Willmott Fuzzy Implication in Fuzzy Databases

The object of the research are fuzzy functional dependencies on given relation scheme, and the question of their obtaining using the classical and innovated techniques. The attributes of the universal set are associated to the elements of the unit interval, and are turned into fuzzy formulas in this way. We prove that the dependency (which is treated as a fuzzy formula with respect to appropriately chosen valuation) is valid whenever it agrees with the attached two-elements fuzzy relation instance. The opposite direction of the claim is proven to be incorrect in this setting. Generalizing things to sets of attributes, we prove that particular fuzzy functional dependency follows form a set of fuzzy dependencies (in both, the world of two-element and the world of arbitrary fuzzy relation instances) if and only if the dependency is valid with respect to valuation anytime the set of fuzzy formulas agrees with the valuation. The results derived in paper show that the classical techniques in the procedure for generating new fuzzy dependencies may be replaced by the resolution ones, and hence automated. The research is conducted with respect to Willmott fuzzy implication operator

Absolutely PHAB

There have been many attempts at classifying the semantic modification relations (ℜ) of N + N compounds but this work has not led to the acceptance of a definitive scheme, so that devising a reusable classification is a worthwhile aim. The scope of this undertaking is extended to other binominal lexemes, i.e. units that contain two thing-morphemes without explicitly stating ℜ, like prepositional units, N + relational adjective units, etc. The 25-relation taxonomy of Bourque (2014) was tested against over 15,000 binominal lexemes from 106 languages and extended to a 29-relation scheme (“Bourque2”) through the introduction of two new reversible relations. Bourque2 is then mapped onto Hatcher’s (1960) four-relation scheme (extended by the addition of a fifth relation, similarity, as “Hatcher2”). This results in a two-tier system usable at different degrees of granularities. On account of its semantic proximity to compounding, metonymy is then taken into account, following Janda’s (2011) suggestion that it plays a role in word formation; Peirsman and Geeraerts’ (2006) inventory of 23 metonymic patterns is mapped onto Bourque2, confirming the identity of metonymic and binominal modification relations. Finally, Blank’s (2003) and Koch’s (2001) work on lexical semantics justifies the addition to the scheme of a third, superordinate level which comprises the three Aristotelean principles of similarity, contiguity and contrast.

FUNCTIONAL CONNECTION (BINDING), ESSENTIAL ELEMENTS AND RATING AS TOOLS FOR DEVELOPING A SEMANTIC CORRECT SCHEME FOR DATABASES

The paper considers an ambiguous representation of the subject area reality in data modelling in terms of the relation scheme. There were some attempts to rectify the relational model drawbacks by determining functional dependences among the relation attributes. Those attempts did not tackle the issue completely due to the specific nature of determining functional dependences during standardization of database scheme. The standardization allows eliminating an anomaly of operation updating caused by incorrect models of the subject area associated with the lack of semantic information in the relation model. To improve the representation process of semantic information, which is applied in designing of subject area, the authors suggest using such terms as essential elements and rating. These terms had been scrutinized ever since the hard-copy document workflow, when they were applied to formalize the document contents. To this purpose, the article describes the main components of the relational model in terms of essential elements and rating. For accomplishing aggregation and generalization operations used in developing the relational model and based on the description, the paper identifies formal criteria enabling to reduce the subjective factor while designing a conceptual database scheme.

ON THE DENSE FAMILIES IN THE RELATIONAL DATAMODEL

In this paper, dense families of relation schemes are introduced. We characterize minimal keys of relation schemes in terms of dense families. Note that, the dense families of database relations were introduced by Jarvinen [6]. We prove that the set of all minimal keys of a relation scheme s= (U, F) is the transversal hypergraphs of a hypergraph D– {∅}, where Dis any s-dense family. We give a necessary and sufficient condition for an abitrary family to be s-dense family. We also present some dense families of relation schemes. Furthermore, in this paper, we also study antikeys by means of dense families. We present connections between antikeys and a dense family of relation schemes. Finally, we study the time complexity of the problem finding antikeys.

On the nonkeys

In this paper we give some results about nonkeys. We show that for relation scheme the problem decide whether there is a nonkey having cardinality greater than or equal to a give integer m is NP-complete. However, for relation this problem can be solved by a polynomial time algorithm.

Some computational problems related to normal forms

In the relational database theory the most desirable normal form is the Boyce-Codd normal form (BCNF). This paper investigates some computational problems concerning BCNF relation scheme and BCNF relations. We give an effective algorithm finding a BCNF relation r such that r represents a given BCNF relation scheme s (i.e., Kr=Ks, where Kr and Ks are sets of all minimal keys of r and s). This paper also gives an effective algorithm which from a given BCNF relation finds a BCNF relation scheme such that Kr=Ks. Based on these algorithms we prove that the time complexity of the problem that finds a BCNF relation r representing a given BCNF relation scheme s is exponential in the size of s and conversely, the complexity of finding a BCNF relation scheme s from a given BCNF relation r such that r represents s also is exponential in the number of attributes. We give a new characterization of the relations and the relation scheme that are uniquely determined by their minimal keys. It is known that these relations and the relation schemes are in the BCNF class. From this characterization we give a polynomial time algorithm deciding whether an arbitrary relation is uniquely determined by its set of all minimal keys. In the rest if this paper some new bounds of the size of minimal Armstrong relations for BCNF relation scheme are given. We show that given a Sperner system K and BCNF relation scheme s a set of minimal keys of which is K, the number of antikeys (maximal nonkeys) of K is polynomial in the number of attributes iff so is the size of minimal Armstrong relation of s.

Structure of multivalued dependencies in relation scheme

As pointed out in [1], Multivalued dependencies (MVD) depend on the context in which they are defined and thus are very hard to visualize. In this paper, continuing the study in [1], we give some results which may provide some more insight regarding the existence of possible MVDs in the relation schemes provided all their FDs are known in advance. Throughout this paper, we assume that the reader is familiar with the basic concepts of the relational database [2,3]. Tóm tắt. Như đã chi rõ trong [1], các phụ thuộc đa trị (MVD) phụ thuộc vào ngữ cảnh trong đó chúng đươc xác đinh và do đó rất khó phát hiện. Trong bài báo này, tiếp tục hướng nghiên cứu trong [1], chúng tôi dưa ra môt số kết quả làm sáng tỏ sự tồn tại của các MVD trong các lược dồ quan hệ vói tất cả các phụ thuộc hàm (FD) đã biết trước.

On the computational algorithm related to antikeys

The keys and antikeys play important roles for the investigation of functional dependency in the relational datamodel. The main purpose of this paper is to prove that the time complexity of finding a set of antileys for a given relation scheme S is exponential in the number of attributes. Some another results connecting the functional dependency are given. Key Word and phrase: Relation, relational datamodel, functionsl dependency, relation scheme, generating Armstrong relation, dependency inference, strong schemen, membership problem, closure, closed set, minimal generater, key, minimal key, antikey.