The main contribution of this paper is to present the systematic and low-complexity translation techniques between a class of hybrid systems referred to as automaton-based DHA and piecewise affine (PWA) systems. As an starting point the general modeling framework of the automaton-based DHA is represented which models the controlled and uncontrolled switching phenomena between linear continuous dynamics including discrete and continuous states, inputs and outputs. The basic theoretical definitions on the state trajectories of the proposed DHA with forward and backward evolutions which yield forward and backward piecewise affine (FPWA and BPWA) systems are given. Next, the well-posedness and equivalency properties are proposed and the sufficient conditions under which the wellposedness property is achieved with the automaton-based DHA and PWA systems are given. It is shown that the graphical structure of the proposed automaton-based DHA makes it possible to obtain analytically the equivalent PWA system with a polynomial complexity in contrast to the existing numerical translation techniques via decomposed structure of the DHA with an exponential complexity. Examples are presented to confirm the effectiveness of the proposed translation techniques.

In this article, after the definitions of the reduced hesitant L-fuzzy automaton (RHLFA) and the minimal hesitant L-fuzzy automaton; we convert a hesitant L-fuzzy automaton (HLFA) to an RHLFA by reducing the number of its states such that its language is equal to the original HLFA language. Then, by defining an equivalence relation on the monoid X*,we construct an HLFA whose language is equal to the language of the transformed RHLFA, and we show that this HLFA is minimal. In conclusion, we delineate the criteria under which, the number of states in the minimal HLFA is equal to the number of states in the RHLFA

Evolutionary algorithms are some of the most crucial random approaches to solve the problems, but sometimes generate low quality solutions. On the other hand, Learning automata are adaptive decision-making devices, operating on unknown random environments, So it seems that if evolutionary and learning automaton based algorithms are operated simultaneously, the quality of results will increase sharply and the algorithm is likely to converge on best results very quickly.This paper contributes an algorithm based on learning automaton to improve the evolutionary algorithm for solving a group of NP problems. It uses concepts of machine learning in search process, and increases the efficiency of evolutionary algorithm (especially genetic algorithm). In fact, the algorithm is prevented from being stuck in local optimal solutions by using learning automaton. Another positive point of the hybrid algorithm is its noticeable stability since standard division of results, which is obtained by different executions of algorithm, is low; that is, the results are practically the same. Therefore, as the proposed algorithm is used for a set of well-known NP problems and the results are very suitable it can be considered as a precise and reliable technique to solve the problems.

In formal language theory, we are mainly interested in the natural language computational aspects of!-languages. Therefore in this respect it is convenient to consider fuzzy!-languages. In this paper, we introduce two subclasses of fuzzy regular!-languages called fuzzy n-local!-languages and B¨ uchi fuzzy n-local!-languages, and give some closure properties for those subclasses. We define a deterministic fuzzy automaton acceptance conditions on fuzzy!-languages and fuzzy n-local automaton. The relationship between deterministic fuzzy n-local automaton and two subclasses of fuzzy regular!-languages are established and proved that every fuzzy!-language accepted by a deterministic fuzzy automaton in 2-mode is a projection of a B¨ uchi fuzzy 2-local!-language.

Graph automaton groups constitute a special class of automaton groups constructed from a graph. In this paper, we show that the action of any graph automaton group on each level of the rooted regular tree gives rise to a Gelfand pair. In particular, we determine the irreducible submodules of the action of such a group on the space of functions defined on each level of the tree, and we exhibit the corresponding spherical functions.

Rosa hybrida is a perennial plant that after cut off head of the stem, lateral buds become free from apical dominance and begin to growth. In each new period of growth, new and young leaves can be formed. The four leaf samples were numbered from apex to base, showing young to mature leaf stages and some biochemical pigment markers changes were studied. The results suggest that during maturation, in addition to morphological differences, some physiological and biochemical markers are change. Data showed age dependent increase in the amount of pigments such as chlorophylls and carotenoids to reach the stage of leaf maturity to improve the leaf photosynthetic system efficiency. Gradually reducing in content of phenolic compounds, anthocyanins and flavonoids suggest reduction on oxidative damage.

As the complexity of the real-world problems increases, many of them can’t be modeled using current approaches. Therefore, to overcome the current challenges and deficits, new computational models should be constantly presented for solving mentioned problems. Many real-world problems are graph-like in nature, for which irregular cellular automaton (ICA) is a desirable tool. However, ICA is not able to represent the fuzzy concepts. To this end, in this paper, a new computational model called irregular fuzzy cellular automaton is proposed. To this end, the present paper introduces a new computational model, namely fuzzy irregular cellular automata. The proposed model is a combination of fuzzy cellular automata and irregular fuzzy cellular automata, with the aim to combine the advantages of the both models and to alleviate their disadvantages. The proposed model is then used for solving the real-world road safety ranking problem. The computer simulations are conducted to show the effectiveness of the proposed mode for rating different sections of roads. Experimental results showed that the proposed method could estimate the road safety problem with 75% accuracy.