Theory of fuzzy integrals and its applications

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm---Volterra integrodifferential equations. The solution meth...

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

R. Babuska, Fuzzy Modeling for Control, Kluwer Academic Publ., Dordrecht, 1998, 288 p. B. Bouchon-Meunier, L. Foulloy, M. Ramdani, Logique Floue Exercices Corriges et Exemples d' Applications, Cepadues Editions. Toulouse, 199B, 200 p. G.Q. Chen, Fuzzy Logic in Data Modeling Semantics, Constraints and Database Design, Kluwer Academic Publ., Boston. 1998, 240 p. K.J. Cios. W. Pedrycz, R.S. Swiniarski. Data Mining Methods for Knowledge Discovery, Kluwer Academic Publ., Dordrecht. 199B. J. Godjevac, Idees Nettes sur la Logique Floue, Presses Polytechniques et Universitaires Romandes. Lausanne, 1997,200 p. E. Hisdal, Logical structures for representation of knowledge and uncertainty, Physica-Verlag, Heidelberg, Germany, 199B. M. Jamshidi, A. Titli, L.A. Zadeh, S. Boverie, Applications of Fuzzy LogiC Towards High Machine Intelligence Quotient Systems, Prentice-Hall, Englewood Cliffs, NJ, 1997,423 p. F. Lootsma, Fuzzy Logic for Planning and Decision Making Applied Optimization 8. Kluwer Academic Publ., Dordrecht, 1998. W. Mielczarski, Fuzzy Logic Techniques in Power Systems, Physica-Verlag, Berlin, 1998, 456 p. J.N. Mordeson, P.S. Nair, Fuzzy Mathematics An Introduction for Engineers and Scientists. Physica-Verlag, Berlin, 1998,270 p. W. Pedrycz, Computational Intelligence An Introduction, CRC Press, Boca Raton, FL, 1997,304 p. M. Reghis, E. Roventa, Classical and Fuzzy Concepts in Mathematical Logic and Applications, CRC Press, Boca Raton, FL, 1998. L. Reznik, Fuzzy Controllers, Newness Press, UK, 1997. Schindler, Fuzzy-Datenanalyse durch kontextbasierte Datenbankanfragen, Deutscher Universitiits Verlag, Leverkusen, Germany, 1998. O. Wolkenhauer, Possibility Theory with Applications to Data Analysis. Research Studies Press, Hertfordshire, UK, 1998, 290 p. Edited volumes

With the growth in computing technologies, cloud computing has added a new paradigm to user services that allows accessing Information Technology services on the basis of pay-per-use at any time and any location. Owing to flexibility in cloud services, numerous organizations are shifting their business to the cloud and service providers are establishing more data centers to provide services to users. However, it is essential to provide cost-effective execution of tasks and proper utilization of resources. Several techniques have been reported in the literature to improve performance and resource use based on load balancing, task scheduling, resource management, quality of service, and workload management. Load balancing in the cloud allows data centers to avoid overloading/underloading in virtual machines, which itself is a challenge in the field of cloud computing. Therefore, it becomes a necessity for developers and researchers to design and implement a suitable load balancer for parallel and distributed cloud environments. This survey presents a state-of-the-art review of issues and challenges associated with existing load-balancing techniques for researchers to develop more effective algorithms.

Issues and Challenges of Load Balancing Techniques in Cloud Computing: A Survey

Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mareš equivalence relation

Fixed point theorems in fuzzy metric spaces

On fuzzy differential equations in the quotient space of fuzzy numbers

On computing generalized Hukuhara differences of Z-numbers

To obtain the group properties of fuzzy quantities, Mares introduced an equivalence relation between fuzzy quantities. However, the Mares's method used to prove his main theorems demands to limit the investigation to fuzzy quantities with finite support. In this paper, we discuss the properties of symmetric fuzzy numbers, show an equivalent characterization of convex fuzzy sets, and present a way to construct a symmetric convex fuzzy set with a convex fuzzy set. Based on these results, we restrict ourselves to fuzzy numbers and prove Mares's results without the limitation to fuzzy numbers with finite support using the refined equivalence relation due to Hong and Do. Our results prove one of Mares's open questions in the literature.

Dong Qiu

Papers

Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mareš equivalence relation

Fixed point theorems in fuzzy metric spaces

On fuzzy differential equations in the quotient space of fuzzy numbers

On computing generalized Hukuhara differences of Z-numbers

Symmetric fuzzy numbers and additive equivalence of fuzzy numbers