International Journal of Statistics and Reliability Engineering

No Publication Cost

Vol 8, No 2:

openaccess

Non-Probabilistic Information Measures of Fuzzy Matrix & their Application in Medical Diagnosis

Omdutt Sharma , Priti Gupta

Abstract

Non-probabilistic information measures have gained attention by researchers due to their wide range of applications in decision making and data related problems.Keeping in view of non-probabilistic nature of experiment, here some information measures related to fuzzy matrices are introduced and their application for feature selection has been presented. Feature selection can eliminate those features which are irrelevant thus it reduces the dimension and improve the predictive accuracy of decision machining problems related to life involve information which may contain uncertain. In this paper, uncertainty and vagueness deal with fuzzy set theory via fuzzy matrix concept.

Full Text

PDF

References

Alka; O. Sharma; P. Gupta; Logarithmic information measures for fuzzy soft matrices, International Journal of Statistics and Reliability Engineering, 7(1), 131-139 (2020).

A. De Luca; S. Termini; A definition of a non-probabilistic entropy in the setting of fuzzy sets theory, Information and Control, 20(4), 301-312 (1972).

A. Renyi; On measure of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, 1, 547-561 (1961).

C. E. Shannon; The mathematical theory of communication, Bell’s System Technical Journal, vol. 27, 379-423 (1948).

D. Bhandari; N. R. Pal; Some new information measure of fuzzy sets, Information Sciences 67, 209-228 (1993).

D. S. Hooda; D Jain; Measures of information of fuzzy matrix and fuzzy binary relation, Journal of Combinatorics, Information and System Sciences, 37, 1-19 (2012).

H. C. Peng; F. H. Long; C. Ding; Feature selection based on mutual information: Criteria of max-dependency, max-relevance and min-redundancy, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 1226-1238 (2005).

L. A. Zadeh; Fuzzy sets and systems, Proceedings of the Symposium on System Theory, 29-37, Polytechnic Institute of Brooklyn, Brooklyn, NY, USA, (1965).

L. A. Zadeh; Fuzzy Sets, Information and Control, 8, 338 – 353 (1965).

L. Sanchez; M. R. Suarez; I. Couso; A fuzzy definition of mutual information with application to design of genetic fuzzy classifiers, In: Proceedings of the IEEE International Conference of Fuzzy Systems, Fuzzieee, (London, UK) (2007).

M. G. Thomason; Convergence of Powers of a Fuzzy Matrix, J. Math. Anal. Appl., 57, 476-480 (1977).

N. R. Pal; S. K. Pal; Entropy: A new definition and its applications, IEEE Transactions on Systems, Man and Cybernetics, vol. 21, No. 5, 1260-1270 (1999).

O. Sharma; & P. Gupta; A Sine Trigonometric Similarity Measures on Fuzzy Rough Sets & It’s Applications in Medical Diagnosis, Aryabhatta Journal of Mathematics and Informatics, 9 (1), 272-283 (2017).

O. Sharma; A. Rani; P. Gupta; Some similarity and distance measures on fuzzy rough sets & it’s applications, International Journal of Engineering, Science and Mathematics, vol.6, issue 5, 85-105 (2017).

O. Sharma; P. Gupta; A. Sheoran; Dimensionality reduction using fuzzy soft set theory, International Journal of Statistics and Reliability Engineering, 4(2), 154-158 (2017).

O. Sharma; P. Gupta; P. Tiwari; A new non-probabilistic divergence measure of fuzzy matrix and its applications, Songklanakarin J. Sci. Technol., 43(2), 372-383 (2021).

O. Sharma; P. Gupta; P. Tiwari; Fuzzy soft matrices entropy- application in data-reduction: fuzzy soft matrices, International Journal of Fuzzy System Applications (IJFSA) Volume 7, Issue 3, Article 4, 56-75 (2018).

O. Sharma; Sonia; P. Gupta; Some Trigonometric Entropy for Fuzzy Rough Set and their Application in Medical Area, International Journal for Research in Engineering Application & Management, 4(3), 570-578 (2018).

P. Gupta; A. Sheoran; Harmonic measures of Fuzzy Entropy and their Normalization, International Journal of Statistika and Mathematika, 10(3), 47-51 (2014).

P. Gupta; A. Sheoran; Some new parametric Fuzzy Entropies, International Journal of Fuzzy Mathematics and Systems, 4(3), 293-298 (2014).

P. Gupta; O. Sharma; Feature Selection: An Overview, Impact: International Journal of Information Engineering and Technology, 1, 1- 12 (2015).

P. Gupta; P. Tiwari; Decision making approach using weighted coefficient of correlation along with generalized parametric fuzzy entropy measure, International Journal of Fuzzy System Application (IJFSA), Vol. 5, Issue 3, Article 3, 30-41, July-September 2016.

P. Gupta; P. Tiwari; H. D. Arora; On Some Generalized Exponential Entropy for Fuzzy Sets, Proc. of International Conf. or Reliability, Infocom Technologies and Optimization (ICRITO) (Trends and Future Directions), 2014 3rd International Conference, pp. 1-4, held at Amity University, Noida from 8-10 Oct 2014.

R. Verma; B. D. Sharma; “Exponential information measures on pairs of fuzzy sets”, Scientiae MathematicaeJaponicae Special Version, 91-98 (2015)

R. Verma; B. D. Sharma; On generalized exponential fuzzy entropy, World Academy of Science, Engineering and Technology, vol. 5. 956-959 (2011).

S. Ding; Z. Shi; S. Xia; F. Jin; Studies on Fuzzy Information Measures, In the Fourth Conference on Fuzzy Systems and Knowledge Discovery, IEEE Computer Society, (2007).

V. Kandaswamy; F. Smarandache; K. Ilanthenral; Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists. (2007).

Z. Pawlak; Rough Sets, International Journal of Information and Computer Sciences”, 11, 341 – 356 (1982).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

Journal Content