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The first relationship can be obtained by [M.sup.s.sub.p,p] [??] [M.sub.p,p] [??] [L.sup.p], where the [M.sub.p,p] [??] [L.sup.p] is a known inclusion relation (see [23]).
This section concerns the class [SP.sup.n.sub.[alpha],[lambda]] ([zeta], [eta]) and its properties, namely, inclusion relation and coefficient bounds.
Rough inclusion relation satisfies the similarity properties of Rough Mereology as mentioned in the next section.
In the theory of interval-valued fuzzy sets, the inclusion relation [subset or equal to] is a partial order on the set 1(U) of all interval-valued fuzzy sets on a given universe U and we also know that (1(U),[intersection],[union]) forms a distributive lattice.
DL and DDL provides powerful reasoning mechanism such as the consistency, satisfiability, inclusion relation between axioms and instances, therefore it can support automatic and intelligent service discovery and composition.
Our first inclusion relation involving [N.sub.j,[delta]],(h) is given in the following theorem.
We suggested calling such a relation an 'information content inclusion relation' (IIR) (Feng 1998).
To answer the latter question first, the types' meaning and extension constitute two ways of establishing the ordering: "in terms of meaning, each type specification is schematic for the one that follows; as for extension, the members of each category include those of the next as the proper subset" (Langacker 1991: 61).6 Depending on the perspective taken, then, the relationship between a type and a subtype (e.g., between mammal and squirrel), appears to be, on the one hand, a relation of schematicity (and, by the same token it reduces to "precision of specification" (Langacker 1991:61)), and on the other hand, a kind of inclusion relation, which obtains between a subset and a set.
The domain and range of the literal inclusion relation, for example, are both the set of pc sets, and the domain and range of the abstract complement relation are both the set of pc set classes.
In Theorem 2.4 we give the inclusion relations between the sets of [[??].sup.[alpha].sub.[lambda]]--statistical convergent sequences of order [alpha] for different [alpha] s.
Inclusion relations of these classes using [delta]-neighbourhood [N.sup.[delta].sub.p](I) p N (I) are also found.
(2008), Vakeel and Tabassum (2010, 2011a and b), Kumar (2007), Subramanian and Misra (2010), have studied the space [[chi square].sub.M] (p, q, u) of double sequences and gave some inclusion relations.