In this paper, the notions of the linear and g-convex combination for implications which extend the notion of convex combination of fuzzy implications on the unit interval to bounded lattices are introduced. A necessary and sufficient condition for the g-convex combination to be an implication is determined. Some basic properties of the g-convex combinations are discussed. Also, some sets which are defined by the linear (g-convex) combination of two implications on a bounded lattice are studied and the relationships between them are discussed. Moreover, the lattice theoretical structure of the mentioned sets is investigated.

Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a convex optimization problem that guarantees the global optimal solution. The convex optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

In this paper, we first characterize the convex L-subgroup of an L-ordered group by means of four kinds of cut sets of an L-subset. Then we consider the homomorphic preimages and the product of convex L-subgroups. After that, we introduce an L-convex structure constructed by convex L-subgroups. Furthermore, the notion of the degree to which an L-subset of an L-ordered group is a convex L-subgroup is proposed and characterized. An L-fuzzy convex structure which results from convex L-subgroup degree is imported naturally, and its L-fuzzy convexity preserving mappings investigated.

A B S T R A C TFor choosing suitable place multiple methods are introduced, which examine the qualities, methods and patterns of location selection. The current methods use global approach and do not pay attention to spatial differences, environmental variation in variables, local changes modeled by local weighting indicators. It has been selected as a case study to evaluate the EMS center of Fars province and to evaluate the indicators of distance from the power plant, distance from logistics centers, industries, transportation terminals, hospitals, hotels and tourism, cities, rural areas and custom centers. has been used, using the AHP method to weight the qualities, and then for local weights, non-overlapping neighborhood filtering within a radius of 25 km are used and calculate the corresponding changes, quantity, ratio Presented in this article, the obtained weights, then the compute local weighted layers, and then local weight was multiplied in the normalized layers and the final layer were obtained. In the next step, it was combined and calculated to compare the data using the global method. The results of the two methods were transferred to the points of the EMS and the results were analyzedExtended AbstractIntroductionIn geographical studies and spatial planning, there are different approaches to choosing the right place for all kinds of applications and uses, and a process is followed to choose the best places. This process includes stating the research problem (cognition), choosing the criteria and preferences of decision makers and how to determine the weight of indicators, combining criteria (design) and finally, choosing the best option. In the current methods of spatial decision, the criteria are given a fixed weight, while in geographical locations, the distribution of geographical phenomena is not uniform. In this case, attention should be paid to the spatial distribution pattern of geographical phenomena based on the principle of sensitivity of the range of changes, the size of the range of changes affects the outputs, and the data with a smaller range of changes also have a lesser effect on the output. The data with a larger range of changes will have a more significant effect on the output. Therefore, in spatial analysis, indicators that have small changes are less important. Local models have been presented to model local changes in spatial multi-criteria decision-making; in this research, the main issue is how to model the local changes that affect the expected outputs. MethodologyThe research process is based on multi-criteria spatial decision-making methods (national and local). First, spatial patterns of indicators were analyzed through exploratory analyzes of ESDA spatial data. Then based on the review of the research criteria, the direct weighting method was used to calculate the weight of the indicators, and the experts were asked to specify the weight of the criteria in the range of 1 to 10. The opinions were combined, and the final weight was obtained. First, the data were spatially modelled to model and calculate the local weights. Then Block Statistics spatial filter without overlap was used to determine the neighborhood. The range of local changes, maximum and minimum values, were calculated, and local weights were obtained based on that. Finally, the information layers were descaled. After that, the unscaled criterion layers were multiplied by the national weights and the final national scores were obtained. In the next step, the data of the evaluated information layers (local and national) were transferred to the points of emergency databases. Based on the analysis, the fit was done. Results and discussionGeneral or global weights pay attention to the relative importance of indicators, which is the starting point for calculating local weights. Based on the research results, the most critical indicators are industries, cities and hospitals, which are more important in the location of road emergency stations. However, in order to achieve better results, it is necessary to build a local weight layer. The results of the research show that the indicators' weight and the difference in the criteria (general weight) are not equal in the entire geographical area, and the areas with a larger range of changes have a higher coefficient.Because, unlike general weights that are obtained based on different methods, local weights are estimated based on the principle of sensitivity of the range of changes and are changed spatially, and a fixed value is not considered for all areas. According to the research findings, the highest level in the general and local evaluation method corresponds to 0.5 to 0.7. Based on the local (geographic) weight method, it is less than the national or general method in the range of 0.9 to 1. Furthermore, this is due to the more precise nature of this method, which models the effects of local changes. To evaluate the compliance of the emergency centers with the final maps of suitability assessment, the information on the suitability maps was transferred to the map of the emergency center points of Fars province. Based on the evaluation of 207 emergency stations, according to the general method, 14 percent are in the high group (0.9-1), and according to the local or geographical method (16.9), percent are in this group. ConclusionAt the level of space and geographical regions, phenomena and geographical complications are not uniformly distributed, some phenomena have a homogeneous distribution, and some have a heterogeneous distribution. On the one hand, the phenomena and decision issues are affected by the context in which they are formed and evolve; on the other hand, these phenomena are placed in the network of mutual relations. Furthermore, the results of the set of phenomena may differ from the results of the phenomena individually and separately; in this article, an attempt has been made to address the issue that in spatial analysis and planning, it is necessary to pay attention to geographical differences in decision-making. Furthermore, it should not be evaluated in general terms of spatial decision problems; one of the methods of modelling these differences and spatial changes is to consider the local weight of the criteria. Based on the research findings, local (geographical) and national analysis results are different and can better show these changes. On the other hand, the pattern of spatial differences also has its spatial pattern, and paying attention to these differences in spatial differences can be the subject of further studies. FundingThere is no funding support. Authors’ ContributionAuthors contributed equally to the conceptualization and writing of the article. All of the authors approved the content of the manuscript and agreed on all aspects of the work declaration of competing interest none. Conflict of InterestAuthors declared no conflict of interest. Acknowledgments We are grateful to all the scientific consultants of this paper.