Fuzzy Weighted Average: Analytical Solution

An algorithm is presented for the computation of analytical expressions for the extremal values of the α-cuts of the fuzzy weighted average, for triangular or trapeizoidal weights and attributes. Also, an algorithm for the computation of the inverses of these expressions is given, providing exact membership functions of the fuzzy weighted average. Up to now, only algorithms exist for the computation of the extremal values of the α-cuts for a fixed value of α. To illustrate the power of our algorithms, they are applied to several examples from the literature, providing exact membership functions in each case

Fuzzy audit risk modeling algorithm

Fuzzy logic has created suitable mathematics for making decisions in uncertain environments including professional judgments. One of the situations is to assess auditee risks. During recent years, risk based audit (RBA) has been regarded as one of the main tools to fight against fraud. The main issue in RBA is to determine the overall audit risk an auditor accepts, which impact the efficiency of an audit. The primary objective of this research is to redesign the audit risk model (ARM) proposed by auditing standards. The proposed model of this paper uses fuzzy inference systems (FIS) based on the judgments of audit experts. The implementation of proposed fuzzy technique uses triangular fuzzy numbers to express the inputs and Mamdani method along with center of gravity are incorporated for defuzzification. The proposed model uses three FISs for audit, inherent and control risks, and there are five levels of linguistic variables for outputs. FISs include 25, 25 and 81 rules of if-then respectively and officials of Iranian audit experts confirm all the rules

The Development of Audit Detection Risk Assessment System: Using the Fuzzy Theory and Audit Risk Model

The result of audit designation is significantly influenced by the audit evidence collected when planning the audit and the degree of detection risk is further depends on the amount of audit evidence. Therefore, when the assessment factors of detection risk are more objective and correct, audit costs and the risk of audit failure can be reduced. Thus, the aim of this paper is to design an audit detection risk assessment system that could more precisely assess detection risk, comparing with the traditional determination method of detection risk in order to increase the audit quality and reduce the possibility of audit failure. First, the grounded theory is used to reorganize 53 factors affecting detection risk mentioned in literatures and then employed the Delphi method to screen the 43 critical risk factors agreed upon by empirical audit experts. In addition, using the fuzzy theory and audit risk model to calculate the degree of detection risk allow the audit staff to further determine the amount of audit evidence collected and set up initial audit strategies and construct the audit detection risk assessment system. Finally, we considered a case study to evaluate the system in terms of its feasibility and validity

Prioritising Emergency Bridgeworks Assessment under Military Consideration using an Enhanced Fuzzy Weighted Average Approach

Prioritising emergency bridgeworks assessment has been a key to winning battles in combat circumstances because of soldier safety, attack or defence tactics, and logistic supply ability. However, an imprecise or vague satisfaction level of importance of criteria may also affect the prioritising evaluation of bridgeworks under military consideration. In this paper, the fuzzy set theory is employed to treat this aspect. With linguistic variables, fuzzy numbers and an enhanced fuzzy weighted average approach will be used. The proposed approach is used to investigate an example to illustrate its applications in emergency bridgeworks assessment. The approach is shown to be useful and effective. In order to make computing and ranking results easier and to increase recruiting productivity, a computer-based decision support system has been developed, which may help the commander make decisions more efficiently.Defence Science Journal, 2010, 60(4), pp.451-461, DOI:http://dx.doi.org/10.14429/dsj.60.48

Simulation-based evaluation of defuzzification-based approaches to fuzzy multi-attribute decision making

This paper presents a simulation-based study to evaluate the performance of 12 defuzzification-based approaches for solving the general fuzzy multiattribute decision-making (MADM) problem requiring cardinal ranking of decision alternatives. These approaches are generated based on six defuzzification methods in conjunction with the simple additive weighting (SAW) method and the technique for order preference by similarity to the ideal solution method. The consistency and effectiveness of these approaches are examined in terms of four new objective performance measures, which are based on five evaluation indexes. The Simulation result shows that the approaches, which are capable of using all the available information on fuzzy numbers, effectively in the defuzzification process, produce more consistent ranking outcomes. In particular, the SAW method with the degree of dominance defuzzification is proved to be the overall best performed approach, which is, followed by the SAW method with the area center defuzzification. These findings are of practical significance in real-world settings where the selection of the defuzzification-based approaches is required in solving the general fuzzy MADM problems under specific decision contexts

Traitement d'imperfections des indicateurs agri-environnentaux

Les indicateurs développés et utilisés en agronomie sont généralement calculés à partir de données et d'informations entachées d'imperfections. Dans cet article, on présente le calcul d'un indicateur agri-environnemental-fondé sur un système de règles de décision-en utilisant une méthode de fusion de la théorie des possibilités au sein de la notion de sous-ensemble maximaux cohérents et une arithmétique sur des intervalles pour calculer les bornes de l'indicateur. La modélisation de données est réalisée dans le cadre de la théorie des possibilités qui fournit des outils de représentation de l'imperfection. Cet article présente les résultats de l'indicateur obtenues par calcul d'intervalles et nous présentons la note de l'indicateur par une méthode de défuzzyfication

Fuzzy Logic Approach to Represent and Propagate Imprecision in Agri-Environmental Indicator Assessment.

International audienceThe indicator of groundwater contamination developed and used in agriculture is calculated from data available in the field or data estimated by an expert. The modeling of this indicator generally requires a large number of parameters whose measure is imprecise. Several information sources provide information about the same imprecise quantities which have to be combined for defining what is called an "indicator of groundwater contamination " (Igro). This indicator estimates the impact of cultivation practices on the groundwater contamination. In this paper, we explore a possibilistic information fusion method by using the notion of maximal coherent subsets to represent the imprecisions of multisource variables of the indicator. We also calculate the bounds of this indicator, and we propagate imprecision by using an interval analysis. Finally, we present the indicator's results for pesticides applied on different crop