In this note, our aim is to present the relation between msets and L-fuzzy sets. We prove that an mset can be viewed as an L-fuzzy set. An mset topology can be viewed as an L-topology. Therefore, it follows that mset topologies are redundant in theoretical sense.

This paper proposes an efficient algorithm based on memetic algorithm (MA) for a REDUNDANCY allocation problem without component mixing (RAPCM) in a series-parallel system when the REDUNDANCY strategy can be chosen for individual subsystems. Majority of the solution methods for the general RAPCM assume that the type of a REDUNDANCY strategy for each subsystem is pre-determined and known a priori. In general, active REDUNDANCY has traditionally received greater attention; however, in practice both active and cold-standby redundancies may be used within a particular system design. The choice of the REDUNDANCY strategy then becomes an additional decision variable. Thus, the problem is to select the best REDUNDANCY strategy, component and REDUNDANCY level for each subsystem in order to maximize the system reliability under system-level constraints. Due to its complexity and NP-hardness, it is so difficult to optimally solve such a problem by using traditional optimization tools. To validate the performance of the proposed MA in terms of solution quality, a number of test problems are examined and the robustness of this algorithm is then discussed. Finally, the related results are reported and it is shown that the proposed MA performs well.

To increase the reliability of a specific system, using redundant components is a common method which is called REDUNDANCY allocation problem (RAP). Some of the RAP studies have focused on k -out-of- n systems. However, all of these studies assumed predetermined active or standby strategies for each subsystem. In this paper, for the first time, we propose a k -out-of-n system with a choice of REDUNDANCY strategies. Therefore, a k-out-of- n series–parallel system is considered when the REDUNDANCY strategy can be chosen for each subsystem. In other words, in the proposed model, the REDUNDANCY strategy is considered as an additional decision variable and an exact method based on integer programming is used to obtain the optimal solution of the problem. As the optimization of RAP belongs to the NP-hard class of problems, a modified version of genetic algorithm (GA) is also developed. The exact method and the proposed GA are implemented on a well-known test problem and the results demonstrate the efficiency of the new approach compared with the previous studies.

Fereidoon Tavallali is one of the modernist pioneer poets in contemporary Persian poetry who had an Influence on younger poets. In this article we investigate REDUNDANCY and repetition in his poetry. Repetition’s study consists of several parts: repetition of the word in the beginning of the line or hemistich, repetition in composition, repetition in figures of speech, and artistic techniques in repetition. This article reveals that one of the stylistic features in Tavallali’s poems is repetition and this trait is there in both period of Tavallali’s poetry: romantic period and classic period. However, REDUNDANCY’s frequency is more in romantic period. Repetition in Tavallali’s poems generally has a rhetoric value.

This paper initially gives an example of a conversation between two persons and studies some problems that appeared out of this conversation. These problems are categorized into two groups: figurative and substantial. Figurative problems section is divided in two parts of physical body and language and its structure. There exists the problem of information transfer in language. Because of close relationship between information theory (in mathematics) and optimality theory (in language), language has been defined as a collection of limitations and the role of these limitation has been given in brief. Then the information theory and the channel of information transfer from source to destination will be explained. In this paper the concepts of antropy and REDUNDANCY are discussed. Evaluation of antropy and REDUNDANCY in English language and an example of an English word, antropy and REDUNDANCY in Farsi language will be explained. Then the results are shown as follows: the antropy of Farsi language on the first letter is 5 bit/ symbol and its REDUNDANCY is 80%.

In this paper kinematics model of a nonholonomic mobile manipulator is formulated. The kinematics equations for a mechanical mobile manipulator are developed in such a way that the kinematics interaction between the mobile platform and mechanical manipulator explicitly appears in the equations. In both conditions the motion constraints and kinematics REDUNDANCY are considered and analyzed. These concepts are expanded in general cases by using special subjects, on linear algebra and functional analysis. A useful and unique kinematics model for REDUNDANCY resolution of mobile manipulators is introduced by defining specified variables. Finally, the application of the model is verified by simulation results in order to find the maximum allowable load of a mobile manipulator.