×

Intuitionistic fuzzy sublattices and ideals. (English) Zbl 1256.06007

Summary: We study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals of a lattice. Some characterizations and properties of these intuitionistic fuzzy sublattices and ideals are established. Also we introduce the sum and product of two intuitionistic fuzzy ideals and prove that the sum and product of two intuitionistic fuzzy ideals of a distributive lattice is again an intuitionistic fuzzy ideal. Moreover, we study the properties of intuitionistic fuzzy ideals under lattice homomorphism.

MSC:

06D72 Fuzzy lattices (soft algebras) and related topics
03E72 Theory of fuzzy sets, etc.
06B10 Lattice ideals, congruence relations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ajmal N, Thomas K V (1994) Fuzzy lattices. Information Sciences Vol.79: 271–291 · Zbl 0798.06014 · doi:10.1016/0020-0255(94)90124-4
[2] Ajmal N, Thomas K V (2002) Fuzzy lattices I and II. Journal of Fuzzy Mathematics Vol.10, No.2: 255–296 · Zbl 1016.06010
[3] Ajmal N, Thomas K V (1994) Homomorphism of fuzzy subgroups, correspondences theorem and fuzzy quotient group. Fuzzy Sets and Systems 61: 329–339 · Zbl 0832.20086 · doi:10.1016/0165-0114(94)90175-9
[4] Atanassov K T (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20(1): 87–96 · Zbl 0631.03040 · doi:10.1016/S0165-0114(86)80034-3
[5] Biswas R (1996) Intuitionistic fuzzy subgroups. Mathematical Forum, Vol.10: 39–44
[6] Banerjee B, Basnet D K (2003) Intuitionistic fuzzy subring and ideals. Journal of Fuzzy Mathematics Vol.II, No.1: 139–155 · Zbl 1034.16049
[7] Brikhoff G (1967) Lattice theory. Published by American Mathematical Society, Providence, Rhode Island
[8] Mordesaon J N, Malik D S (1998) Fuzzy cummutative algebra. World Scientific Publishing Co. USA
[9] Zadeh L A (1965) Fuzzy sets. Information and Control 8: 331–352 · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.