Evidential reasoning using extended fuzzy Dempster-Shafer theory for handling various facets of information deficiency

Abstract

2École supérieure d'aménagement du territoire et de développement régional, Université Laval, Quebec City, QC G1V 0A6, CanadaThis work investigates the problem of combining deficient evidence for the purpose of quality assessment. The main focus of the work is modeling vagueness, ambiguity, and local nonspecificity in information within a unified approach. We introduce an extended fuzzy Dempster-Shafer scheme based on the simultaneous use of fuzzy interval-grade and interval-valued belief degree (IGIB). The latter facilitates modeling of uncertainties in terms of local ignorance associated with expert knowledge, whereas the former allows for handling the lack of information on belief degree assignments. Also, generalized fuzzy sets can be readily transformed into the proposed fuzzy IGIB structure. The reasoning for quality assessment is performed by solving nonlinear optimization problems on fuzzy Dempster-Shafer paradigm for the fuzzy IGIB structure. The application of the proposed inference method is investigated by designing a reasoning scheme for water quality monitoring and validated through the experimental data available for different sampling points in a water distribution network. C 2011 Wiley Periodicals, Inc.

Multi-level information fusion for spatiotemporal monitoring in water distribution networks

“…Online measurements of common WQPs including residual Chlorine (Cl f ) concentration and turbidity (Tur) are available. Information fusion in one sampling location of the Quebec City's main WDN using fuzzy evidential reasoning and fuzzy rule-based systems has been previously addressed (Aghaarabi et al, 2014;Aminravan et al, 2011). To formulate the monitoring problem in the distributed setting for the Quebec City's main WDN, a spanning tree G = (V, E) as presented in Fig.…”

“…The extended FDST (Aminravan et al, 2011) was proposed to model vagueness in the focal elements and interval uncertainty including interval-valued belief degree and global ignorance in the BBA. In this model, an extended list of fuzzy subsets of the frame of discernment as…”

“…Extended FDST (Aminravan et al, 2013) is a generalization of FDST (Yen, 1990(Yen, , 1992 to aggregate the belief structures that represent additional interval uncertainty patterns including interval-valued BBA and local ignorance. The belief structure that can represent these patterns of interval uncertainty in addition to ambiguity and vagueness in the grades is called interval grade and interval-valued belief (IGIB) structure (Aminravan et al, 2011). In the extended FDST for combining IGIB structures, the minimum and maximum values of pignistic probability of a continuous fuzzy hypothesisH as ðH; ½BetP À ðHÞ; BetP þ ðHÞÞ are found by solving the optimization problem…”

“…A well-known BRB system called ''rule base inference methodology using evidential reasoning (RIMER)'' has been employed in various applications that involve uncertainty and incompleteness (Wang, Yang, Xu, & Chin, 2006;Xu et al, 2007;Yang & Xu, 2002a, 2002b. BRB systems were successfully employed for improved water quality assessment in one sampling location (Aghaarabi Aminravan et al, 2011;Aminravan, Sadiq, Hoorfar, Rodriguez, & Najjaran, 2012). However, BRB systems have never been adopted for spatiotemporal monitoring in the WDN.…”

Application of neuro-fuzzy based expert system in water quality assessment

“…WQPs are classified in two groups including microbial and physicochemical. In order to assign quality grades for each group, two different FRBSs are developed for assessing physicochemical and microbial states of water quality levels (Aghaarabi et al 2014;Aminravan et al 2011).…”