Induction of shadowed sets from fuzzy sets
- 115 Downloads
A new method for computing a threshold value of an \(\alpha\)-cut for the induction of shadowed sets from fuzzy sets is proposed by modifying the formula for balance of uncertainty; which is required for transforming a fuzzy set into its resulting shadowed set. In order to reach a compromise between retention of the original amount of information in a fuzzy set and the optimality of a specific threshold level, the proposed method anchors on the average of the balance of uncertainties under various feasible \(\alpha\)-cuts. We describe and exemplify an algorithm which illustrates our proposed method. Finally, a number of randomly generated fuzzy sets are used as test samples to compare and point out the advantage of the proposed method over existing method.
KeywordFuzzy set Shadowed set Uncertainty Three-way decision
The authors are thankful to the Editors-in-Chief: Professor Withold Pedrycz and Professor Shyi-Ming Chen for their technical comments and to the anonymous Reviewers for their suggestions, which have improved the quality of this paper.
Compliance with ethical standards
Conflict of interest
The authors declare that there is no conflict of interest toward the publication of this manuscript.
- Chen SM (1996) A fuzzy reasoning approach for rule-based systems based on fuzzy logics. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics 26(5):769–778Google Scholar
- Deng XF, Yao YY (2013), Mean-value-based decision-theoretic shadowed sets, Proceedings of 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 1382–1387Google Scholar
- Pedrycz W (1999) Shadowed sets: bridging fuzzy and rough sets. In: Pal SK, Skowron A (eds) Rough fuzzy hybridization: a new trend in decision-making. Springer, Singapore, pp 179–199Google Scholar
- Pedrycz W (2005) Granular computing with shadowed sets. In: Slezak D, Wang GY, Szczuka M, Dntsch I, Yao YY (eds) RSFDGrC 2005, 3641. LNCS(LNAI) Springer, Heidelberg, pp 23–32Google Scholar
- Pedrycz W, Chen SM (2015b) Granular computing and decision-making: interactive and iterative approaches, vol 502. Springer, HeidelbergGoogle Scholar
- Tsai PW, JPan JS, Chen SM, Liao BY, Hao SP (2008) Parallel cat swarm optimization, Proceedings of the 2008 International Conference on Machine Learning and Cybernetics, Kunming, China, 6(1): 3328–3333Google Scholar