Publications

Fuzzy models offer a convenient way to describe complex and nonlinear systems. Fuzzy relational equations, viewed as a certain class of fuzzy models, play a pivotal role in fuzzy modeling. Their theory supports ways in which these equations could be solved and offers a characterization of the resulting families of solutions. Assuming that the corresponding relational equation or a system of relational equations is solvable, the theory provides a suite of analytical results. If this essential solvability assumption is not satisfied, we have to resort to approximate solutions and optimization techniques. In this study, we review several approaches to construct fuzzy relational models. Those methods include analytical methods, gradient-based (GB) methods, particle swarm optimization (PSO), and differential evolution (DE). We compare these methods with a hybridization of the different techniques, namely PSO-GB and DE-GB. The optimization techniques are used to design a fuzzy logic processor (FLP), which employs fuzzy logic operations in the realization of this network. Fuzzy C-Means (FCM) transforms real-world numeric data into fuzzy sets, which are used to design the fuzzy model.

The existing methods of determining an α-cut of a fuzzy set to construct its underlying shadowed set do not fully comply with the concept of shadowed sets, namely, a retention of the total amount of fuzziness and its localized redistribution throughout a universe of discourse. Moreover, no closed formula to calculate the corresponding α-cut is available. This paper proposes analytical formulas to calculate threshold values required in the construction of shadowed sets. We introduce a new algorithm to design a shadowed set from a given fuzzy set. The proposed algorithm, which adheres to the main premise of shadowed sets of capturing the essence of fuzzy sets, helps localize fuzziness present in a given fuzzy set. We represent the fuzziness of a fuzzy set as a gradual number. Through defuzzification of the gradual number of fuzziness, we determine the required threshold (i.e., some α-cut) used in the formation of the shadowed set. We show that the shadowed set obtained in this way comes with a measure of fuzziness that is equal to the one characterizing the original fuzzy set.

In computing with words, it has been stressed that words mean different things for different people, which entails that decision makers (DMs) have personalized individual semantics (PISs) attached to linguistic expressions in linguistic group decision making (GDM). In particular, the PISs of DMs are not fixed, and they will be changing during the consensus building process, which indicates the necessary of continual PIS learning. Therefore, in this article, we propose a continual PIS-learning-based consensus approach in linguistic GDM. Specifically, a continual PIS learning model with the consistency-driven methodology is proposed to update the PISs taking into account all the linguistic preference data given by DMs during the consensus process. Then, the consensus measurement and feedback recommendation based on PIS are developed to detect the consensus process. Finally, numerical examples and simulation analysis are presented to illustrate and justify the use of the continual PIS-learning-based consensus approach.

This paper is concerned with the organization and retrieval of reusable software components with the aid of unsupervised learning. The methods considered of unsupervised learning include FUZZY ISODATA and Kohonen self-organizing maps. The key issues addressed in the study include information retrieval in the presence of incomplete information, and domain specific enhancements of unsupervised learning, including those of partial supervision. The primary intention is to reveal how the learning mechanism can accommodate individual preferences (profile) of the users viewed as a significant component of organization and retrieval algorithms. Numerical examples use a set of MS-DOS system commands and a collection of reusable C++ classes. © 1997 by John Wiley & Sons, Ltd.