Approximate reasoning with fuzzy soft set

Document Type : Research Paper

Authors

1 Department of Mathematics, Visva-Bharati, West Bengal, India

2 Department of Mathematics, Faculty of Mathematics, Visva-Bharati, West Bengal, India

Abstract

In this work, we develop a reasoning mechanism under uncertainty for a typical class of decision making problems based on the theory of fuzzy soft set. Accordingly, we consider a logic of fuzzy soft sets. In the sequel, implication operations dealing with fuzzy soft sets over different universal sets and different sets of parameters have been studied extensively. An algorithm for rule based reasoning has been developed for a modus ponens type rule of inference using the proposed logical structure. The entire proposal is illustrated with an example. Results of application of our proposed inference are compared with those obtained by Mondal and Raha on the problem of management of hypertension using a medical diagnostic support system.

Keywords

References

[1] B. Ahmad, A. Kharal, On fuzzy soft sets, Advances in Fuzzy Systems, 2009 (2009), 1-6.
[2] M. I. Ali, M. Shabir, Logic connectives for soft sets and fuzzy soft sets, IEEE Transactions on Fuzzy System, 22(6) (2014), 1431-1442.
[3] S. Das, S. Kar, Group decision making in medical system: An intuitionistic fuzzy soft set approach, Applied Soft Computing, 24 (2014), 196-211.
[4] S. Das, M. B. Kar, S. Kar, T. Pal, An approach for decision making using intuitionistic trapezoidal fuzzy soft set, Annals of Fuzzy Mathematics and Informatics, 16(1) (2018), 99-116.
[5] S. Das, M. B. Kar, T. Pal, S. Kar, Multiple attribute group decision making using interval-valued intuitionistic fuzzy soft matrix, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), (2014), 2222-2229.
[6] S. Das, D. Malakar, S. Kar, T. Pal, Correlation measure of hesitant fuzzy soft sets and their application in decision making, Neural Computing and Applications, 31 (2017), 1023-1039.
[7] D. Dubois, H. Prade, A note on measures of specificity for fuzzy sets, International Journal of General Systems, 10 (1985), 279-283.
[8] S. Enginoglu, N. Cagman, F. Citak, Fuzzy soft set theory and its application, International Journal of Fuzzy Systems, 8(3) (2011), 137-147.
[9] J. A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Application, 18 (1967), 145-174.
[10] J. A. Goguen, The logic of inexact concepts, Synthese, 19 (1969), 325-373.
[11] E. Guner, H. Aygun, Spherical fuzzy soft sets: Theory and aggregation operator with its applications, Iranian Journal of Fuzzy Systems, 19(2) (2022), 83-97.
[12] P. K. Maji, R. Biswas, R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (2001), 589-602.
[13] P. K. Maji, R. Roy, A fuzzy set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, 203 (2007), 412-418.
[14] P. Majumdar, S. K. Samanta, Generalized fuzzy soft sets, Computers and Mathematics with Applications, 59 (2010), 1425-1432.
[15] W. K. Min, Similarity in soft set theory, Applied Mathematics Letter, 25 (2012), 310-314.
[16] D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999), 19-31.
[17] B. Mondal, S. Raha, Approximate reasoning in management of hypertension, Facets of Uncertainties and Applications, 125 (2015), 225-233.
[18] E. S. Palmeira, B. C. Bedergal, Extension of fuzzy logic operators defined on bounded lattices via retractions, Computers and Mathematics with Application, 63 (2012), 1026-1038.
[19] Z. Pei, K. Qin, D. Meng, Y. Xu, A medical diagnostic support system for the management of hypertension (MED DIAG), Journal of Scientific Multidisiplinary Research, 3 (2011), 16-30.
[20] K. Rezaei, H. Rezaei, New distance and similarity measures for hesitant fuzzy soft sets, 16 (2019), 159-176.
[21] M. Shabir, M. I. Ali, M. Naz, Algebraic structures of soft sets associated with new operations, Computers and Mathematics with Application, 61 (2011), 2647-2654.
[22] R. R. Yager, Measuring tranquility and anxiety in decision making: An application of fuzzy sets, International Journal of General Systems, 8 (1982), 139-146.
[23] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
[24] M. A. Zehrui, W. Wangming, Logical operators on complete lattices, Information Sciences, 55 (1991), 77-97.
Iranian Journal of Fuzzy Systems
Volume 19, Issue 4
July and August 2022
Pages 107-124

Files

Share

How to cite

Statistics