The millennium villages initiative could achieve more integrated sustainable settlements if sustainability aims such as those set out in the proposed evaluation framework (minimizing resource consumption; maximizing environmental capital; quality of life; social inclusion; community participation) were adopted as central objectives. The term "sustainability" was offered in 1987 by the United Nation's World Commission on Environment and Development in its report Our Common Future. According to that document, "Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. "Ultimately, the goal of sustainability is to enhance people's well-being. Sustainability is a concept that allows a comfortable way of living by balancing the resource demands of technological, economical and social requirements with the environment’s ability to meet present and future needs. "Sustainable communities encourage people to work together to create healthy communities where natural and historic resources are preserved, jobs are available, sprawl is contained, neighborhoods are secure, education is lifelong, transportation and health care are accessible, and all people (in rural and urban regions) have opportunities to improve the quality of their lives. Sustainable development has three principal dimensions: economic growth, social equity and protection of the environment. Maximization of social well being and poverty alleviation through the optimal and efficient utilization of the natural resources is the economic dimension. The social aspects refer to the improving access to health and education services, fulfilling standards of security and respect for human rights. The issue of equity, i. e. , the distribution of benefits and access to resources remains an essential component of both the economic and social dimensions of sustainable development. The environmental dimensions, on the other hand, are concerned with the conservation and enhancement of the physical and biological resource base and eco-systems. So sustainability indicators look at economic, social and environmental information in an integrated manner and are growing in importance with the advent and follow-up to Agenda 21. They are now challenging countries and the development community to: develop better information collection and reporting systems especially for natural resources (environmental) indicators; integrate environmental, social and economic indicators for greater sensitivity in planning and decision-making toward sustainable development; and report regularly and reliably on conditions and trends. This paper aims at explaining the role and importance measurement and ranking of social sustainability in rural regions with emphasis on FUZZY TOPSIS by referring to example of objective indicators in Dehestan Homeh in Central District of Khodabandeh. So the focus of the paper is on consideration of how to use objective indicators to monitor social sustainability in a relevant and useful manner. A central question in this paper is whether the required decision making arrangements for measuring and ranking of social sustainability in rural regions, or whether FUZZY TOPSIS is suitable method for ranking of rural settlements. Above all, we want to find out, how can measure social sustainability based on objective indicators and how can rank rural settlements with emphasis on Multi-Attribute Decision Making (MADM) methods. The paper is organized as follows: After presenting a framework for the analysis of sustainable development and social sustainability, we have explained some basic objectives indicators of social sustainability in rural settlements and decision making methods with emphasis on FUZZY TOPSIS in order to ranking of rural settlements. This study proposed 17 objective indicators for social sustainability. These are pragmatic choice, to encapsulate in a convenient and practical way the main features or characteristics against which rural settlements could be appraised. They are: social participation, social interactions, introspection, social solidarity, social responsibility, social trust, satisfaction of organizations, fear of abnormal, sense of social exclusion, satisfaction of housing, satisfaction of income, job satisfaction, satisfaction of accessibility to services (quantity and quality), sense of place, expectancy to the future, sense of good luck. Then we have pointed out some essential arrangements which are necessary for gathering data and measuring indicators by questionnaire in 21 rural settlements and 306 rural households. Finally we showed that this model and objectives indicators are able to truly illustrate local circumstances.

In this paper, we determine the FUZZY SIMILARITY measures of the U. S. state rankings with respect to domestic violence, female homicide, and sexual violence against teens. We find that the FUZZY SIMILARITY measures are low. We then consider the best state rankings and determine the FUZZY SIMILARITY measures of this ranking a with the previous three rankings. We also develop some theoretical results concerning FUZZY SIMILARITY measures.

Introduction: Spatial planning concepts have become prominent in discussions and strategies that focus on regional and rural development. At the heart of this policy framework is an understanding that competition between regions is one of the primary driving forces influencing social and economic development and hence cohesion. It is also understood that some regions have greater advantages in terms of their location and resources than others. Recognition of the fact that resources and conditions for social and economic development vary spatially, gave rise to the concept of territorial cohesion. Rural point is domain in Iran. Although the term rural is frequently used, it is rarely defined. This issue is compounded by the choice of spatial units that form the basis for analysis. The literature on the topic of rural development is populated by uncritical use of terms such as rural regions, rural areas and rurality ….

In this paper, we discuss the importance of nuclear power for the future of the world with respect to climate change. In  particular, we examine the involvement of nuclear power by countries in several different ways. We consider first the   involvement of countries with respect to the amount of nuclear power produced, global energy transition, and capacity  factor. Countries are ranked with respect to these three involvement areas. The FUZZY SIMILARITY measures of these  rankings are found to be low in most cases. We next place countries in their respective regions. We rank the countries  with respect to their carbon dioxide emissions and their greenhouse gas emissions. We then determine the FUZZY  SIMILARITY measures of the countries with respect to the rankings. We found that one of the FUZZY SIMILARITY measures  involving green house gas emissions is high.

