-This paper presents some important properties o f the Fuzzy ART neural network algorithm introduced by Carpenter, Grossberg, and Rosen. The properties described in the paper are distinguished into a number o f categories. These include template, access, and reset properties, as well as properties related to the number of list presentations needed for weight stabilization. These properties prov...

A. George and P. Veeramani, 1994. On some results in fuzzy metric space, Fuzzy Sets and Systems, vol. 64, 395-399. B. Schweizer, H. Sherwood, and R. M. Tardi®,1988. Contractions on PMspace examples and counter examples, Stochastica vol. 1, 5–17. D. Mihet, 2004. A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, vol. 144, 431–439. D. Mihet, 2008. Fuzzy -contractive mapp...

An n× n fuzzy matrix A is called regular if there is an n× n fuzzy matrix G such that AGA = A. We study the problem of characterizing those linear operators T on the fuzzy matrices such that T (X) is regular if and only if X is. Consequently, we obtain that T strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices P and Q such that it has the form T (X) = P...

This paper is a contribution to the discussion about the problem, whether is there a fuzzy logic that can be considered as “The” fuzzy logic, i.e. only one formal system of fuzzy logic that would fit all our requirements and could serve as a general formal frame for the development of fuzzy set theory and all its applications. The reason is that after a monograph of P. Hajek was published, a pl...

K e y w o r d s T o p o l o g y , C-scattered and scattered topological spaces. ('ompactness, Fuzzy perfect maps, S-paracompactness, S*-paracompactness. Fuzzy paracompactness. *-Fuzzy paracompactness. 1. I N T R O D U C T I O N The concept of C-sca t te red topological space has been defined by Telg{,rsky [1]. A space X is said to be C-sca t te red if each of its nonempty closed subspaces conta...

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. A multivalent fuzzy measure with infinitely many solutions based on Pmeasure was proposed by our previous work, called completed L-measure. In this paper, a further improved fuzzy measure, called extensional completed L-measure, is proposed. This new fuzzy measure is proved that it is not only an extension...

Since fuzzy quality data are ubiquitous in the real world, under this fuzzy environment, the supplier selection and evaluation on the basis of the quality criterion is proposed in this paper. The Cpk index has been the most popular one used to evaluate the quality of supplier’s products. Using fuzzy data collected from q P 2 possible suppliers’ products, fuzzy estimates of q suppliers’ capabili...

Combustion control of an industrial stoker-"red boiler is to provide a continuous supply of steam at the desired condition of pressure. Because no e$cient mathematical model of the stoker-"red boiler is available, it would be very hard to design its controller by using any traditional model-based method. Therefore, the most widely used controller for the boiler system is a conventional PID-type...

1. I n t r o d u c t i o n ~ ]e concep t o f fuzzy s e t s d e f i n e d by Zadeh 1 ) g i v e s an i m p o r t a n t m a t h e m a t i c a l c l u e f o r an approach to s t u d i e s o f sys tems w i th no sha rp b o u n d a r i e s . L a t e l y , t h e fuzzy i n t e g r a l 2 ) b a s e d on t h e fuzzy s e t t h e o r y has been proposed and a p p l i e d t o t he measurement o f fuzzy o b j...

most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. for making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. in line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...