AN EXTENSION OF TOPSIS FOR FUZZY MCDM BASED ON VAGUE SET THEORY

1.Introduction The multicriteria decision-making problem(Kickert1978)is a kind of problem that all the alternatives in the choice set can be evaluated according to a number of criteria.A MCDM problem can be concisely expressed in matrix format as C1C2C n11112122122212nnm m m mnA x x xMA x x xA x x x=W={w1,w2,,wn}where A1,A2,,Am are possible alternatives among which decision-makers have to choose,C1,C2,,C n are the criteria with which alternative performance are measured,xi j is the rati…

An extension of TOPSIS for fuzzy MCDM based on vague set theory

This paper extends the TOPSIS to fuzzy MCDM based on vague set theory, where the characteristics of the alternatives are represented by vague sets. A novel score function is proposed in order to determine the vague positive-ideal solution (VPIS) and vague negative-ideal solution (VNIS). We present a weighted difference index to calculate the distance between vague values, by means of which the distance of alternatives to VPIS and VNIS can be calculated. Finally, the relative closeness values of various alternatives to the positive-ideal solution are ranked to determine the best alternative. An example is shown to illustrate the procedure of the proposed method at the end of this paper.