### فهرست مطالب

• Volume:14 Issue:2, 2017
• تاریخ انتشار: 1396/02/23
• تعداد عناوین: 8
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Chance theory is a mathematical methodology for dealing with indeterminate phenomena including uncertainty and randomness. Consequently, uncertain random variable is developed to describe the phenomena which involve uncertainty and randomness. Thus, uncertain random variable is a fundamental concept in chance theory. This paper provides some practical quantities to describe uncertain random variable. The typical one is the expected value, which is the uncertain version of the center of gravity of a physical body. Mathematically, expectations are integrals with respect to chance distributions or chance measures. In fact, expected values measure the center of gravity of a distribution; they are measures of location. In order to describe a distribution in brief terms there exist additional measures, such as the variance which measures the dispersion or spread, and moments. For calculating the moments of uncertain random variable, some formulas are provided through chance distribution and inverse chance distribution. The main results are explained by using several examples.
Keywords: Chance Theory, Uncertain Random Variable, Chance Distribution, Moments
• M. S. Kordafshari, A. Movaghar *, M. R. Meybodi Pages 23-44
Network throughput and energy conservation are two conflicting important performance metrics for wireless sensor networks. Since these two objectives are in conflict with each other, it is difficult to achieve them simultaneously. In this paper, a joint duty cycle scheduling and energy aware routing approach is proposed based on evolutionary game theory which is called DREG. Making a trade-off between energy conservation and network throughput, the proposed approach prolongs the network lifetime. The paper is divided into the following sections: Initially, the discussion is presented on how the sensor nodes can be scheduled to sleep or wake up in order to reduce energy consumption in idle listening. The sensor wakeup/sleep scheduling problem with multiple objectives is formulated as an evolutionary game theory. Then, the evolutionary game theory is applied to find an optimal wakeup/sleep scheduling policy, based on a trade-off between network throughput and energy efficiency for each sensor. The evolutionary equilibrium is proposed as a solution for this game. In addition, a routing approach is adopted to propose an energy aware fuzzy logic in order to prolong the network lifetime. The results show that the proposed routing approach balances energy consumption among the sensor nodes in the network, avoiding rapid energy depletion of sensors that have less energy. The proposed simulation study shows the more efficient performance of the proposed system than other methods in term of network lifetime and throughput.
Keywords: Wireless sensor network, Duty cycle scheduling, Energy aware routing, Evolutionary game theory, Distributed reinforcement learning
The efficiency of transportation system management plays an important role in the planning and operation efficiency of flexible manufacturing systems. Automated Guided Vehicles (AGV) are part of diversified and advanced techniques in the field of material transportation which have many applications today and act as an intermediary between operating and storage equipment and are routed and controlled by an intelligent computer system. In this study, a two-objective mathematical programming model is presented to integrate flow shop scheduling and routing AVGs in a flexible manufacturing system. In real-life problems parameters like demand, due dates and processing times are always uncertain. Therefore, in order to solve a realistic problem, foregoing parameters are considered as fuzzy in our proposed model. Subsequently, to solve fuzzy mathematical programming model, one of the most effective technique in the literature is used. To solve the problem studied, two meta-heuristic algorithms of Non-dominated Sorting Genetic Algorithm-II (NSGAII) and multi-objective particle swarm optimization (MOPSO) are offered that the accuracy of mathematical models and efficiency of algorithms provided are assessed through numerical examples.
Keywords: Scheduling, Routing, Automated guided vehicle, Meta-heuristic algorithm, Flexible manufacturing
• Naim L. Braha *, Mikail Et Pages 79-92
Fuzzy set theory has entered into a large variety of disciplines of sciences, technology and humanities having established itself as an extremely versatile interdisciplinary research area. Accordingly different notions of fuzzy structure have been developed such as fuzzy normed linear space, fuzzy topological vector space, fuzzy sequence space etc. While reviewing the literature in fuzzy sequence space, we have seen that the notion of Tauberian theorems for the Euler-N\"{o}rlund mean-convergent sequences of fuzzy numbers has not been developed. In the present paper, we introduce some new concepts about statistical convergence of sequences of fuzzy numbers. The main purpose of this paper is to study Tauberian theorems for the Euler-N\"{o}rlund mean-convergent sequences of fuzzy numbers and investigate some other kind of convergences named Euler-N\"{o}rlund mean-level convergence so as to fill up the existing gaps in the literature. The results which we obtained in this study are much more general than those obtained by others.
Keywords: Statistical convergence, Tauberian theorems, Fuzzy numbers
• Jinming Fang, Youyan Li *, Wenyi Chen Pages 93-105
This paper focuses on the relationship between an \$L\$-subset and the system of level-elements induced by it, where the underlying lattice \$L\$ is a complete residuated lattice and the domain set of \$L\$-subset is an \$L\$-partially ordered set \$(X,P)\$. Firstly, we obtain the sufficient and necessary condition that an \$L\$-subset is represented by its system of level-elements. Then, a new representation theorem of intersection-preserving \$L\$-subsets is shown by using union-preserving system of elements. At last, another representation theorem of compatible intersection-preserving \$L\$-subsets is obtained by means of compatible union-preserving system of elements.
Keywords: Complete residuated lattice, \$L\$-partially ordered set, \$L\$-subset, System of level-elements, Union-preserving system of elements, Compatible union-preserving system of elements, Representation theorem
• Hoang Viet Long *, Nguyen Thi Kim Son, Ngo Van Hoa Pages 107-126
In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.
Keywords: Fractional PDEs, Caputo gH-derivatives, Fuzzy weak solutions, Weakly contractive mapping, Partially ordered space
• Ali Shakiba, Mohammadreza Hooshmandasl *, Bijan Davvaz, Seyed Abolfazl Shahzadeh Fazeli Pages 127-154
In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and maximum rejection error, these spaces are interpreted in three-way decision systems by defining the corresponding positive, negative and boundary regions.
Keywords: Fuzzy S-approximation Spaces, Fuzzy Sets, Three-way Decisions, Monotonicity, Weak Complement Compatibility, Rough Set Theory, Rough Mereology
• Jiyu Wu *, Yueli Yue Pages 155-164
In this paper, the poset \$BX\$ of formal balls is studied in fuzzy partial metric space \$(X,p,*)\$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset \$BX\$ of formal balls is a dcpo if and only if \$(X,p,*)\$ is layered complete fuzzy partial metric space.
Keywords: Fuzzy partial metric, Formal ball, \$mathcal{Q}\$-category, Domain