A similarity-based inference engine for non-singleton fuzzy logic systems

In non-singleton fuzzy logic systems (NSFLSs) input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty such as sensor noise. The performance of NSFLSs in handling such uncertainties depends both on the actual input fuzzy sets (and their inherent model of uncertainty) and on the way that they affect the inference process. This paper proposes a novel type of NSFLS by replacing the composition-based inference method of type-1 fuzzy relations with a similarity-based inference method that makes NSFLSs more sensitive to changes in the input's uncertainty characteristics. The proposed approach is based on using the Jaccard ratio to measure the similarity between input and antecedent fuzzy sets, then using the measured similarity to determine the firing strength of each individual fuzzy rule. The standard and novel approaches to NSFLSs are experimentally compared for the well-known problem of Mackey-Glass time series predictions, where the NSFLS's inputs have been perturbed with different levels of Gaussian noise. The experiments are repeated for system training under both noisy and noise-free conditions. Analyses of the results show that the new method outperforms the standard approach by substantially reducing the prediction errors

A similarity-based inference engine for non-singleton fuzzy logic systems

In non-singleton fuzzy logic systems (NSFLSs) input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty such as sensor noise. The performance of NSFLSs in handling such uncertainties depends both on the actual input fuzzy sets (and their inherent model of uncertainty) and on the way that they affect the inference process. This paper proposes a novel type of NSFLS by replacing the composition-based inference method of type-1 fuzzy relations with a similarity-based inference method that makes NSFLSs more sensitive to changes in the input's uncertainty characteristics. The proposed approach is based on using the Jaccard ratio to measure the similarity between input and antecedent fuzzy sets, then using the measured similarity to determine the firing strength of each individual fuzzy rule. The standard and novel approaches to NSFLSs are experimentally compared for the well-known problem of Mackey-Glass time series predictions, where the NSFLS's inputs have been perturbed with different levels of Gaussian noise. The experiments are repeated for system training under both noisy and noise-free conditions. Analyses of the results show that the new method outperforms the standard approach by substantially reducing the prediction errors

Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets

AbstractWe begin the paper studying the axioms that the indicators of the grade of inclusion of a fuzzy set in another fuzzy set must satisfy. Next, we present an expression of such indicator, first for fuzzy sets and then for interval-valued fuzzy sets, analyzing in both cases their main properties. Then, we suggest an expression for the similarity measure between interval-valued fuzzy sets. Besides, we study two methods for inference in approximate reasoning based on interval-valued fuzzy sets, the inclusion grade indicator and the similarity measure. Afterwards, we expose some of the most important properties of the methods of inference presented and we compare these methods to Gorzalczany's. Lastly, we use the indicator of the grade of inclusion for interval-valued fuzzy sets as an element that selects from the different methods of inference studied, the one that will be executed in each case

Determining firing strengths through a novel similarity measure to enhance uncertainty handling in non-singleton fuzzy logic systems

Non-Singleton Fuzzy Logic Systems (NSFLSs) have the potential to tackle uncertainty within the design of fuzzy systems. The inference process has a major role in determining results, being partly based on the interaction of input and antecedent fuzzy sets (in generating firing levels). Recent studies have shown that the standard technique for determining firing strengths risks substantial information loss in terms of the interaction of the input and antecedents. To address this issue, alternative approaches, which employ the centroid of intersections (cen-NS) and similarity measures (sim-NS), have been developed. More recently, a novel similarity measure for fuzzy sets has been introduced, but as yet this has not been used for NSFLSs. This paper focuses on exploring the potential of this new similarity measure in combination with the sim-NS approach to generate a more suitable firing level for non-singleton input. Experiments are presented for fuzzy systems trained using both noisy and noise-free time series. The prediction results of NSFLSs for the novel similarity measure and the current approaches are compared. Analysis of the results shows that the novel similarity measure, used within the sim-NS approach, can be a more stable and suitable method suitable to be used in real world applications

