Formulation of linguistic regression model based on natural words

Abstract

When human experts express their ideas and thoughts, human words are basically employed in these expressions. That is, the experts with much professional experiences are capable of making assessment using their intuition and experiences. The measurements and interpretation of characteristics are taken with uncertainty, because most measured characteristics, analytical result, and field data can be interpreted only intuitively by experts. In such cases, judgments may be expressed using linguistic terms by experts. The difficulty in the direct measurement of certain characteristics makes the estimation of these characteristics imprecise. Such measurements may be dealt with the use of fuzzy set theory. As Professor L. A. Zadeh has placed the stress on the importance of the computation with words, fuzzy sets can take a central role in handling words [12, 13]. In this perspective fuzzy logic approach is offten thought as the main and only useful tool to deal with human words. In this paper we intend to present another approach to handle human words instead of fuzzy reasoning. That is, fuzzy regression analysis enables us treat the computation with words. In order to process linguistic variables, we define the vocabulary translation and vocabulary matching which convert linguistic expressions into membership functions on the interval [0–1] on the basis of a linguistic dictionary, and vice versa. We employ fuzzy regression analysis in order to deal with the assessment process of experts’ from linguistic variables of features and characteristics of an objective into the linguistic expression of the total assessment. The presented process consists of four portions: (1) vocabulary translation, (2) estimation, (3) vocabulary matching and (4) dictionary. We employed fuzzy quantification theory type 2 for estimating the total assessment in terms of linguistic structural attributes which are obtained from an expert.