Many objective optimizations (MaOO) algorithms that intends to solve problems with many objectives (MaOP) (i.e., the problem with more than three objectives) are widely used in various areas such as industrial manufacturing, transportation, sustainability, and even in the medical sector. Various approaches of MaOO algorithms are available and employed to handle different MaOP cases. In contrast, the performance of the MaOO algorithms assesses based on the balance between the convergence and diversity of the non-dominated solutions measured using different evaluation criteria of the quality performance indicators. Although many evaluation criteria are available, yet most of the evaluation and benchmarking of the MaOO with state-of-art algorithms perform using one or two performance indicators without clear evidence or justification of the efficiency of these indicators over others. Thus, unify a set of most suitable evaluation criteria of the MaOO is needed. This study proposed a distinct unifying model for the MaOO evaluation criteria using the fuzzy Delphi method. The study followed a systematic procedure to analyze 49 evaluation criteria, sub-criteria, and its performance indicators, a penal of 23 domain experts, participated in this study. Lastly, the most suitable criteria outcomes are formulated in the unifying model and evaluate by experts to verify the appropriateness and suitability of the model in assessing the MaOO algorithms fairly and effectively.
Let R be a commutative ring with identity. A proper ideal I of R is called semimaximal if I is a finite intersection of maximal ideals of R. In this paper we fuzzify this concept to fuzzy ideals of R, where a fuzzy ideal A of R is called semimaximal if A is a finite intersection of fuzzy maximal ideals. Various basic properties are given. Moreover some examples are given to illustrate this concept.
Let R be a commutative ring with unity. In this paper we introduce the notion of chained fuzzy modules as a generalization of chained modules. We investigate several characterizations and properties of this concept
Let R be a commutative ring with unity. In this paper we introduce and study fuzzy distributive modules and fuzzy arithmetical rings as generalizations of (ordinary) distributive modules and arithmetical ring. We give some basic properties about these concepts.
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
Calculating the Inverse Kinematic (IK) equations is a complex problem due to the nonlinearity of these equations. Choosing the end effector orientation affects the reach of the target location. The Forward Kinematics (FK) of Humanoid Robotic Legs (HRL) is determined by using DenavitHartenberg (DH) method. The HRL has two legs with five Degrees of Freedom (DoF) each. The paper proposes using a Particle Swarm Optimization (PSO) algorithm to optimize the best orientation angle of the end effector of HRL. The selected orientation angle is used to solve the IK equations to reach the target location with minimum error. The performance of the proposed method is measured by six scenarios with different simulated positions of the legs. The proposed
... Show MoreIn the present study, the effect of new cross-section fin geometries on overall thermal/fluid performance had been investigated. The cross-section included the base original geometry of (triangular, square, circular, and elliptical pin fins) by adding exterior extra fins along the sides of the origin fins. The present extra fins include rectangular extra fin of 2 mm (height) and 4 mm (width) and triangular extra fin of 2 mm (base) 4 mm (height). The use of entropy generation minimization method (EGM) allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by con
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