A fuzzy application of the group Zn to complete hypergroups

• Published in: Soft computing (Berlin, Germany) Vol. 24; no. 5; pp. 3543 - 3550
• Main Authors: Cristea, Irina, Hassani Sadrabadi, Elhan, Davvaz, Bijan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computational Intelligence; Control; Decomposition; Engineering; Fuzzy sets; Graphs; Integers; Mathematical Logic and Foundations; Mechatronics; Methodologies and Application; Prime numbers; Robotics; Complete hypergroup; Intuitionistic fuzzy subhypergroup; Intuitionistic fuzzy set; Wieferich prime
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-019-04121-0

The purpose of this paper is the study of intuitionistic fuzzy subhypergroups of some special finite complete hypergroups. More exactly, in this paper we determine all m -tuples, characterizing the considered complete hypergroups, such that the grade intuitionistic fuzzy set ( μ ¯ , λ ¯ ) is an intuitionistic fuzzy subhypergroup of such hypergroups. Here, we deal with complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo p 2 or modulo pq , with p and q distinct odd primes. This article is a continuation of a previous work, concerning the complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo p or modulo 2 p , with p a prime number. It represents the starting point, the mathematical base, for writing a general algorithm for characterizing all complete hypergroups obtained from a group G and having the grade intuitionistic fuzzy set as an intuitionistic fuzzy subhypergroup.