A Gentle Introduction to Cognitive Map Based on Input Output Linguistic Variables

This paper studies on feedback graph model of linguistic variables which is generated from Hedge algebra. We also introduce a visual graphic model for input - output cognitive maps.


Introduction
In everyday life, people use natural language (NL) for analyzing, reasoning, and finally, m ake their decisions. Computing with words (CWW) [2,9,[11][12][13][14]20] 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 [3,10,17,18], 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 [16] on interval [0,1] but not in linguistic values, However, many applications cannot model in numerical domain , for example, linguistic summarization problems [13]. 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 modeling 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 of an HA is specified by 3-Tuple HA = (X, H, ≤ ) in [9]. In [8] to easily simulate fuzzy knowledge, two terms G and C are inserted

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) [13], 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 [8,9].
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 [9], 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;

Fig. 2. A new FCM model
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.
∨ is a binary function.

New model fuzzy cognitive map
The first F uzzy C ognitive M aps ( FCM) w as introduced in [10,15] and fast developed in many applications [3,17]. Fig.1 is a simple FCM with its matrix in Fig.3. In [1,19], that is a new FCM model with input signals.

Input-Output Linguistic Cognitive maps
Linguistic cognitive maps LCM have been applying and studying in many areas of artificial intelligence [4][5][6][7] Definition 3.1. . A linguistic cognitive map (LCM) is a 4-Tuple: In which: . . , C n } is the set of N concepts forming the nodes of a graph.
In the paper, we modify LCM to have a new LCM with input-output linguistic variables. Fig.5 illustrates a new abstract LCM and Fig.6  Our next study will investigate algorithms to construct and compute state space for new LCM.