Abstract
In this paper, we develop the initial theory of complex fuzzy soft hypergroup by introducing the novel concept of complex fuzzy soft hypergroup, complex fuzzy soft hyperring. Consequently, a major part of this work is dedicated to extend the theory of complex fuzzy soft set, complex fuzzy hypergroup. Complex fuzzy soft quasihypergroup, complex fuzzy soft semihypergroup and complex fuzzy soft subhypergroup also discussed in this paper.
Highlights
Soft set theory is a generalization of fuzzy set theory, which was proposed by Molodtsov [10] in 1999 to deal with uncertainty in a non-parametric manner
Complex fuzzy set (CFS) [11]-[12] is a new development in the theory of fuzzy systems [14]
This paper is organized as follows: Section 2 reviews the concept of complex fuzzy hypergroup based on complex fuzzy set on complex fuzzy spaces
Summary
Soft set theory is a generalization of fuzzy set theory, which was proposed by Molodtsov [10] in 1999 to deal with uncertainty in a non-parametric manner. One of the most important steps for the theory of Soft Sets was to define mappings on soft sets, this was achieved in 2009 by mathematician Athar Kharal, though the results were published in 2011. Mappings on fuzzy soft sets[2,9] were defined and studied in the ground breaking work of Kharal and Ahmad. Complex fuzzy set (CFS) [11]-[12] is a new development in the theory of fuzzy systems [14]. Complex fuzzy hyperstructure [1], complex fuzzy hypergroup [1] is a latest development in the theory of complex fuzzy set. This paper is organized as follows: Section 2 reviews the concept of complex fuzzy hypergroup based on complex fuzzy set on complex fuzzy spaces.
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