A fuzzy neural relational model of software quality derived from the McCall hierarchical software quality measurement framework (HSQF), is introduced. The HSQF has three fundamental levels (factors/spl rarr/criteria/spl rarr/metrics) which has a rather natural generalization in the context of fuzzy sets. Vectors of factors, criteria, and metrics are treated as fuzzy sets. On each level, fuzzy objects (fuzzy set and fuzzy relation) are introduced. A learning algorithm is proposed to calibrate the relations at the topmost levels of the software quality model. A learning scenario and detailed learning formulas are given. A brief illustration of the model is also given.
Feature selection plays an important role in pattern recognition and machine learning. Feature evaluation and classification complexity estimation arise as key issues in the construction of selection algorithms. To estimate classification complexity in different feature subspaces, a novel feature evaluation measure, called the neighborhood decision error rate (NDER), is proposed, which is applicable to both categorical and numerical features. We first introduce a neighborhood rough-set model to divide the sample set into decision positive regions and decision boundary regions. Then, the samples that fall within decision boundary regions are further grouped into recognizable and misclassified subsets based on class probabilities that occur in neighborhoods. The percentage of misclassified samples is viewed as the estimate of classification complexity of the corresponding feature subspaces. We present a forward greedy strategy for searching the feature subset, which minimizes the NDER and, correspondingly, minimizes the classification complexity of the selected feature subset. Both theoretical and experimental comparison with other feature selection algorithms shows that the proposed algorithm is effective for discrete and continuous features, as well as their mixture.
Fuzzy inference is a method to describe nonlinear input-output relationships using fuzzy if-then rules. Continuous values of the inputs and outputs are converted into granules by fuzzy sets, and each granule is labeled with a symbol. Fuzzy inference has a multigranular architecture consisting of continuous values and symbols, and this architecture has worked well to incorporate experts' know-how into fuzzy controls. One of the important problems of fuzzy control is to guarantee stability of the fuzzy control system. The authors have applied Petri nets to the stability analysis of the fuzzy control system. A theory of asymptotic stability has been derived for the symbolic representation of the control system. The paper presents a new method to bridge between the stability analysis on the symbolic level and the actual behavior of the control system on the numerical level. The new method uses a generalized fuzzy Petri net model and its neural network representation. The paper introduces a guideline for designing a fuzzy control system which guarantees the validity of the stability analysis on the symbolic representation of the control system.
In this paper we will study fuzzy systems, analyzing their origin, various ways of their characterization and fundamental problems associated with them. A thorough discussion is centered around types of fuzzy systems, their relevancy and its influence on the formulation of so-called direct and inverse tasks. Moreover, a theory of relational equations as applied to system analysis is investigated. Special attention is focussed on links between the theory of fuzzy systems viewed from a standpoint of general system theory and a variety of applications (e.g., control, knowledge-based system, pattern recognition etc.). Then, specific interpretations to direct and inverse problems are given, bearing in mind the selected area of application.
The paper aims to define a new kind of logic, referred to as Archimedean-Compensatory Logic, which is constructed from the unification of two different fuzzy logic systems, namely a continuous Archimedean fuzzy logic and a compensatory fuzzy logic. The paper introduces basic definitions and properties of this new theory. Continuous Archimedean logic is a t-norm and t-conorm logic system and Compensatory Fuzzy Logic can be obtained from quasi-arithmetic mean operators. We will prove the property that the preference over a pair of truth-value vectors is the same for certain predicates in the Compensatory Fuzzy Logic and the Continuous Archimedean Logic.
In large-scale group decision making (LSGDM), the consensus result is expected to be realized explicitly through reconciling various preferences provided by decision makers based on their personalized viewpoints. A information granule consensus-based decision brings about high flexibility and promising aspects in group decision making. The consensus reaching proposals reported so far paid little attention to the merits of Granular Computing for managing LSGDM problems. This paper concerns an extension of the well-known analytic hierarchy process to the LSGDM scenario using the optimizing information granule-based consensus reaching method. The consensus measurement is first quantified using coverage and specificity to derive the optimal cluster using the Fuzzy C-Means algorithm. Then, based on the optimization model of an information granule leading from numerical to interval representation, a novel construction model of information granule from interval representations to type-2 interval representation is developed, which yields the consistency of the obtained result instead of proceeding with an extra revision. To achieve the desired consensus, a preference modification algorithm is designed to detect the adjusted decision maker and further provide adjustment suggestions following the reference decision maker. Finally, a numeric study illustrates the effectiveness and flexibility of the proposed method.
