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This paper presents an integrated model based on a compromised solution method to solve fuzzy belief multi-objective large-scale nonlinear programming (FBMOLSNLP) problem with block angular structure. A new method is proposed to transfer each belief decision-making problem into some fuzzy problems. Furthermore, we propose a new compromise method of decision-making as one of the most efficient methods based on the particular measure of closeness to the ideal solution to aggregate multi-objective decision-making (MODM) problems into a single problem. The decomposition algorithm based on Dantzig–Wolfe is utilized to reduce the large-dimensional objective space into a two-dimensional space. Then, Zimmerman method is applied to transfer each bi-objective to a single-objective. Moreover, TOPSIS and VIKOR are utilized as two independent solution methods to aggregate each multi-objective sub-problem. Finally, a new single-objective nonlinear programming problem is solved to find the final solution. To justify the proposed model, two illustrative examples are provided, and the results of three decision methods are compromised.

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During the past two decades, economic crises and climate change have triggered mass migrations from rural areas to big cities and metropolises. Considering that the destination cities often lack the required capacity to systematically accommodate these newcomers, immigrants settle in unofficially on city margins. Since these immigrants have different ethnicities, the informal settlements constructed by them turn into multiethnic informal Settlements in which development of proper social ties becomes impeded. As a result, social cohesion is weakened and eventually ceases to exist among the residents in open community spaces. In this regard, the present study aims to analyze this process and the effects of multiethnicity on social cohesion in the open community spaces of poor urban areas and the role of environmental factors in this mechanism. The Hesar Imam Khomeini neighborhood, which is located in Hamadan Province and has a rural core, has given shelter to Lurish, Kurdish, Turkish and Persian-speaking immigrants during recent years, which makes it a suitable sample for study. Because of the existing limitations and in order to achieve the goal of the study, the grounded theory was used to conduct the research. In-depth interview was carried out on sixteen residents of the neighborhood, four individuals from each ethnicity. After coding the interviews using the theory, a grounded model of the study was formed. The results indicate that multiethnicity has negatively affected behavior settings, vibrancy and consequently social cohesion in the open community spaces of the area of study through the three factors of “different expectations from neighborhood space”, “different time of attendance in open spaces” and “different residence size”. It can be proposed that “creating spatial shared values” is one of the most effective strategies which can be used for narrowing gaps and increasing social cohesion in multiethnic neighborhoods.

This paper proposes a compromise model, based on a new method, to solve the multi-objective largescale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. In this compromise programming method, two concepts are considered simultaneously. First of them is that the optimal alternative is closer to fuzzy positive ideal solution (FPIS) and farther from fuzzy negative ideal solution (FNIS). Second of them is that the proposed method provides a maximum ''group utility'' for the ''majority'' and a minimum of an individual regret for the ''opponent''. In proposed method, the decomposition algorithm is utilized to reduce the large-dimensional objective space. A multi objective identical crisp linear programming is derived from the fuzzy linear model for solving the problem. Then, a compromise solution method is applied to solve each sub problem based on TOPSIS and VIKOR simultaneously. Finally, to illustrate the proposed method, an illustrative example is provided.