Based on the fully implicational idea, we investigate the interval-valued fuzzy reasoning with multiantecedent rules. First, we construct a class of interval-valued fuzzy implications by means of a type of implications and a parameter on the unit interval, then use them to establish three kinds of fully implicational reasoning methods for the interval-valued fuzzy reasoning with multi-anteceden...

Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...

25 years ago, in [7], it was proved that the Hauber's law is an intuitionistic fuzzy tautology. In this case, used implication standard one. present paper, we check which implications, defined during these years, satisfy as a tautology and if them –

In this work, our primary focus is to determine the intersections that exist between the family of QL-implications and the families of (S, N)and R-implications. Toward this end, firstly, we investigate the conditions under which a QL-operation becomes a fuzzy implication. Since the exchange principle and the ordering property of fuzzy implications play an important role in this study, we propos...

In order to obtain a demanded fuzzy implication, a number of properties have been proposed, among which the first place antitonicity, the second place monotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, Rand QL-implications all satisfy the second place monotonicity and the boundary condit...

Recently Burusco introduced interval-valued fuzzy formal contexts into fuzzy formal concept analysis. The most interesting work mainly including fuzzy attribute implications from fuzzy formal context, however, were presented under the framework of residuated lattice. In this paper, we first show that the study of interval-valued fuzzy set can be fitted into the framework of residuated lattice. ...

This paper proposes a novel method for on-line modeling and robust adaptive control via Takagi–Sugeno (T-S) fuzzy models for nonaffine nonlinear systems, with external disturbances. The T-S fuzzy model is established to approximate the nonaffine nonlinear dynamic system in a linearized way. The so-called second type adaptive law is adopted, where not only the consequent part (the weighting fact...