L-E-Fuzzy Lattices

详细信息    查看全文

• 作者：Branimir 艩e拧elja ; Andreja Tepav膷evi膰
• 关键词：Fuzzy lattice ; Fuzzy identity ; Fuzzy congruence ; Fuzzy equality ; Complete lattice ; 08A72 ; 06D72 ; 03E72
• 刊名：International Journal of Fuzzy Systems
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：17
• 期：3
• 页码：366-374
• 全文大小：
• 参考文献：1.Goguen, J.A.: \(L\) -fuzzy sets. J. Math. Anal. Appl. 18, 145鈥?74 (1967)MathSciNet CrossRef MATH
  2.Di Nola, A., Gerla, G.: Lattice valued algebras. Stochastica 11, 137鈥?50 (1987)MathSciNet MATH
  3.艩e拧elja, B., Tepav膷evi膰, A.: Partially ordered and relational valued algebras and congruences. Rev. Res. Fac. Sci. Math. Ser. 23, 273鈥?87 (1993)MATH
  4.B. 艩e拧elja, A. Tepav膷evi膰, L-E-Fuzzy Lattices. In: Proceedings of the of iFUZZY, p. 108. Kaohsiung, Taiwan, 26鈥?8 Nov 2014
  5.H枚hle, U., 艩ostak, A.P.: Axiomatic Foundations of Fixed-basis Fuzzy Topology. Springer, Dordrecht (1999)CrossRef
  6.B臎lohl谩vek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic/Plenum Publishers, New York (2002)CrossRef
  7.Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall PTR, Upper Saddle River, NJ (1995)MATH
  8.H枚hle, U.: Quotients with respect to similarity relations. Fuzzy Sets Syst. 27, 31鈥?4 (1988)CrossRef MATH
  9.M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations part I: fuzzy functions and their applications, part II: vague algebraic notions, part III: constructions of vague algebraic notions and vague arithmetic operations, Int. J. Gen. Syst. 32 (3) (2003) 123鈥?55, 157鈥?75, 177鈥?01
  10.B臎lohl谩vek, R., Vychodil, V.: Algebras with fuzzy equalities. Fuzzy Sets Syst. 157, 161鈥?01 (2006)CrossRef MATH
  11.B. 艩e拧elja, A. Tepav膷evi膰, Fuzzy Identities. In: Proceedings of the 2009 IEEE International Conference on Fuzzy Systems 1660鈥?664
  12.Budimirovi膰, B., Budimirovi膰, V., 艩e拧elja, B., Tepav膷evi膰, A.: Fuzzy identities with application to fuzzy semigroups. Inf. Sci. 266, 148鈥?59 (2014)CrossRef
  13.Budimirovi膰, B., Budimirovi膰, V., 艩e拧elja, B., Tepav膷evi膰, A.: Fuzzy equational classes are Fuzzy varieties. Iran. J. Fuzzy Syst. 10, 1鈥?8 (2013)
  14.Tepav膷evi膰, A., Trajkovski, G.: L-fuzzy lattices: an introduction. Fuzzy Sets Syst. 123, 209鈥?16 (2001)CrossRef MATH
  15.Jun-Fang Zhang, A Novel Definition of Fuzzy Lattice Based on Fuzzy Set, The Scientific World Journal Volume: 2013. Article ID 678586, (2013). doi:10.鈥?155/鈥?013/鈥?78586
  16.Zhang, Q., Xie, W., Fan, L.: Fuzzy complete lattices. Fuzzy Sets and Syst. 160, 2275鈥?291 (2009)MathSciNet CrossRef MATH
  17.Demirci, M.: A theory of vague lattices based on many-valued equivalence relations I: general representation results. Fuzzy Sets Syst. 151, 437鈥?72 (2005)MathSciNet CrossRef MATH
  18.Demirci, M.: A theory of vague lattices based on many-valued equivalence relations II: complete lattices. Fuzzy Sets Syst. 151, 473鈥?89 (2005)MathSciNet CrossRef MATH
  19.Ajmal, N., Thomas, K.V.: Fuzzy lattices. Inf. Sci. 79, 271鈥?91 (1994)MathSciNet CrossRef MATH
  20.Zimmermann, H.J.: Fuzzy Set Theory and its Applications. Kluwer, Boston (2011)
  21.B. Budimirovi膰, V. Budimirovi膰, B. 艩e拧elja, A. Tepav膷evi膰, Fuzzy equational classes, Fuzzy Systems (FUZZ-IEEE), IEEE International Conference, pp. 1鈥? (2012)
  22.Engesser, K., Gabbay, D.M., Lehmann, D. (eds.): Handbook of Quantum Logic and Quantum Structures: Quantum Structures. Elsevier, Amsterdam (2011)
  23.Ganter, B., Wille, R.: Formal Concept Analysis, vol. 284. Springer, Berlin (1999)CrossRef MATH
  24.Burris, S., Sankappanavar, H.P.: A Course in Universal Algebra. Springer, New York (1981)CrossRef MATH
  25.Filep, L.: Study of fuzzy algebras and relations from a general viewpoint. Acta Math. Acad. Paedagog. Nyh谩zi 14, 49鈥?5 (1998)MathSciNet MATH
  26.艩e拧elja, B., Tepav膷evi膰, A.: On generalizations of fuzzy algebras and congruences. Fuzzy Sets Syst. 65, 85鈥?4 (1994)CrossRef MATH
  
• 作者单位：Branimir 艩e拧elja (1)
  Andreja Tepav膷evi膰 (1)
  
  1. Department of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovi膰a 4, 21000, Novi Sad, Serbia
  
• 刊物类别：Computational Intelligence; Artificial Intelligence (incl. Robotics); Operations Research, Managemen
• 刊物主题：Computational Intelligence; Artificial Intelligence (incl. Robotics); Operations Research, Management Science;
• 出版者：Springer Berlin Heidelberg
• ISSN：2199-3211

文摘

A new definition of a fuzzy lattice ( L-E-fuzzy lattice) as a particular fuzzy algebraic structure is introduced in the framework of fuzzy equalities and fuzzy identities. The membership values structure is a complete lattice. An L-E-fuzzy lattice is defined on a bi-groupoid M, as its fuzzy sub-bi-groupoid 渭 equipped with a fuzzy equality E, fulfilling fuzzy lattice identities. It is proved that the new notion is a generalization of known lattice-valued structures. Basic properties of the introduced new fuzzy lattices are presented. In particular, it is proved that the quotients of cuts of 渭 over the corresponding cuts of E are classical lattices. By a suitable example, it is shown how the new introduced structures can be applied. Keywords Fuzzy lattice Fuzzy identity Fuzzy congruence Fuzzy equality Complete lattice