Evaluation of fuzzy inference systems using fuzzy least squares

Efforts to develop evaluation methods for fuzzy inference systems which are not based on crisp, quantitative data or processes (i.e., where the phenomenon the system is built to describe or control is inherently fuzzy) are just beginning. This paper suggests that the method of fuzzy least squares can be used to perform such evaluations. Regressing the desired outputs onto the inferred outputs can provide both global and local measures of success. The global measures have some value in an absolute sense, but they are particularly useful when competing solutions (e.g., different numbers of rules, different fuzzy input partitions) are being compared. The local measure described here can be used to identify specific areas of poor fit where special measures (e.g., the use of emphatic or suppressive rules) can be applied. Several examples are discussed which illustrate the applicability of the method as an evaluation tool

Integration of Expert Judgment into Remaining Useful Lifetime Prediction of Components

AbstractAccurate estimates of renewal instances are necessary to avoid both machine breakdowns as well as unnecessary replacements. These instances are based upon a prognosis of the remaining useful lifetime of the components investigated but their usability is limited because of insufficient failure time data. Therefore the paper at hand deals with the integration of expert knowledge into lifetime estimation methods to enhance the prediction result. A model has been developed and simulated. Furthermore a parameter study analyzes the model's effectiveness, which produces promising results

Transitivity of implicative aBE algebras

We prove that every implicative aBE algebra satisfies the transitivity property. This means that every implicative aBE algebra is a Tarski algebra, and thus is also a commutative BCK algebra

Retraction and Generalized Extension of Computing with Words

Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.Comment: 13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy System

Similarity-based non-singleton fuzzy logic control for improved performance in UAVs

As non-singleton fuzzy logic controllers (NSFLCs) are capable of capturing input uncertainties, they have been effectively used to control and navigate unmanned aerial vehicles (UAVs) recently. To further enhance the capability to handle the input uncertainty for the UAV applications, a novel NSFLC with the recently introduced similarity-based inference engine, i.e., Sim-NSFLC, is developed. In this paper, a comparative study in a 3D trajectory tracking application has been carried out using the aforementioned Sim-NSFLC and the NSFLCs with the standard as well as centroid composition-based inference engines, i.e., Sta-NSFLC and Cen-NSFLC. All the NSFLCs are developed within the robot operating system (ROS) using the C++ programming language. Extensive ROS Gazebo simulation-based experiments show that the Sim-NSFLCs can achieve better control performance for the UAVs in comparison with the Sta-NSFLCs and Cen-NSFLCs under different input noise levels

Fuzzy Inference System (FIS) model for the seismic parameters of code-based earthquake response spectra

The response spectra defined in seismic design codes include crisp classifications of seismic parameters, which directly affect the spectra’s shape and greatly alter seismic design loads. The optimum design phase seismic forces have an important role in the efficiency of the construction costs and structural safety. Various parameters are used to calculate the seismic design forces, especially presented in the codes with earthquake design spectra. This study presents a rule-based fuzzy inference model with fuzzy sets to determine these parameters using fuzzy inference system (FIS) modelling, which is the most appropriate approach among the different alternatives because both the input and output variables have numerical and linguistic uncertainties in the earthquake problem. Using the seismic zone factor of the region and shear wave velocity of the soil profile as inputs, the model generates the seismic coefficients and peak ground acceleration values of the response spectra specified in the Uniform Building Code (UBC, 1997). The response spectra in this code can be easily generated with these seismic coefficients after their fuzzification. Response spectra of twenty-five different sample cases with and without the FIS model are generated, which provide comparisons for the model superiority assessment. Significant differences are observed between the crisp logic and the FIS model-generated spectra. It is suggested that the FIS model can be modified and applied to various parameters to generate response spectra in different seismic design codes.Istanbul Medipol Universit

Real-world utility of non-singleton fuzzy logic systems: a case of environmental management

The potentials of non-singleton fuzzy logic systems (NSFLSs) in dealing with uncertainties are widely known. However, their utilities and possible challenges in real-world applications, particularly beyond fuzzy controls, are still not widely examined. This paper presents some user-centric design approaches in making NSFLSs usable in a real-world problem of environmental management. In previous work, a singleton FLS was developed based on an established environmental management framework. After further investigation of the users’ requirements, it was realized that the effective capture, representation and visualization of the system’s inputs and outputs are critical, particularly when there are uncertainties involved in data collection and decision-making processes. For addressing the new requirements, the system has been extended to a NSFLS, so it can make use of non-singleton fuzzification in handling uncertain (e.g., noisy) environmental data. Inspired by the user-centric design of this particular system extension, the contribution of this paper is the development of some practical methods to capture/represent input/output uncertainties in NSFLSs. Subject to further users evaluation, the explained methods have potential to be employed in many similar real-world applications, thus extending the NSFLSs applicability to a wider context than the present

Imprecise measurements in quantum mechanics

In this thesis the structure and properties of imprecise quantum measurements are investigated. The starting point for this investigation is the representation of a quantum observable as a normalized positive operator measure. A general framework to describe measurement inaccuracy is presented. Requirements for accurate measurements are discussed, and the relation of inaccuracy to some optimality criteria is studied. A characterization of covariant observables is given in the case when they are imprecise versions of a sharp observable. Also the properties of such observables are studied. The case of position and momentum observables is studied. All position and momentum observables are characterized, and the joint positionmomentum measurements are discussed.Siirretty Doriast

On Fuzzy Matroids

The aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy C- flats, fuzzy alternative-sets and fuzzy i-flats. Moreover, we characterize some peculiar fuzzy matroids via these notions. Finally, we provide a decomposition of fuzzy strong maps