Picture Fuzzy Lattices, Ideals and Homomorphism

Mohammad Kamrul Hasan ¹ ( Department of Mathematics and Statistics, Bangladesh University of Business and Technology, Dhaka, Bangladesh. )

Submited date : 2024-08-05 Accepted date : 2024-09-25

Keywords: Picture fuzzy set, Picture fuzzy lattice, Picture fuzzy ideal, Picture fuzzy homomorphism, Picture fuzzy epimomorphism.,

Abstract :

Picture fuzzy set (PFS) is a novel concept for dealing with uncertainty and a generalization of the traditional fuzzy set (FS) and intuitionistic fuzzy set (IFS) and can easily manage the uncertain nature of human thoughts by incorporating the positive, neutral, negative and refusal membership degrees of an object. Many conceptual ideas on PFSs have been developed so far and applied in diversified fields. In this paper, the concept of picture fuzzy sublattices and picture fuzzy ideals are developed and some of their associated properties are established in detail. Moreover, the sum and product of two picture fuzzy ideals are introduced with their properties. Finally, some properties of picture fuzzy ideals under lattice homomorphism are explored.

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