Two Novel Generalized Information Measures for Fuzzy Sets

Document Type : Research Paper

Authors

1 Applied Sciences, Faculty, Chitkara University, Himachal Pradesh, India

2 Deen Bandhu Chhotu Ram University of Science and Technology, Haryana-131039, India

3 Chitkara University School of Engineering and Technology, Chitkara University, Himachal Pradesh, India

4 Atal Shiksha Kunj, Atal Nagar, Barotiwala, Solan, Himachal Pradesh

5 Government College Haryana-126102, India

Abstract

In the present manuscript, it is our utmost aim and objective to comprehensively and extensively expound upon two highly innovative and remarkably novel information measures that have been adeptly and appropriately extended to encompass fuzzy sets. These measures have undergone a rigorous and meticulous scrutiny and examination with regard to axiomatic principles, and have evinced numerous and manifold advantageous properties, thus providing a compelling and highly persuasive validation of their reliability, credibility, and overall effectiveness. It is of paramount importance to note that the measures in question have been meticulously and painstakingly designed with the express aim and purpose of effectively quantifying the extent of information that is inextricably embedded and enmeshed within fuzzy sets, and are firmly grounded in the foundational and bedrock principles of information theory, which is an indisputably and irrefutably significant and substantial academic discipline. Our contributions to the field of study are truly and incontestably unparalleled, and offer a fresh, innovative, and unprecedented perspective on the study of fuzzy sets and their associated information content, which is of immense and inestimable value to the overall advancement and progress of the academic discipline.

Keywords

References

Bhandari, D., and Pal, N. R. (1993). Some new information measures for fuzzy sets. Information Sciences, 67(3), 209-228.
Havrda, J., and Charvat, F. (1967). Quantification method of classiffication Processes. Concept of Structrual α-Entropy. Kybernetika, 3, 30-35.
Kapur, J. N. (1997). Measures of fuzzy information. Mathematical Sciences Trust Society, New Delhi.
Kaufmann, A. (1980). Fuzzy subsets: Fundamental Theoretical Elements, 3, Academic Press, New York.    
Kosko, B. (1986). Fuzzy entropy and conditioning. Information Sciences, 40, 165-174.
Liang, D., Xu, Z., Liu, D., and Wu, Y. (2018). Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Information Sciences, 435, 282-295.
Li, F., Lu, Z. H., and Cai, L. J. (2003). The Entropy of Vague Sets based on Fuzzy Sets. J. Huazhong Univ. Sci. Tech., 31(1), 24-25.
Li, P., and Liu, B. (2008). Entropy of credibility distributions for fuzzy variable. IEEE Trans. Fuzzy Systems, 16, 123-129.
Luca, A. D., and Termini, S. (1972). A definition of a Non-Probabilistic Entropy in Setting of Fuzzy Sets. Information and Control, 20, 301-312.
Mahmood, T., and Ur Rehman, U. (2022). A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures. International Journal of Intelligent Systems, 37(1), 535-567.
Parkash, O. (1998). A new parametric measure of fuzzy entropy. Information Processing and Management of Uncertainty, 2, 1732-1737.
Peng, X. (2019). New similarity measure and distance measure for Pythagorean fuzzy set. Complex & Intelligent Systems, 5, 101-111.
Renyi, A. (1961). On measures of entropy and information. Proc. 4 Bearkly Symposium on Statistics and Probability, University of California Press, 547-561.
Shannon, C. E. (1948). A Mathematical Theory of Communication. The Bell System Technical Journal, 27, 379-423.
Suman, S., Gandotra, N., and Gupta, M., 2022. New picture fuzzy entropy in regarding to multi-criteria decision-making application. AIP Conference Proceedings, 2357 (1). AIP Publishing.
Tomar, V. P., and Ohlan, A. (2014). Two new parametric generalized R-norm fuzzy information measures. International Journal of Computer Applications, 93(13), 22-27.
Tomar, V. P., and Ohlan, A. (2014). Sequence of fuzzy divergence measures and inequalities. AMO - Advanced Modeling and Optimization, 16(2), 439-452.
Tomar, V. P., and Ohlan, A. (2014). Sequence of inequalities among fuzzy mean difference divergence measures and their applications, SpringerPlus, 3, 623, 1-20.
Tomar, V. P., and Ohlan, A. (2014). New parametric generalized exponential fuzzy divergence measure. Journal of Uncertainty Analysis and Applications, 2(1), 1-14.
Tomar, V. P., and Ohlan, A. (2015). A new generalized fuzzy divergence measure and applications. Fuzzy Information and Engineering, 7(4), 507-523.
Verma, R., and Merigó, J.M. (2019). On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision‐making. International Journal of Intelligent Systems, 34(10), 2556-2583.
Verma, R., and Sharma, B. D. (2011). On Generalized Exponential Fuzzy Entropy. World Academy of Science, Engineering and Technology, 60, 1402-1405.           
Zadeh, L. A. (1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications, 23, 421-427.
Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8, 338-353.
International Journal of Supply and Operations Management
Volume 11, Issue 1
February 2024
Pages 43-53

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