Despite increasing attention to human resource area of research as a value generating asset, managing its risks have not been studied systematically. In this study a quantitative approach for analyzing and assessing the human resources risks has been adopted. First, the multiple dimensions of human resource risks and their components were identified through semi-structured interviews with experts of human resources field in one of the major organizations in the power industry. In the next step, five criteria were presented to analyze the risks and causal interaction between the human resources risks as one of the criteria of analysis were identified using FUZZY DEMATEL TECHNIQUE. In the final step, the estimated level of risks were compared according to analysis criteria and human resources risks were ranked based on the five given indicators using FUZZY SIMILARITY TECHNIQUE. The results showed that human resource operational risks have the greatest total effect both given and received in the network of interrelationships among risks and have the highest priority based on analyzing criteria compared to other four main areas of human resource risks.

In this paper, we present a revised SIMILARITY measure based on Chen-and-Chen’s SIMILARITY measure for FUZZY risk analysis. The revised SIMILARITY measure uses the corrected formulae to calculate the centre of gravity points, therefore it is more effective than the Chen-and-Chen’s method. The revised SIMILARITY measure can overcome the drawbacks of the existing methods. We have also proposed a new SIMILARITY measure between type-2 FUZZY numbers and a method for handling FUZZY risk analysis problem.

Just as we humans use many different types of inferential procedures to help us understand things or to make decisions,  there are many different FUZZY logic inferential procedures, including SIMILARITY-based approaches. SIMILARITY measures can be seen not only as a general notion but also as a particular family of FUZZY relations which play  crucial roles for the motivation and the whole design of SIMILARITY-based reasoning. In the context of SIMILARITY-based reasoning, several issues merit concern. One is the representation of implication relation and two is the composition of a FUZZY implication relation with an observed system fact. The others are  continuity and robustness of these systems which are the soul that must be inherited in the newly setup frameworks. Therefore, the purpose of this study is to introduce a new SIMILARITY-based approximate reasoning system which is based on introducing a new class of SIMILARITY measure on the space of $LR$-FUZZY numbers. Therefore,  first, a new class of SIMILARITY measures is introduced between FUZZY sets. The SIMILARITY measure is needed in order to activate rules which are in terms of linguistic variables. Second,  it is proved that the proposed measures satisfy the properties of the axiomatic definition as well as the other properties by a theorem. Next,  we validate the effectiveness of the   proposed SIMILARITY measure in a bidirectional approximate reasoning system in order to provide a  nonlinear mapping of FUZZY  input data into FUZZY output data. Finally,  using existing experimental data from Uniaxial Compressive Strength (UCS) testing,  the FUZZY inference system constitutive model is produced to describe the influence of joint geometry (joint location, trace length and orientation) on the UCS of rock. The numerical results will show that the proposed model based on SIMILARITY-based approximate reasoning systems has better performance compared with the Mamdani FUZZY inference systems and the  multivariate regression.

In this paper, we expose cosine, jaccard and dice SIMILARITY measures and rough interval Pythagorean mean operator. Some of the important properties of the defined SIMILARITY measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

Real-world systems often exhibit relationships with inherent vagueness and imprecision, which FUZZY graphs effectively capture. Determining how similar two FUZZY graphs are remains essential for pattern recognition, social network analysis, and molecular biology applications where both edge strengths and node attributes carry uncertainty. Conventional approaches to measuring graph SIMILARITY struggle with the subtle uncertainties that characterize FUZZY graph structures. This paper presents FUZZYCLSim, a deep learning architecture for computing FUZZY graph SIMILARITY that integrates uncertainty quantification via FUZZY set theory. The proposed approach comprises three main innovations: a FUZZY graph convolutional network (F-GCN) propagating membership degrees together with features, a FUZZY weighted bilinear tensor network (F-WBTN) capturing directional FUZZY relationships between graphs, and a cross-level FUZZY feature extraction module combining node-level with graph-level FUZZY embeddings. Experimental results across three benchmark datasets demonstrate substantial improvements over existing methods, with average MSE reductions of 34\% and correlation gains of 7\%, validating our uncertainty-aware design choices.

The most important issue with trajectory analysis is calculating SIMILARITY between trajectories. In this paper a novel method for measuring SIMILARITY between trajectories based on the cost to match a set of trajectories segments was introduced. The SIMILARITY between two trajectories is defined as a minimum cost to match a trajectory to the other one. For this purpose, the segment based distance was introduced to as a cost of matching two trajectories segments. In addition, the dynamic programming TECHNIQUE is used to implement the time warp method. We performed some experiments to compare the proposed SIMILARITY measure with the similar approaches in the application of trajectory classification. The empirical quality of the proposed SIMILARITY measure was evaluated on 1-nearest neighbor (1-NN) classification task using 13 publicly available data sets. Compared to the other well-known SIMILARITY measures, the proposed method proved to be effective in the considered experiments based on the accuracy of classification.