The linear multi objective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conflicting in nature. This paper presents an application of fuzzy goal programming to the linear multi objective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership Functions to solve multi objective transportation problem. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. To illustrate the methodology some numerical examples are presented.

In this paper the problem under consideration is multi objective non-linear fractional programming problem involving semilocally convex and related Functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multi objective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality conditions are obtained for efficient and properly efficient solutions. Some duality results are established for multi objective Schaible type dual.

Improving participation in voluntary activities in Iran is important because increasing productivity among young people, given the country's young population, contributes to community sustainability. Therefore, a better understanding of volunteer motivation in Iranian youth is needed. The Volunteer Functions Inventory (VFI) for assessing volunteer motivations has good psychometric properties and is adapted to several languages, but no validated Iranian translation yet exists. The purpose of this study was to investigate the psychometric Characteristics of voluntary Functions inventory in members of Iranian Red Crescent Society. Sample size was 595 members of Youth Organization of Iranian Red Crescent Society from 31 provinces and 175 cities of Iran that were selected by multi-stage cluster sampling method and responded to voluntary Functions inventory. Data were collected using a demographic sample and voluntary Functions inventory (VFI). Confirmatory factor analysis using principal components method was used for data analysis. The results of the present study showed that the voluntary Functions inventory had validity and reliability. Also, the factor structure showed that 29 items and 6 factors well assess people's attitudes to volunteering, and the structure of this inventory was well-fitted and confirmed all goodness of fit models. The present study provides the use of the Iranian translation of the Voluntary Functions Inventory (6 scales and 29 items) to assess volunteer motivation among young Iranian volunteers.

In this paper, an alternative approach in operational modal analysis is presented, utilizing image processing technique and transmissibility Functions. Imaging sensors do not impose additional mass on the structure due to their non-contact nature, while transmissibility Functions, independent of excitation type, can directly extract mode shapes. The innovation of this research lies in combining these two techniques to record dynamic responses and identify modal properties. To capture the temporal response history from video signals, the block-matching method with sub-pixel accuracy was employed. Validation was conducted by recording the response of the tip of a cantilevered steel beam subjected to impact excitation, using a high-speed camera and a laser vibrometer, simultaneously. The RMSE plots in the time domain and the PSD in the frequency domain indicate high accuracy of this method. Using this approach, the displacement time histories of various points on the structure were extracted from the video signals, and the modal properties, including natural frequencies, damping ratios, and mode shapes, were identified using the transmissibility matrix method. The results obtained from the proposed method were compared with the stochastic subspace identification (SSI) method and analytical solutions. The findings reveal the accuracy of the modal identification approach introduced in this article. The highest relative error in estimating the natural frequencies of the first and second modes, compared to the values from the laser method, are 0.19% and 0.13%, respectively, and in comparison to the analytical values, they are 0.34% and 1.5%, respectively.

In this study, a multiobjective optimization is applied to Optimal Power Flow Problem (OPF). To effectively achieve this goal, a Multiobjective Ant Lion algorithm (MOALO) is proposed to find the Pareto optimal front for the multiobjective OPF. The aim of this work is to reach good solutions of Active and Reactive OPF problem by optimizing 4-conflicting objective Functions simultaneously. Here are generation cost, environmental pollution emission, active power losses, and voltage deviation. The performance of the proposed MOALO algorithm has been tested on various electrical power systems with different sizes such as IEEE 30-bus, IEEE 57-bus, IEEE 118-bus, IEEE 300-bus systems and on practical Algerian DZ114-bus system. The results of the tests proved the versatility of the algorithm when applied to large systems. The effectiveness of the proposed method has been confirmed by comparing the results obtained with those obtained by other algorithms given in the literature for the same test systems.

The sewer layout in flat areas significantly influences the construction and operational costs as well as reliability of the network performance. To find an optimum design of sewer networks for flat areas, this study presents a Multi-Objective optimization problem with the objective Functions of 1- the cost and 2- the reliability. The reliability criterion is defined as the effect of a clogging in a sewer on its upstream population. To solve the problem, the NSGA-II Algorithm is coupled to two self-adaptive design algorithms for generating the layout and sizing of sewers. A case study is solved using the proposed model to demonstrate its application and advantages.

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example.