Fuzzy logic or
multi-valued logic is based on fuzzy set theory proposed by Zadeh [1], for helping in modeling knowledge in a more natural way.
We use AND-gates on
multi-valued attributes with wildcards as follows:
Here [D.sup.[delta]] is the standard Riemann-Liouville fractional derivative, and F : J x R [right arrow] P(R) is a
multi-valued map (P (R) is the family of all nonempty subsets of R), and [lambda] [member of] R with [lambda] [not equal to] 0.
For the
multi-valued case, see Vrabie [16] and [18].
Smarandache, A Unifying Field in Logic: Neutrosophic Field,
Multi-Valued Logic, 3(2002)(special issue on Neutrosophy and Neutrosophic Logic, 385-438.
of Hong Kong) and robotics and expert systems authority Pham cover fuzzy set theory, including interval arithmetic and operations on fuzzy sets, fuzzy logic theory, including classical logic theory, Boolean algebra,
multi-valued logic, fuzzy logic, approximate reasoning and fuzzy relations, and then give several applications including product quality evaluation and performance evaluation.
Peng et al [13] introduced the concept of
multi-valued neutrosophic set, gave two
multi-valued neutrosophic power aggregation operators.
Berinde, "On a general class of
multi-valued weakly Picard mappings," Journal of Mathematical Analysis and Applications, vol.
Ciric et all [3] proved fixed point theorems for single-valued mappings, extended to a coincid ence theorems for a pair of a random operator f : X X and a
multi-valued random operator T : X CB( X ) .
The existence of stationary points (or endpoints) of
multi-valued mappings have been studied by several authors (cf.
where, [[delta].sub.o] : A [right arrow] p(A) is a
multi-valued mapping function of an e-Learning activity ([alpha] [member of] A) to its power-set of immediate successors with post-requisites in the e-Learning sequencing behavior, and [[delta].sub.i] : A [right arrow] p (A) is a
multi-valued mapping function of an activity to its power-set of immediate predecessors with pre-requisites in the e-Learning sequencing behavior;
Bogatirev, Continous branches of
multi-valued mapping with non-convex right hands-side (Russian), Math.
We have given the logo a more modern, three-dimensional look for its aesthetic appeal and its ability to attract attention, but also because general semantics itself represents a multidimensional outlook in contrast to what Hebert Marcuse described as the one-dimensional man and consistent with a
multi-valued rather than two-valued orientation.
[8] Smarandache F., Neutrosophy, A new Branch of Philosophy,
Multi-Valued Logic, 3(2002) (special issue on Neutrosophy and Neutrosophic Logic), 297-384.
[13] introduced
multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems.
