Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis

Abstract

We present the methods to evaluate the similarity measures between sequence of triangular fuzzy numbers for making contributions to fuzzy risk analysis. Firstly, we calculate the COG (center of gravity) points of sequence of triangular fuzzy numbers. After, we present the methods to measure the degree of similarity between sequence of triangular fuzzy numbers. In addition, we give an example to compare the methods mentioned in the text. Furthermore, in this paper, we deal with the(t1,t2)type fuzzy number. By defining the algebraic operations on the(t1,t2)type fuzzy numbers we can solve the equations in the formx+u(t1,t2)=v(t1,t2), whereu(t1,t2)andv(t1,t2)are fuzzy number. By this way, we can build an algebraic structure on fuzzy numbers. Additionally, the generalized difference sequence spaces of triangular fuzzy numbers[l∞(Ft)]B(r^,s^),[c(Ft)]B(r^,s^), and[c0(Ft)]B(r^,s^), consisting of all sequencesu∗=(u(t1,t2)k)such thatBr^,s^u∗is in the spacesl∞(Ft),c(Ft), andc0(Ft), have been constructed, respectively. Furthermore, some classes of matrix transformations from the spacecFtB(r^,s^)andμ(Ft)toμ(Ft)andcFtB(r^,s^)are characterized, respectively, whereμ(Ft)is any sequence space.