Publications

Expert-Based and Computational Methods for Developing Fuzzy Cognitive Maps

A study on the self-organizing polynomial neural networks

We introduce and investigate a class of neural architectures of polynomial neural networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose topology is developed through learning; it is a self-organizing network. PNN has two kinds of networks, polynomial neuron-based and fuzzy polynomial neuron (FPN)-based networks, according to a polynomial structure. The essence of the design procedure of PN-based self-organizing polynomial neural networks(SOPNN) dwells on the group method of data handling. Each node of the SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN-based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulations involve a series of synthetic as well as experimental data used across various neuro-fuzzy systems. A detailed comparative analysis is also included.

Identifying Fuzzy Rules

On solution of fuzzy functional equations

DECOMPOSITION PROBLEM OF FUZZY RELATIONS

Abstract The paper deals with a problem of decomposition of a binary fuzzy relation defined in the Cartesian product of a finite space. We propose an algorithm which produces the decomposition or indicates that the given relation is non-decomposable, within a finite sequence of steps. INDEX TERMS: Fuzzy relationdecomposition of relationfuzzy relation equation. Additional informationNotes on contributorsANTONIO DI NOLA Under the auspices of C.N.R. (G.N.S.A.G.A.), Italy. SALVATORE SESSA Under the auspices of C.N.R. (G.N.S.A.G.A.), Italy.

A Fuzzy Clustering Validity Index Induced by Triple Center Relation

The existing clustering validity indexes (CVIs) show some difficulties to produce the correct cluster number when some cluster centers are close to each other, and the separation processing mechanism appears simple. The results are imperfect in case of noisy data sets. For this reason, in this study, we come up with a novel CVI for fuzzy clustering, referred to as the triple center relation (TCR) index. The originality of this index is twofold. On the one hand, a new fuzzy cardinality is built on the strength of the maximum membership degree, and a novel compactness formula is constructed by combining it with the within-class weighted squared error sum. On the other hand, starting from the minimum distance between different cluster centers, the mean distance as well as the sample variance of cluster centers in the statistical sense are further integrated. These three factors are combined by means of product to form a triple characterization of the relationship between cluster centers, and hence a 3-D expression pattern of separability is formed. Subsequently, the TCR index is put forward by combining the compactness formula with the separability expression pattern. By virtue of the degenerate structure of hard clustering, we show an important property of the TCR index. Finally, based on the fuzzy C -means (FCMs) clustering algorithm, experimental studies were conducted on 36 data sets (incorporating artificial and UCI data sets, images, the Olivetti face database). For comparative purposes, 10 CVIs were also considered. It has been found that the proposed TCR index performs best in finding the correct cluster number, and has excellent stability.

Intelligent Control of Sintering Process

Rough Sets

FUZZY RELATIONAL EQUATIONS: BRIDGING THEORY, METHODOLOGY AND PRACTICE

This study delivers a general overview of the theory and practice of fuzzy relational equations. We discuss various methods leading to the solutions of these equations starting from analytical approaches, moving through semi-analytic methods and finally elaborating on the neural-like style of finding solutions to relational constructs. The paper addresses important aspects of knowledge representation worked out by these equations and proposes a number of structural enhancements of the existing relational architectures.

Granular Aggregation of Fuzzy Rule-Based Models in Distributed Data Environment

Quite often, complex systems or phenomena are observed from various points of view yielding the particular subsets of data usually being composed of locally available attributes. Such datasets give rise to individual models. As is reflective of the local behavior of the system (global data), each model can produce different, albeit similar results. A critical issue is to aggregate the results coming from the individual models. In virtue of the diversity of the produced results, the aggregation process has to be reflective of this variety. Equally important is a way of quantifying the diversity of the individual results. In this article, we provide an efficient and original way of aggregation of the results by engaging a principle of justifiable granularity and in this manner leading to interval-valued results summarizing the results produced by a collection of models. We develop an overall design process and discuss the associated optimization mechanism leading to a granular fuzzy model of a global nature. The detailed scheme of the principle of justifiable granularity is discussed along with the related performance indexes; in particular, two modes of design of information granules are investigated. The quality of the granular model is quantified with the aid of the criteria of coverage and specificity.

