Falsity Membership Research Articles

Applications of intuitionistic fuzzy set aggregation operators in transport multi-factor project evaluation

An intuitionistic fuzzy set (IFS) is a generalisation of a fuzzy set characterised by a truth membership function and a false membership function. The former is a lower bound on the grade of membership of the evidence in favour of a particular element belonging to the set and the latter is a lower bound on the negation of that element belonging to the set derived from evidence against that element belonging to the set. A similar concept is a vague set, though vague sets have been shown to be identical to IFSs. In the context of project evaluation, an IFS may be used to represent the degree to which a project satisfies a criterion and the degree to which it does not. Aggregation of such IFSs has been considered in recent years to identify a best project in terms of several criteria or factors. A particular desirable way to aggregate IFS is in terms of an ordered weighted average (OWA) which can be expressed in different forms such as arithmetic and geometric. In an OWA operator, weights are applied to the position of an element in the aggregation. In addition, hybrid OWA operators may be developed to not only weight the position of elements in the aggregation but the element itself. An example is given relating to the Kuranda Range Road upgrade (Queensland, Australia) which is limited by grade, poor overtaking opportunities, poor horizontal alignment and other constraints and the road is expected to become increasingly congested over the next few years. A more flexible multi-factor decision method is used to identify a ‘best’ project from a set of four alternative projects.

A Vague Decision Method for Analog Circuit Fault Diagnosis Based on Description Sphere

This paper proposes a vague decision method for analog circuit fault diagnosis based on description sphere. Firstly, the proposed method uses the wavelet transform as the preprocessor to extract fault features from the output voltages of the circuit under test (CUT). And then, each class sample is trained to produce a minimum description sphere. Finally, the test samples are detected by a defined vague decision rule, which is based on the vague weight distance between the test data and the center of description sphere. The defined decision rule fuses the truth and false membership degrees of the test sample and the weight of the description sphere, and it can effectively deal with the uncertain information. The reliability of the defined decision rule is proved theoretically. This new diagnostic method is first applied to testing two actual circuits, and then it is compared with other two diagnostic methods. The experimental results show that the proposed technique can achieve good performance and reduce the diagnostic time.

Environmental Project Evaluation Using Intuitionistic Fuzzy Information

An intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set characterized by a truth membership function and a false membership function. The former is a lower bound on the grade of membership of the evidence in favor of a particular element belonging to the set and the latter is a lower bound on the negation of that element belonging to the set, derived from evidence against that element belonging to the set. A similar concept is a vague set, though vague sets have been shown to be identical to IFSs. In the context of project evaluation, an IFS may be used to represent the degree to which a project satisfies a criterion or factor and the degree to which it does not. Aggregation of such IFSs has been considered in recent years to identify a best project in terms of several factors. A particular desirable way to aggregate IFSs is in terms of an ordered weighted average (OWA) which can be expressed in different forms, such as arithmetic and geometric. In an OWA, weights are applied to the position of an element in the aggregation. In addition, hybrid OWA operators may be developed to not only weight the position of elements in the aggregation but the element itself. A simple example based on a hypothetical but realistic example by Horsak and Damico [4] is given which involves the location of a hazardous waste disposal facility (PCB-contaminated transformer fluids) at one of three sites based on 10 factors.

Binary classification using ensemble neural networks and interval neutrosophic sets

This paper presents an ensemble neural network and interval neutrosophic sets approach to the problem of binary classification. A bagging technique is applied to an ensemble of pairs of neural networks created to predict degree of truth membership, indeterminacy membership, and false membership values in the interval neutrosophic sets. In our approach, the error and vagueness are quantified in the classification process as well. A number of aggregation techniques are proposed in this paper. We applied our techniques to the classical benchmark problems including ionosphere, pima-Indians diabetes, and liver-disorders from the UCI machine learning repository. Our approaches improve the classification performance as compared to the existing techniques which applied only to the truth membership values. Furthermore, the proposed ensemble techniques also provide better results than those obtained from only a single pair of neural networks.