Journal article Open Access

Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique

Shazia Rana; Madiha Qayyum; Muhammad Saeed; Florentin Smarandache; Bakhtawar Ali Khan

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is
introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy
Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to
Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of
Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole
membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft
set (in which multi attributes and their subattributes are represented with individual memberships
case of having interior view). Thus, the speciality of PFWHSS is its presentation of an exterior and
interior view of a situation simultaneously. Later, the PFWHSS is employed in development of
multi attributes decision making scheme named as Frequency Matrix Multi Attributes Decision
making scheme (FMMADMS). This innovative technique is not only simpler than any of the former
MADM techniques, but also has a unique capability of dealing mathematically a variety of human
mind psychologies at every level that are working in different environments (fuzzy, intuitionistic,
neutrosophic, plithogenic). Besides, FMMADMS also provides the percentage authenticity of the
final ranking which in itself is a new idea providing a transparent and unbiased ranking. Moreover,
the new introduced idea of frequency matrix handles the ranking ties in the best possible way and
has an ability to provide the authenticity comparative analysis of previously developed schemes.
Lastly, application of this FMMADMS is described as a numerical example for a case of ranking and
selecting the best alternative.

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