Chi-MFlexDT:Chi-square-based multi flexible fuzzy decision tree for data stream classification

Associations and rules in data mining: a linkage analysis

We discuss a problem of synthesis and analysis of granular rules emerging in data mining. Two descriptors of the rules (that is relevance and consistency) being viewed individually and en block are introduced. The relevance of the rules is quantified in terms of the data being covered by the antecedents and conclusions standing there. While this index describes each rule individually, the consistency of the rule deals with the quality of the rule viewed vis-a-vis other rules. It expresses how much the rule "interacts" with others in the sense that its conclusion is distorted by the conclusion parts coming from other rules. We show how the rules are formed by means of fuzzy clustering and their quality can be evaluated in terms of the above indexes. Global characteristics of a set of rules are also discussed and related to the number of information granules being constructed in the data space.

Prediction model of burn-through point with fuzzy time series for iron ore sintering process

Logic-based neurons: Extensions, uncertainty representation and development of fuzzy controllers

PROCESSING OF FUZZY NUMBERS BY FUZZY RELATION EQUATIONS

In this paper we deal with fuzzy numbers that modelize uncertain quantities present in many fields of applications, such as man‐machine systems. Main attention is paid to inverse operations for fuzzy numbers which allow one to solve equations or systems of equations with fuzzy numbers. The relevance of the method proposed for the determination of parameters of fuzzy models is also stressed.

An analysis of potentially imprecise class labels using a fuzzy similarity measure

Accurate classification of biomedical data is often confounded by potentially imprecise class labels assigned by an external reference test. We present a gradation method using fuzzy set theory and a dispersion-adjusted similarity measure to assign, for each pattern in a design set, a degree of belongingness to each class. After training a classifier using this adjusted design set, its performance is measured using a validation set of patterns with their original class labels. We empirically demonstrate the effectiveness of this method using three publicly available biomedical datasets. Using the same classifier, we benchmark the results against the original datasets without gradation.

Analysis of Ranking Consistency in Linguistic Multiple Attribute Decision Making: The Roles of Granularity and Decision Rules

Linguistic multiple attribute decision making (LMADM) has been widely used in different decision contexts to achieve a final solution, e.g., obtaining the ranking of alternatives. Evaluation information using linguistic scales in LMADM is usually expressed in simple discrete linguistic terms. In this article, we consider that each simple linguistic term in LMADM actually has a continuous representation (denoted as a linguistic two tuples) whose rounding operation matches the linguistic term. Under such conditions, the ranking of alternatives based on the simple linguistic terms may not be consistent with that based on the linguistic two tuples. Thus, this article studies the linguistic scale ranking consistency issue in LMADM under seven classical and commonly used decision rules: weighted averaging, ordered weighted averaging, weighted geometric averaging, ordered weighted geometric averaging, preference ranking organization method for enrichment evaluation, technique for order preference by similarity to an ideal solution, and elimination et choice translating reality. We first define the concept of the linguistic scale ranking consistency in LMADM. Afterward, several consistency conditions are presented analytically for the selected decision rules to guarantee the linguistic scale ranking consistency. Finally, we present the detailed theoretical and simulation-based comparisons. The theoretical comparisons show the roles of decision rules and granularity in the consistency conditions, and the simulation-based comparisons demonstrate the performance of the selected decision rules in defending against the ranking inconsistency in LMADM.

Oracle Based Privacy-Preserving Cross-Domain Authentication Scheme

The Public Key Infrastructure (PKI) system is the cornerstone of today's security communications. All users in the service domain covered by the same PKI system are able to authenticate each other before exchanging messages. However, there is identity isolation in different domains, making the identity of users in different domains cannot be recognized by PKI systems in other domains. To achieve cross-domain authentication, the consortium blockchain system is leveraged in the existing schemes. Unfortunately, the consortium blockchain-based authentication schemes have the following challenges: high cost, privacy concerns, scalability and economic unsustainability. To solve these challenges, we propose a scalable and privacy-preserving cross-domain authentication scheme called Bifrost-Auth. Firstly, Bifrost-Auth is designed to use a decentralized oracle to directly interact with blockchains in different domains instead of maintaining a consortium blockchain and enables mutual authentication for users lying in different domains. Secondly, users can succinctly authenticate their membership of the domain by the accumulator technique, where the membership proof is turned into zero knowledge to protect users' privacy. Finally, Bifrost-Auth is proven to be secure against various attacks, and thorough experiments are carried out and demonstrate the security and efficiency of Bifrost-Auth.