Research Of Linguistic Regression Model Based On Type-2 Fuzzy Set Theory

Fuzzy always encountered in our daily lives, because most descriptive words have no clear boundaries, such as cold and heat, more and less, etc, the extend could not be decided easily. Fuzzy theory emerged in order to solve this problem, given birth by the US scientist Zadah[1]. When an element is not or not entirely belong to a set(i.e. whose”degree” belong to a set is in closed interval [0,1]), we employ the membership grade to emphasis its characteristics. Relevant research of its mathematical features breakthrough constantly. In particular, the introduction of type-2 fuzzy set theory from 1975, respect to an ordinary fuzzy set(named as type-1 fuzzy set, respectively), which has a threedimensional membership function, so that the membership function itself became a fuzzy set located in [0,1]. Type-2 fuzzy set theory focuses the membership function of their own shape or the presence of uncertainty, and therefore type-2 fuzzy set theory is better applied to the cases of multiple uncertainties, that is, when an element’s ”degree” belonging to a given set is not sure, turn to type-2 fuzzy set theory is helpful.There is also known its related applications’ great progress recent years. It has been widely used in a number of fields s uch a s fi nancial an alysis, pa ttern re cognition, fuzzy logic, fuzzy systems. Fuzzy system is an important research direction of this being. It is from fuzzy set and based on the knowledge or rule-based systems, whose core is composed of IF-THEN rules. Similar to traditional fuzzy set system, type-2 fuzzy set system is also constructed through a combination of IF-THEN rules, but because of its theoretical basis for type-2 fuzzy set theory, more uncertainty information can be controlled directly, speaking to an ordinary one.This thesis emphasizes the concepts of fuzzy regression system, keen on the development of knowledge and type-2 fuzzy sets, combined with an important tool for fuzzy theory-credibility theory after then, it committed to solve the problem of fuzzy probability distribution space. For the huge computational complexity of the type-2 fuzzy sets, the existing mainstream solution for the type reduction, through the experimental analysis of the pros and cons of each algorithm, pointing out the selection criteria of the algorithm.In order to solve the linguistic regression model, began with the construction of the linguistic dictionary, chosen the model of planning completed and the parameters to solve the problem of data processing, the model combines the confidence intervals and fuzzy regression models to make the results for the reliability enhancements. Finally, a heuristic algorithm is proposed to solve the specific problem. Combined with the practical application, an example is given in the last part.Through the analysis of the results, It could be seen the model’s high working efficiency and accuracy, well accomplishes the research objectives of the thesis, the following research is carrying out after the good inspiration.