International Research journal of Management Science and Technology

  ISSN 2250 - 1959 (online) ISSN 2348 - 9367 (Print) New DOI : 10.32804/IRJMST

Impact Factor* - 6.2311


**Need Help in Content editing, Data Analysis.

Research Gateway

Adv For Editing Content

   No of Download : 54    Submit Your Rating     Cite This   Download        Certificate

FUZZY MATHEMATICS AND ITS EVOLUTION

    1 Author(s):  SUMAN RANI

Vol -  8, Issue- 7 ,         Page(s) : 156 - 161  (2017 ) DOI : https://doi.org/10.32804/IRJMST

Abstract

Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic. It started in 1965 after the publication of Lotfi Asker Zadeh's seminal work Fuzzy sets. A fuzzy subset A of a set X is a function A:X→L, where L is the interval [0,1]. This function is also called a membership function. A membership function is a generalization of a characteristic function or an indicator function of a subset defined for L = {0,1}. More generally, one can use a complete lattice L in a definition of a fuzzy subset A .

1. Arabacioglu, B. C. (2010). "Using fuzzy inference system for architectural space analysis". Applied Soft Computing. 10 (3): 926–937. doi:10.1016/j.asoc.2009.10.011.
2. Biacino, L.; Gerla, G. (2002). "Fuzzy logic, continuity and effectiveness". Archive for Mathematical Logic. 41 (7): 643–667. ISSN 0933-5846. doi:10.1007/s001530100128.
3. Cox, Earl (1994). The fuzzy systems handbook: a practitioner's guide to building, using, maintaining fuzzy systems. Boston: AP Professional. ISBN 0-12-194270-8.
4. Gerla, Giangiacomo (2006). "Effectiveness and Multivalued Logics". Journal of Symbolic Logic. 71 (1): 137–162. ISSN 0022-4812. doi:10.2178/jsl/1140641166.
5. Hájek, Petr (1998). Metamathematics of fuzzy logic. Dordrecht: Kluwer. ISBN 0-7923-5238-6.
6. Hájek, Petr (1995). "Fuzzy logic and arithmetical hierarchy". Fuzzy Sets and Systems. 3 (8): 359–363. ISSN 0165-0114. doi:10.1016/0165-0114(94)00299-M.
7. Halpern, Joseph Y. (2003). Reasoning about uncertainty. Cambridge, Mass: MIT Press. ISBN 0-262-08320-5.
8. Höppner, Frank; Klawonn, F.; Kruse, R.; Runkler, T. (1999). Fuzzy cluster analysis: methods for classification, data analysis and image recognition. New York: John Wiley. ISBN 0-471-98864-2.
9. Ibrahim, Ahmad M. (1997). Introduction to Applied Fuzzy Electronics. Englewood Cliffs, N.J: Prentice Hall. ISBN 0-13-206400-6.
10. Klir, George J.; Folger, Tina A. (1988). Fuzzy sets, uncertainty, and information. Englewood Cliffs, N.J: Prentice Hall. ISBN 0-13-345984-5.
11. Klir, George J.; St Clair, Ute H.; Yuan, Bo (1997). Fuzzy set theory: foundations and applications. Englewood Cliffs, NJ: Prentice Hall. ISBN 0-13-341058-7.
12. Klir, George J.; Yuan, Bo (1995). Fuzzy sets and fuzzy logic: theory and applications. Upper Saddle River, NJ: Prentice Hall PTR. ISBN 0-13-101171-5.
13. Kosko, Bart (1993). Fuzzy thinking: the new science of fuzzy logic. New York: Hyperion. ISBN 0-7868-8021-X.

*Contents are provided by Authors of articles. Please contact us if you having any query.






Bank Details