This paper presents an adaptive fuzzy controller for a class of completely pure-feedback nonlinear systems. Takagi-Sugeno type fuzzy logic systems are used to approximate the unknown nonlinear functions. The controller synthesis is developed by the backstepping technique and the small gain approach. The closed-loop control system is proved to be semi-globally uniformly ultimately bounded (SGUUB...

In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pu...

The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MValgebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given. A linear mapping between two semilinear s...

In many scientific and engineering applications, the fuzzy set concept plays an important role. The fuzziness appears when we need to perform, on manifold, calculations with imprecision variables. The fuzzy set theory was introduced initially by Zadeh [1] in 1965. In the theory and applications of fuzzy sets, convexity is a most useful concept. In fact, in the basic and classical paper [1], Zad...

The identiication of fuzzy models can sometimes be a diicult problem, often characterized by lack of data in some regions, collinearities and other data deecien-cies, or a sub-optimal choice of model structure. Regu-larization is suggested as a general method for improving the robustness of standard parameter identiication algorithms leading to more accurate and well-behaved fuzzy models. The p...

Soft set theory [1] was firstly introduced byMolodtsov in 1999 as a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. He has shown several applications of this theory in solvingmany practical problems in economics, engineering, social science, medical science, and so forth, in [1]. In the recent years, papers about soft sets theory and their applications ...

In this paper, the relationships between semicontinuity and preinvexity of fuzzy mappings are investigated. The concepts of intermediate-point preinvex fuzzy mappings and weakly preinvex fuzzy mappings are first introduced, and the authors establish a characterization for a weakly preinvex fuzzy mapping in terms of its epigraph. In this context, a characterization of a preinvex fuzzy mapping in...

By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a Banach space. Applications are given in providing fuzzy KKT conditions for semi-infinite programming.

In this paper, we define Some domination parameters on IVIFG and derive some relations and then verify by using Interval valued intuitionistic fuzzy graphs and discussed some properties. Also, we introduced Immoderate semi-complete IVIFG and its properties.

A propositional proof system is weakly automatizable if there is a polynomial time algorithm that separates satisfiable formulas from formulas that have a short refutation in the system, with respect to a given length bound. We show that if the resolution proof system is weakly automatizable, then parity games can be decided in polynomial time. We give simple proofs that the same holds for dept...