A New Approach to Derive Priority Weights from Additive Interval Fuzzy Preference Relations Based on Logarithms

Abstract

This paper investigates the consistency definition and the weight-deriving method for additive interval fuzzy preference relations (IFPRs) using a particular characterization based on logarithms. In a recently published paper, a new approach with a parameter is developed to obtain priority weights from fuzzy preference relations (FPRs), then a new consistency definition for the additive IFPRs is defined, and finally linear programming models for deriving interval weights from consistent and inconsistent IFPRs are proposed. However, the discussion of the parameter value is not adequate and the weights obtained by the linear models for inconsistent IFPRs are dependent on alternative labels and not robust to permutations of the decision makers’ judgments. In this paper, we first investigate the value of the parameter more thoroughly and give the closed form solution for the parameter. Then, we design a numerical example to illustrate the drawback of the linear models. Finally, we construct a linear model to derive interval weights from IFPRs based on the additive transitivity based consistency definition. To demonstrate the effectiveness of our proposed method, we compare our method to the existing method on three numerical examples. The results show that our method performs better on both consistent and inconsistent IFPRs.

Sliding Mode Control with Adaptive Fuzzy Compensation for Uncertain Nonlinear System

“…, 25, 1 2 is the fuzzy set of the conclusion. Then the first step and the 25th fuzzy rule can be expressed as (1) : IF 1 is 1 1 and 2 is 1 2 THEN̂is 1 . .…”

“…Fuzzy control method is widely used in control theory and control engineering systems due to its great theoretical value and successful applications in complex practical systems. Adaptive fuzzy control is efficient to control uncertain nonlinear system [1]. Since the adaptive fuzzy approaches can approximate the complex nonlinear functions through fuzzy rules, the application of the fuzzy logic to deal with the chattering problem is proven as an effective way; it has been used in many engineering applications, such as robot systems and active suspension system [2,3].…”