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Call for chapters for the collective book “Plithogenics
and New Types of Soft Sets”
Submit your chapter to:
No publication fees.
Proposals Submission Deadline: September 24, 2023
Full Chapters Due: October 22, 2023
Introduction
A plithogenic set P is a set whose elements are
characterized by one or more attributes (parameters), and each attribute
(parameter) may have many values. Each attribute’s value v has a corresponding
degree of appurtenance d(x,v) of the element x, to the set P, with respect to
some given criteria. These attributes (parameters) and their values may be
independent, dependent, or partially independent and dependent – according to
the applications: http://fs.unm.edu/NSS/PlithogenicSetAnExtensionOfCrisp.pdf http://fs.unm.edu/Plithogeny.pdf
Symbolic Plithogenic Algebraic Structures:
The new types of soft sets are: the HyperSoft Set
(2018), IndetermSoft Set (2022), IndetermHyperSoft Set (2022),
and TreeSoft Set (2022), see http://fs.unm.edu/TSS/.
Definition of IndetermSoft Set
Let U be a universe of discourse, H a non-empty subset of
U, and P(H) be the powerset of H. Let a be an attribute, and A be a set of this
attribute-values. Then F: A → P(H) is called an IndetermSoft Set if at least
one of the bellow occurs:
i) the set A has some indeterminacy;
ii) the sets H or P(H) have some indeterminacy;
iii) the function F has some indeterminacy, i.e. there exist at least an
attribute-value v that belongs to A, such that F(v) = indeterminate (unclear,
incomplete, conflicting, or not unique).
IndetermSoft Set, as extension of the classical
(determinate) Soft Set, deals with indeterminate data, because there are
sources unable to provide exact or complete information on the sets A, H, or
P(H), nor on the function F. We did not add any indeterminacy, we found the
indeterminacy in our real world. Because many sources give
approximate/uncertain/incomplete/conflicting information, not exact information
as in the Soft Set, as such we still need to deal with such situations.
Herein, ‘Indeterm’ stands for ‘Indeterminate’ (uncertain,
conflicting, incomplete, not unique outcome).
Similarly, distinctions between determinate and
indeterminate operators are taken into consideration. Afterwards, an
IndetermSoft Algebra is built, using a determinate soft operator (joinAND), and
three indeterminate soft operators (disjoinOR, exclussiveOR, NOT), whose
properties are further on studied.
The classical Soft Set is based on a determinate function
(whose values are certain, and unique), but in our world there are many sources
that, because of lack of information or ignorance, provide indeterminate
(uncertain, and not unique – but hesitant or alternative) information. They can
be modeled by operators having some degree of indeterminacy due to the
imprecision of our world.
Editors
Prof. Dr. Florentin Smarandache, University of New Mexico, United States Prof. Dr. Maikel Yelandi Leyva Vázquez, University of the Andes UNIANDES,
Ecuador
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May 12th, 2023 
Daniela Lopez de Luise 
Posted in Congress 
