Semantic quantitation of linguistic values embedded in complete linear hedge algebras and querying in the linguistic database

This article is about quantification semantics of linguistic terms embedded in Complete Linear Hedge Algebras and a application in querying in the database having the linguistic terms. The calculation is done both to the language values and real numbers. Query results are quite reasonable.
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Semantic quantitation of linguistic values embedded in complete linear hedge algebras and querying in the linguistic database JOURNAL OF SCIENCE OF HNUE Interdisciplinary Science, 2013, Vol. 58, No. 5, pp. 30-38 This paper is available online at http://stdb.hnue.edu.vn SEMANTIC QUANTITATION OF LINGUISTIC VALUES EMBEDDED IN COMPLETE LINEAR HEDGE ALGEBRAS AND QUERYING IN THE LINGUISTIC DATABASE Nguyen Tan An1 and Nguyen Van Quyen2 1 Faculty of Information Technology, Hanoi National University of Education 2 Department of Post Graduate, Hai Phong University Abstract. In fuzzy databases represented by linguistic values, linguistic terms carry qualitative semantics. However, when it comes to calculating linguistic terms or when a comparison between linguistic terms is needed, it is necessary to quantify their semantics. If the method of quantitation is suitable, the computational efficiency at the next step will be higher. When a database is embedded in Complete Linear Hedge Algebras, each base language values may have accompanying emphasis hedges. In such cases, the semantics of linguistic terms are quantified to become subintervals of an interval [0, 1]. This article is about quantification semantics of linguistic terms embedded in Complete Linear Hedge Algebras and a application in querying in the database having the linguistic terms. The calculation is done both to the language values and real numbers. Query results are quite reasonable. Keywords: Computation with words, semantics of terms, hedge algebras, linguistic representation model.1. Introduction Systems support making decisions increasingly tend to approach human processinginformation. This is how information processing of collected data or information thatis none-precise, incomplete, uncertain and/or vague and described by words in naturallanguages take place. The processing of vague data represented by linguistic values usually occurs infollowing ways: i) Using fuzzy set theory: Each linguistic value is represented by a fuzzy setcharacterized by a membership function or a membership function plus a no-membershipfunction.Received March 2, 2013. Accepted June 5, 2013.Contact Nguyen Tan An, e-mail address: nguyentanan@yahoo.com30 Semantic quantitation of linguistic values embedded in complete linear hedge algebras... ii) Based on the possibility theory: Each language value is given an possibilitydistribution to receive values in the reference domain. iii) With an approach in hedge algebras, each language database is embedded in thehedge algebras. Each method involves a series of subsequent problems, such as the integration offuzzy values, a comparison of fuzzy values, computing the distance between fuzzy valuesand measuring the similarity between the fuzzy values. Therefore the quality of the fuzzysystems when different methods are applied is not the same. When the language database is embedded in the hedge algebras, each base languagevalue may have accompanying emphasis hedges. While this presents, a convenient wayfor computing, the semantics of linguistic terms are quantified to become subintervals ofan interval [0, 1]. This paper presents the embedding language databases in the CompleteLinear Hedge Algebra (ComLin-HA) and the application of semantic quantitation in orderto query the data in this case. This paper include main contences: ComLin-HA, semantic quantitation of thelanguage values, a example of queries in fuzzy databases and the last one, someconclusions.2. Content2.1. An overview of ComLin-HA2.1.1. Hedge algebra (HA)Definition 2.1. An algebra X = (X, G, H, ≤), where X is a term domain, G is a set ofprimary terms, H is a set of linguistic hedges, and ≤ is an semantically ordering relation(SOR) on X, is called a hedge algebra (HA) if it satisfies the following [1]: (A1). Each hedge is either positive or negative the others, including itself; (A2). If terms u and v are independent, then, ∀x ∈ H(u), we have x ∈ / H(v). Inaddition, if u and v are incomparable, i.e., u ≮ v and v ≮ u, then so are x and y, forevery x ∈ H(u) and y ∈ H(v); / H(hx), and if h 6= k and hx ≤ kx , then h′ hx ≤ k ′ kx, for (A3). If x 6= hx , then x ∈ ′ ′all h, k, h , k ∈ H and x ∈ X. Moreover, if hx 6= kx , then hx and kx are independent; (A4) If u ∈/ H(v) and uleqv ((u ≥ v), then u ≤ hv (u ≥ hv) for any h ∈ H.2.1.2. ComLin-HA P A ComLin-HA is is presented by 7-tuple AX = (X, G, C, H, , φ, ≤), where: X ∈ Dom(X) with Dom(X) being the set of all terms of X; G = {0; c− ; W ; c+ ; 1} is the set of its primary terms, in which W is the neutralconcept positioned in between the two primary terms, i.e. we have 0 ≤ c− ≤ W ≤c+ ≤ 1; C = {c− ; c+ } is called a set of basic words; H is the set of hedges considered as to be unary operations on X. H = H − ∪ H + ; 31 Nguyen Tan An and Nguyen Van Quyen The effect of h acting on x is expressed by the fact that either hx ≥ x or hx ≤ x.In the case that kx ≥ hx ≥ x or y ≥ hy ≥ ky, for a certain x or y, we say that the effectof k is greater than the effect of h, and write k ≥ h. H is divided into H + and H − : H + = {h ∈ H : hc− ≤ c− or hc+ ≥ c+ } H − = {h ∈ H : hc− ≥ c− or hc+ ≤ c+ } In this paper, we denote by H − = {h0 ; h1 ; . . . ; h−q }, h0 < h1 < . . . < hp and +H = {h0 ; h1 ; . . . ; hp }, h0 < h−1 < . . . < ...