International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 13, No. 1, 8 Feb. 2021
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Application of Generalized Measure of 'Useful' R-norm Inaccuracy and Total Ambiguity
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Author(s)
Index Terms
Fuzzy sets, inaccuracy measures, R-norm information measures, ‘useful’ information measures, total ambiguity measures, multi-criteria decision making
Abstract
In the present paper, we introduce generalized measure of 'useful' R-norm inaccuracy having two parameters and its analogue 'useful' R-norm total ambiguity measure by merging together the concepts of probability, fuzziness, R-norm, 'useful' information and inaccuracy. Along with the basic properties, some other important properties of these two proposed measures are stated. These measures are generalizations of some well-known inaccuracy measures. Further, the monotonic behaviour of the proposed 'useful' R-norm inaccuracy measures is studied and the graphical overview is given. The measure of information improvement for both the measures is also obtained. Lastly, the application of 'useful' R-norm total ambiguity measure is presented in terms of multi-criteria decision making. For all the numerical calculations R software is used.
Cite This Paper
Saima Manzoor, Safina Peerzada, Mirza A. K. Baig, "Application of Generalized Measure of 'Useful' R-norm Inaccuracy and Total Ambiguity", International Journal of Intelligent Systems and Applications(IJISA), Vol.13, No.1, pp.17-33, 2021. DOI:10.5815/ijisa.2021.01.02
Reference
[1]D. Kerridge, “Inaccuracy and inference”, Journal of Royal Statistical Society B, vol. 23, no. 1, 184-194, 1961.
[2]C. E. Shannon, “A mathematical theory of communication”, Bell System Technical Journal, vol. 27, 379-423, 623-656, 1948.
[3]D. S. Hooda and A. Ram, “Characterization of a generalized measure of R-norm entropy”, Caribbean Journal of Mathematical Computing Science, vol. 8(1 & 2), 18-31, 1998.
[4]L. A. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, No. 3, 338-353, 1965.
[5]R. K. Verma and B. D. Sharma, “A measure of inaccuracy between two fuzzy sets”, Cybernetics and Information Technologies, vol. 11, no. 2, 13-23, 2011.
[6]D. S. Hooda and D. K. Sharma, “Generalized R-norm information measures”, Journal of Applied Mathematics, Statistics and Informatics, vol. 4, no.2, pp.153–168, 2008.
[7]D. E. Boekee and V. D. Lubbe, “The R-norm information measure”, Information and Control, 45,136-155, 1980.
[8]D. S. Hooda and R. K. Bajaj, “On generalized R-norm measures of fuzzy information”, Journal Of Applied Mathematics, Statistics And Informatics, vol. 4, no. 2, 199-212, 2008.
[9]R. Verma and B. D. Sharma, “A new inaccuracy measure for fuzzy sets and its application in multi-criteria decision making”, International Journal of Intelligent Systems and Applications, vol. 05, 62-69, 2014.
[10]A. H. Bhat, M. A. Bhat, M. A. K. Baig and S. Manzoor, “Noiseless coding theorems of generalized useful fuzzy inaccuracy measure of order alpha and type beta,” International Journal of Fuzzy Mathematical Archive, vol. 13, no. 2, 135-143, 2017.
[11]A. H. Bhat, M. J. Dar and M. A. K. Baig, “Two parametric new generalized average code-word length and its bounds in terms of new generalized inaccuracy measure and their characterization”, Pakistan Journal of Statistics, vol. 34, no. 2, 147-162, 2018.
[12]S. M. Sofi, S. Peerzada and A. H. Bhat, “Two parametric generalized ‘useful’ R-norm information measure & its coding theorems”, Pakistan Journal of Statistics, vol. 35, no. 2, 109-126, 2019.
[13]S. M. Sofi, S. Peerzada, R. Jamil and M. A. K. Baig, “Applications of Two Parametric Generalized ‘Useful’ R-Norm Directed Divergence Measures” unpublished.
[14]H. Theil, “Economics and information theory”, North-Holland Publishing Company, Amesterdam, 1967.
[15]S. Peerzada, S. M. Sofi and R. Jamil, “On parametric generalized R-norm: inaccuracy and fuzzy inaccuracy information measures”, Journal of Applied Probability and Statistics, vol. 15, no. 3, 79-92, 2020.
[16]S. M. Sofi, S. Peerzada and M. A. K. Baig, “Parametric generalizations of ‘useful’ R-norm fuzzy information measures”, International Journal of Scientific Research in Mathematical and Statistical Sciences, vol. 5, no. 6, 164-169, 2018.