Equivalence and transformation of extended algebraic operators in fuzzy relational databases

An Extended Type-2 Fuzzy Relational Database Model for Aggregate and Grouping Operations

“…Thus, new FRDB models still continue to be developed for modeling data objects of the real world. Some FRDB models, such as [8], [9], [10] and [11], represented a fuzzy relation as a set of tuples whose each attribute may take a fuzzy set or a possibility distribution inferred from a fuzzy set. Fuzzy relational algebraic operations on these models were defined by employing similarity relations on the domain of the attributes and proximity binary relations on fuzzy sets or employing the possibility theory and proximity binary relations on possibility distributions.…”

Fuzzy Relational Database Model and Managemant System for Imprecise Information

“…So far, there have been many fuzzy relational database models studied and built (e.g. [4][5][6][7][8][9][10][11][12][13][14][15], [18][19][20][21][22][23][24][25][26]) based on the fuzzy set theory [2,3] to overcome the limitations of the classical relational database model in representing and handling uncertain and imprecise information of objects in practice.…”

“…There are two main approaches to represent fuzzy relations in fuzzy relational database models: (1) representing each fuzzy relation as a set of tuples whose each attribute may take a fuzzy set or a possibility distribution is inferred from a fuzzy set (e.g. [4][5] or [6][7][8][9][10][11], respectively), whereby the membership degree of tuples for the relation is hidden in that of their attribute values; (2) representing each fuzzy relation as a fuzzy set of tuples whose each attribute only takes a single and precise value (e.g. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]), whereby the membership degree of tuples for the relation also is the membership degree of elements for the fuzzy set expressing that fuzzy relation.…”

“…Meanwhile, regarding the proposes in [6][7][8][9], the attribute value of relations was represented by a possibility distribution, the fuzzy relational algebraic operations were defined by using the possibility theory and proximity binary relations on possibility distributions. Also, but the works in [10] and [11] only focused on the proof for the set of the operations {∪, ×, −, σ, Π} to be a complete set of all fuzzy relational algebraic operations and the equivalence and transformation on them, respectively. The models based on the first approach are capable of expressing well imprecise information due to the attribute values of relations are explicitly represented by fuzzy sets or possibility distributions but are limited the performance in handling such information because of the high complexity in manipulating and computing similarity relations, proximity binary relations on fuzzy sets and possibility distributions.…”

Analysis of functional dependencies in relational databases using fuzzy logic

“…Međutim, ako za  uzmemo vrednost 0.9 koja nije čvorna tačka, imaćemo rezultat koji se ne razlikuje pri gornjoj i donjoj toleranciji od 10%.Fazi relacioni model baza podataka predložen od strane Buckles-a i Petry-a, zasnovan na teoriji sličnosti, predstavlja generalizaciju klasične relacione baze podataka. Shenoi i Melton[25,27,62] zamenjuju relaciju sličnosti sa relacijom bliskosti i na taj način proširuju fazi relacioni model baza podataka. Uvođenjem relacije bliskosti značajno se pojednostavljuje generisanje fazi upita nad fazi relacionim bazama podataka, što je i prikazano u ovom poglavlju.…”