2008) A linguistic truth-valued reasoning approach in decision making with incomparable information. J Intell Fuzzy Syst 19(4–5):335–343MATH
33.
Zurück zum Zitat Zou L, Liu X, Wu Z, Xu Y (2008) A uniform approach of linguistic truth values in sensor evaluation. Int J Fuzzy Optim Decis Making 7(4):387–397MATHCrossRef Zou L, Liu X, Wu Z, Xu Y (2008) A uniform approach of linguistic truth values in sensor evaluation. Int J Fuzzy Optim Decis Making 7(4):387–397MATHCrossRef
34.
Zurück zum Zitat Zou L, Pei Z, Liu X, Xu Y (2009) Semantics of linguistic truth-valued intuitionistic fuzzy proposition calculus. Int J Innov Comput Inf Control 5(12):4745–4752 Zou L, Pei Z, Liu X, Xu Y (2009) Semantics of linguistic truth-valued intuitionistic fuzzy proposition calculus. Int J Innov Comput Inf Control 5(12):4745–4752
35.
Zurück zum Zitat Zou L, Ruan D, Pei Z, Xu Y (2011) A linguistic-valued lattice implication algebra approach for risk analysis. J Multi-Valued Logic Soft Comput 17:293–303MathSciNetMATH Zou L, Ruan D, Pei Z, Xu Y (2011) A linguistic-valued lattice implication algebra approach for risk analysis. J Multi-Valued Logic Soft Comput 17:293–303MathSciNetMATH
Metadaten
Titel
Implication operators on the set of ∨-irreducible element in the linguistic truth-valued intuitionistic fuzzy lattice
verfasst von
Li Zou
Xin Liu
Zheng Pei
Degen Huang
Publikationsdatum
01.08.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 4/2013
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-012-0100-1

Weitere Artikel der Ausgabe 4/2013

International Journal of Machine Learning and Cybernetics 4/2013 Zur Ausgabe