Integration of Sorensen and Cosine Similarity Measure for Solving Fuzzy Decision Making Problems

Similarity measure has been used in many fields of study to measure common features between objects. The fuzzy similarity measure is popularized when elements of vagueness and subjectivity are incorporated in the comparison process. It is a preferred approach to some distance methods since in obtaining the distances, the defuzzification process will be involved that may cause loss of some vital information due to simplification process to a single value. Several fuzzy similarities have been proposed to cater different setting and for better discrimination. Nevertheless, in many cases, an extreme degree of similarity may occur due to the characteristic of the similarity measure itself. In particular, the Cosine similarity measure gives a too low degree of similarity while the Sorensen similarity measure gives a too high degree of similarity where in return the utilization of these similarities may not give the acceptable measurement of similarity. An integration of two or more similarity measures may assist to eradicate this problem. In this paper, the Sorensen and Cosine similarity measure were integrated based on the variation coefficient representation under fuzzy environment. A procedure of ranking alternatives is proposed using the new integrated similarity measure and is used to solve the grading problem of oil palm fruit bunch. The proposed integrated fuzzy similarity measure of Cosine and Sorensen has an advantage of being able to compromise the extreme values produced by the two similarity measures and has the potential to be applied to solving various fuzzy decision making problems.