An Improved Fuzzy Number Approximation using Shadowed Sets

Abstract

ABSTRACT The shadowed sets are proposed by Pedrycz as a granule manner to approximate the fuzzy sets with preserving the uncertainty features. Many methods have been made in this context to maintain various characteristics of uncertainty for fuzzy sets. In this paper, a new method is proposed which it is preserve more than one kind of uncertainty in fuzzy sets. The new technique is based on the use of measures of uncertainty directly to induce ideal values of shadowed set. It's more simply and accurate for describing uncertainty. The features of new method are important for decision applications. General Terms Soft Computing, Uncertainty, Granular Computing . Keywords Fuzzy sets, Shadowed sets, Fuzziness measure, Non-specificity measure. 1. INTRODUCTION Fuzzy sets proposed by Zadeh [1] are very important in modeling and process vague information. Membership functions play vital role to describe vagueness and imprecision in linguistic terms. The shadowed sets are proposed by Pedrycz [2] for representing uncertainty in fuzzy sets and simplify computations complexity. In the literature, two other methods proposed to induce shadowed sets. One method [3] constructed shadowed sets based on fuzziness set induced from fuzzy sets and preserve fuzziness measure of fuzzy sets. Another method[4], induced shadowed sets based on combine two interval approximations for values possibly belong to fuzzy sets and another almost surely belong to fuzzy sets. This approach preserves uncertainty of fuzzy sets in the form of expected interval and width of fuzzy sets. In this paper, we will propose a new method to construct shadowed sets using non-specificity measure and fuzziness measure which it is maintenance two types of uncertainty in fuzzy sets. It is also, very simple in calculations. This paper is organized as follows: in section 2, we present brief review about shadowed sets and different methods proposed to induce it. In section 3, we display uncertainty measures of fuzzy sets and types used in every method for construct shadowed sets. In section 4, we display proposed approach for building shadowed sets. In section 5, we use fuzzy numbers examples to apply new method to illustrate the proposed algorithm and discussion the new method with previous methods. Finally conclusions have been evolved in section 6.