A Novel Fault Detection Model Based on Atanassov’s Interval-Valued Intuitionistic Fuzzy Sets, Belief Rule Base and Evidential Reasoning

Abstract

In engineering practice, fault detection, with the fundamental characteristics of randomness, uncertainty, and great damage, has attracted much attention from academia. The chief aim of this paper is to research the problem of flush air data sensing (FADS) system, an advances airborne sensor, with Atanassov's interval-valued intuitionistic fuzzy sets (AIVIFSs), belief rule base (BRB) and evidential reasoning (ER). First of all, this paper proposes some relevant concepts and similarity calculation operators between AIVIFSs, meanwhile, extracts a new similarity calculation approach based on previous researches. Then, a new score function that is applied to quantify the information contained in AIVIFSs is presented with the idea of p-norm, which is defined on the basis of the information measure from the reference level, regarding the positive and negative information depicted in terms of the AIVIFSs. Next, AIVIFSs and BRB that are characteristic of describing the randomness and uncertainty are combined to set up the fault detection model with ER. Finally, the algorithm process is presented and the proposed model is applied to the fault detection of FADS for the first time to confirm the validity and feasibility. INDEX TERMS Fault detection, flush air data sensing (FADS), Atanassov's interval-valued intuitionistic fuzzy sets (AIVIFSs), belief rule base (BRB), evidential reasoning (ER).

A Comparative Analysis of the Ranking Functions for the IVIFVs and A New Score Function

“…While the value range of the score function and accuracy function developed by Xu is [-1,1] and [0.1], respectively, it is observed that the value ranges of the score functions and accuracy functions developed later differed. While the maximum values obtained by accuracy ranking functions in [17,24] and score function [19] are smaller than 1, the maximum value obtained by score function [13] is bigger than 1. Besides, minimum and maximum values calculated by accuracy functions in [12,15,17,18] are equal, and this equality is unacceptable.…”

“…Jia et al [19] introduced a score function (. ) J in Equation ( 24) utilized to quantify the information included in IVIFV with the idea of p-norm.…”

“…Theorem 3. The score functions in [12,15,19] and accuracy function in [24] give ranking value 0 when the midpoints of the membership and the non-membership coincide, namely LL…”

“…The decision matrix 45 X R (Table 5) includes information related to the evaluation of alternatives on criteria. Lee [13] Tu and Chen,1 [6] Tu and Chen,2 [6] Bai [14] Wang and Niu [15] Garg [9] Nayagam et al [10] Wang and Chen [16] Wang and Chen [17] Gong and Ma [18] Jia et al [19] This Nayagam et al [20] Wang and Niu [15] Kang et al [22] Joshi and Kharayat [7] Şahin [23] Zhang and Xu [24] Joshi and Kumar [25] Wang and Chen [17] Gong and Ma [ (Table 6) includes information related to the evaluation of teachers on criteria.  =[0.11,0.37], [0.17, 0.32].…”

“…Several approaches have been developed for ranking IVIFVs. Among these, score functions [6,9,10,[12][13][14][15][16][17][18][19] and accuracy functions [5,7,12,15,17,18,[20][21][22][23][24][25] are frequently preferred approaches. However, in some cases, the existing score or accuracy functions for ranking IVIFVs do not yield sufficient performance and they cannot distinguish comparable IVIFVs.…”