The Constructive Implementation of New Applications of Fuzzy Languages and Fuzzy Automata Ƒ * – Pure Semi groups for Generating Theorems


M. Suresh Babu,E. Keshava Reddy,



Ƒ* - pure semi groups,Sequences,Group fuzzy congruence’s,Lattice Groups and fuzzy sub groups,


Introducing the idea of Ƒ* - pure semi group and shows that a semi group ‘S ‘is regular and Ƒ* - pure iff ' S ′ is a semi lattice of groups. Also shows with the purpose of a semi group' S ′ be Ƒ* - pure iff S3 is a semi lattice of groups. Additionally, learning the group congruence’s as well as semi lattice congruence’s on such a semi group and give a number of properties of fuzzy congruence’s on Ƒ* - pure semi groups. A nonempty set X, a fuzzy subset of X is, by definition, an arbitrary mapping A: X → [0,1], where [0,1] is the usual interval of real numbers. The important concept of fuzzy automata set position onwards by Zadeh [I]. Has opened up keen insights and applications in a wide range of scientific fields. It offers tools and a new approach to model imprecision and uncertainty present in phenomena that do not have sharp boundaries. Since then, a series of research on fuzzy automata sets has come out expounding the importance of the concept and its applications to logic, set theory, algebra theory, real analysis, topology, etc. [III]. Fleck A. C. used the notion of a fuzzy subsets of a set to introduce the notion of fuzzy group of a group, Rosenfeld’s paper motivated the development of fuzzy algebras [X]. Following the formulation of fuzzy subgroups by Rosenfeld, Dib introduced the concept of a fuzzy automata space as a replacement for the concept of universal set in the ordinary case. Recently, some basic concepts of fuzzy algebras such as fuzzy homomorphism’s were introduced and discussed by using the new approach of fuzzy space and fuzzy automata groups introduced. In this paper we introduce concepts of fuzzy automata inverse semi groups and redefine fuzzy automata inverse sub-semi groups using the concept of fuzzy spaces introduced by K. A. Dib [II].


I. A. Ada, On the Non-deterministic communication complexity of Regular
Languages, Developments in Language theory. Springer Berlin
Heidelberg, 205-209, 2008.
II. A. H. Clifford and G. B. Preston the algebraic theory of semi groups
vol.1, American Math, Soc., Providence, RI, 1961.
III. A. K. Srivastava and W. Shukla, “ A Topology for Automata II” ,
Internat. Jour. Math.and Math.Sc.,9:425- 428, 1986.
IV. D. S. Malik, J. N. Moderson, M. K. Sen Submachine’s of fuzzy finite
state machine, Journal of fuzzy mathematics, 2 ( 1994 ), 781-792.
V. D. S. Malik, J. N. Moderson, Fuzzy discrete structures, Physica Verlag
Newyork, (2000).
VI. E. Lughofer and O. Buchtala, “Reliable all-pairs evolving fuzzy
classifiers, “IEEE T. Fuzzy Systems, vol.21, no.4, pp. 625-641, 2013.
VII. F. Meng and X. Chen, (2016). “A new method for a triangular fuzzy
compare wise judgment matrix process based on consistency analysis,”
International Journal of Fuzzy Systems, vol.309, PP. 119-1375,2015.
VIII. J. R. Gonzalez de Mendivil, J. R. Garitagoitia, ” Fuzzy languages with
infinite range accepted by fuzzy automata: Pumping lemma and
determinization procedure,” Fuzzy sets Syst., vol.249, pp.1-26, 2014.
IX. J. Wang, M. Yin. And W. Gu.” Fuzzy multi-set finite automata and their
languages, “Soft compute. vol.17. no.3, pp. 381-390, March-2013.
X. K. T. Atarassov, Instuitionistic fuzzy sets, Fuzzy sets and systems 20,
87 – 96,1986.
XI. K. T. Atanassov, New operations defined over the intuitionistic fuzzy
sets, fuzzy sets and systems 61 ,137 – 142, 1994.

XII. K. Peeva, “Finite L-fuzzy machines”, Fuzzy sets and systems, 141, 415-
437, 2004.
XIII. M. K. Muyeba and L. Han, “Fuzzy classification in web usage mining
using fuzzy quantifiers,” 2013 IEEE/ACM International Conference on
Advances in Social Networks Analysis and Mining (ASONAM), 2013.
XIV. M, Kudlek, V. Mitrana, Closure properties of Multiset Language
Families, Fundum Inforum, 49 , 193- 203, 2002.
XV. M. Kudlek, P. Totzke, G. Zetzche, Properties of Multiset Languge
classes defined by multiset push down automata, Fundum inform, 93 ,
235-244, 2009.
XVI. R. Fierimonte, M. Barbato, A. Rosato, and M. Panella, “Distributed
learning of random weights fuzzy neural networks,” Proc.of IEEE int.
Conf. on Fuzzy Systems-2016.
XVII. S. Shelke and S. Apte, “A Fuzzy based classification scheme for
unconstrained handwritten devanagari character recognition,” 2015.
International Conference on Communication, Information & Computing
Technology (ICCICT), 2015.
XVIII. X. P. Wang and W. J. Liu, Fuzzy regular subsemigroups in semi groups,
inform.sci.68:225-231 ,1983.
.XIX. X. Z. Zhao and Y. Q. Guo, Sturdy frames of type (2, 2) algebras and
their applications to semi rings, Fundamental Mathematicae ,69-
XX. Y. L. He, X. Z. Wang, and J. Z. Huang, “Fuzzy nonlinear regression
analysis using a random weight Network,” Information Sciences,
vol.364, pp. 222-240, 2016.
XXI. Y. M. Li, “Finite Automata theory with membership values in Lattices,
Information Sciences”, 176, 3232- 3255, 2006.

View Download