In this paper, we introduce a new concept of hesitant intuitionistic fuzzy set (HIFS), which refines the dual hesitant fuzzy set and could be viewed as a more flexible tool to describe the uncertain information in reality. Since the uncertainty in HIFSs may be divided into three facets: fuzziness, intuitionism and hesitancy, we develop a fresh information-theoretic framework of uncertainty measures. We firstly propose the axiomatic principles of hesitant intuitionistic fuzzy entropy and give some distance-based entropy formulas. Then, a hesitant intuitionistic fuzzy cross-entropy is addressed to measure the discrimination of uncertain information between different HIFSs; the relationships between cross-entropy and entropy for HIFSs are also discussed. Moreover, some parameterized cross-entropy and entropy measures of HIFSs are investigated, and the decomposition formula suggests that hesitant intuitionistic fuzzy entropy may be expressed as the weighted average of fuzzy entropy, intuitionistic entropy and hesitant entropy. Finally, we demonstrate the efficiency of the proposed uncertainty measures for medical diagnosis and decision-making approach.
This is a preview of subscription content, log in to check access.
The authors are highly grateful to any anonymous referee for their careful reading and insightful comments, and the views and opinions expressed are those of the authors. The work is supported by the Talent Introduction Project of Anhui University (No. J01006134) and the Natural Science Key Project of Anhui Sanlian University (No. kjzd 2016001).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211MathSciNetCrossRefMATHGoogle Scholar
Chen YF et al (2014) Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information. J Intell Fuzzy Syst 26:2547–2556MathSciNetMATHGoogle Scholar
Wang L et al (2014c) Distance and similarity measures of dual hesitant fuzzy sets with their applications to multiple attribute decision making. 2014 International conference on progress in informatics and computing (PIC). IEEE, pp 88–92Google Scholar
Wei Y, Qiu J, Karimi HR (2017) Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults. IEEE Trans Circuits Syst I Regul Pap 64(1):170–181CrossRefGoogle Scholar
Wei Y, Qiu J, Lam HK et al (2016a) Approaches to T–S fuzzy-affine-model-based reliable output feedback control for nonlinear Itô stochastic systems. IEEE Trans Fuzzy Syst 99:1–14Google Scholar
Wei Y, Qiu J, Lam HK (2016b) A novel approach to reliable output feedback control of fuzzy-affine systems with time-delays and sensor faults. IEEE Trans Fuzzy Syst 11:1–15Google Scholar
Wei Y, Qiu J, Shi P et al (2016c) A new design of H-infinity piecewise filtering for discrete-time nonlinear time-varying delay systems via T–S fuzzy affine models. IEEE Trans Syst Man Cybern Syst 99:1–14CrossRefGoogle Scholar
Wei Y, Qiu J, Shi P et al (2016d) Fixed-order piecewise-affine output feedback controller for fuzzy-affine-model-based nonlinear systems with time-varying delay. IEEE Trans Circuits Syst I Regul Pap 12:945–958Google Scholar