Steps Towards Modeling and Querying Based on Linguistic Fuzzy Graph Database

In this paper, we introduce a method for computing with words on linguistic fuzzy graph database ( LGD ). Computation consists of two processes: Modeling and Querying. The former models LGD as a fuzzy graph whose nodes contain linguistic data table and the later queries linguistic data from node’s data tables.


Introduction
In everyday life, people use natural language (NL) for analyzing, reasoning, and finally, m ake their decisions. Computing with words (CWW) [2,6,[8][9][10][11]17] is a mathematical solution of computational problems stated in an NL. CWW based on fuzzy set and fuzzy logic, introduced by L. A. Zadeh is an approximate method on interval [0,1]. In linguistic domain, linguistic hedges play an important role for generating set of linguistic variables. A well known application of fuzzy set is fuzzy graph [3,7,14,16], combined fuzzy set with graph theory. Fuzzy graph (FG) has a lots of applications in both modeling and reasoning fuzzy knowledge such as Human trafficking, in ternet ro uting, il legal im migration [13] on interval [0,1] but not in linguistic values, However, many applications cannot model in numerical domain , for example, linguistic summarization problems [10]. To solve this problem, in the paper, we use an abstract algebra, called hedge algebra (HA) as a tool for computing with words. The remainder of paper is organized as follows: Section 2 reviews some main concepts of computing with words based on HA. Important section 3 studies a graph database to model with words using HA and its properties. Section 4 outlines conclusions and future work.

2.1
Hedge algebra In this section, we review some HA knowledges related to our research paper and give basic definitions. First definition o f a n H A i s s pecified by 3-Tuple HA = (X, H, ≤ ) in [6]. In [5], to easily simulate fuzzy knowledge, two terms G and C are inserted to 3-Tuple so HA = (X, G, C, H,

EAI Endorsed Transactions on Context-Aware Systems and Applications
Nguyen Van Han, Phan Cong Vinh The truth and meaning are fundamental important concepts in fuzzy logic, artificial intelligence and machine learning. In RCT (restriction-centered theory) [10], truth values are organized as a hierarchy with ground level or first-order and second-order. First order truth values are numerical values whereas second order ones are linguistic truth values. A linguistic truth value, say ℓ, is a fuzzy set. We study linguistic truth values on POSET L whose elements are comparable [5,6].
Consists of a universe L ∅ together with an interpretation of: • each constant symbol c j from ρ as an element • each a i -ary function symbol f a i from ρ as a function: In HA, ℓ ∈ L and there are order properties: Theorem 2.1. In [6], let ℓ 1 = h n . . . h 1 u and ℓ 2 = k m . . . k 1 u be two arbitrary canonical representations of ℓ 1 and ℓ 2 , then there exists an index j ≤ {m, n} + 1 such that h i = k j , for ∀i < j, and: 2. ℓ 1 = ℓ 2 iff m = n = j and h j x j = k j x j ; 3. ℓ 1 and ℓ 2 are incomparable iff h j x j and k j x j are incomparable; in which {V true, Ptrue, L true} stand for : very true, possible true and less true are linguistic truth values generated from variable truth. Assume propositions p = "Lucie is young is V true" and q = "Lucie is smart is Ptrue", interpretations on H are: • truth(p) = V true ∈ H, truth is a unary function.

Linguistic fuzzy graph
The first F G ( fuzzy g raph) w as i ntroduced i n [16], which vertices and edges's values are in unit interval [0, 1]. Many FG's theories were developed in [12,13] in which computational phases have a bit complex due to converting from linguistic to number value to compute. To reduce complexity, in [4] by applying computing with word method [10] on FG to produce LG, in which L is domain of both vertices V and E as in Fig. 1 Definition 2 .3. In [4], a linguistic graph LG = (V, ρ, δ) consists of set V, a fuzzy vertex set ρ on V and a fuzzy edge set δ on V so that Fig. 1 shows a simple LG. Let be an HA with order as L < M < V ( L for less, M for more and V for very are hedges ).