Fault Detection in Systems-A Fuzzy Approach

The task of fault detection is important when dealing with failures of crucial nature. After detection of faults in a system, it is advisable to suggest maintenance action before occurrenceof a failure. Fault detection may be done by observing various symptoms of the system during its operational stage. Sometimes, symptoms cannot be quantified easily but can be expressedin linguistic terms. Since linguistic terms are fuzzy quantifiers, these can be represented by fuzzy numbers. In this paper, two cases have been discussed, where a fault likely to affect a particular systemlsystems, is detected. In the first case, this is done by means of a compositional rule of inference. The second case is based on modified similarity measure. For both these  cases, linguistic terms have been expressed as trapezoidal fuzzy number

On the semantics of fuzzy logic

AbstractThis paper presents a formal characterization of the major concepts and constructs of fuzzy logic in terms of notions of distance, closeness, and similarity between pairs of possible worlds. The formalism is a direct extension (by recognition of multiple degrees of accessibility, conceivability, or reachability) of the najor modal logic concepts of possible and necessary truth.Given a function that maps pairs of possible worlds into a number between 0 and 1, generalizing the conventional concept of an equivalence relation, the major constructs of fuzzy logic (conditional and unconditioned possibility distributions) are defined in terms of this similarity relation using familiar concepts from the mathematical theory of metric spaces. This interpretation is different in nature and character from the typical, chance-oriented, meanings associated with probabilistic concepts, which are grounded on the mathematical notion of set measure. The similarity structure defines a topological notion of continuity in the space of possible worlds (and in that of its subsets, i.e., propositions) that allows a form of logical “extrapolation” between possible worlds.This logical extrapolation operation corresponds to the major deductive rule of fuzzy logic — the compositional rule of inference or generalized modus ponens of Zadeh — an inferential operation that generalizes its classical counterpart by virtue of its ability to be utilized when propositions representing available evidence match only approximately the antecedents of conditional propositions. The relations between the similarity-based interpretation of the role of conditional possibility distributions and the approximate inferential procedures of Baldwin are also discussed.A straightforward extension of the theory to the case where the similarity scale is symbolic rather than numeric is described. The problem of generating similarity functions from a given set of possibility distributions, with the latter interpreted as defining a number of (graded) discernibility relations and the former as the result of combining them into a joint measure of distinguishability between possible worlds, is briefly discussed

Information Technology Project Benefit Realization in Military Enterprises of Sri Lanka Using Integrated Fuzzy Dempster - Shafer Algorithm

There are Information Technology (IT) projects in military organizations of Sri Lanka. However, these projects lack a scientific mechanism to measure and realize project benefits while quantifying qualitative project outcomes. This paper outlines a Fuzzy Inference System (FIS) for measuring the extent to which benefits could be realized. The objectives of the study are firstly, to formulate a fuzzy logic to measure the extent to which the project benefits are realized and secondly, to analyze its impact on benefit policy. The study mainly utilized the quantitative methodology of Dempster-Shafer algorithm to aggregate the selected experts’ opinions by filtering similarity of experts. Ninety-five IT project managers representing the Army, Navy and Air Force were selected based on their expertise. The study employed field-based tacit experts to find inputs for each level namely, project, program, portfolio, enterprise and hybrid. The findings of the study posited nine fuzzy rules and five benefit realization levels for organizational projects. Also, the approach pronounced an organizational project policy. The study recommended a strategic benefit approach with policy implications that can be used by managers to monitor the expected project outcomes both on short term and futuristically. The application of the study cannot  be generalized to all projects of the technology-domains thereby posing a limitation. Also the study is curtailed in its application to non-IT projects which singularly yield financial benefits. The study can be employed by policy makers to streamline benefit process emphasizing government IT infrastructure projects and private sector IT projects with a futuristic value. Keywords: Benefit Realization, Benefit Measurement, Fuzzy Inference Systems, Dempster-Shafer Algorithm, Benefit Polic