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Flood is a common natural disaster in the world. Flood often takes place around the river and plains, which indicates a higher risk of flooding in these areas. In order to represent the consequences (affected area, the number of deaths, housing collapse, direct economic losses) of flood disaster picture fuzzy sets have been used. Picture fuzzy sets are the extensions of intuitionistic fuzzy sets. Picture fuzzy sets based models may be adequate in situations when we face human opinions involving more answers of the type: yes, abstain, no, refusal. In this paper, we propose several distance and similarity measures for picture fuzzy sets which considers the degree of positive membership, degree of neutral membership, the degree of negative membership and degree of refusal membership. Geometrical interpretation of the picture fuzzy sets has been investigated. On the basis of proposed similarity measures a clustering algorithm is adopts to assess flood disaster risk in South region of India. A case study of 2009 Indian flood is captured to investigate the risk analysis of flood disaster considering some important criterion such as affected area, the number of deaths, housing collapse and direct economic losses. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the variational method for geometric contours which helps the level set function remain close to the sign distance function, therefor it remove the need of expensive re-initialization procedure and thus, level set method is applied on magnetic resonance images (MRI) to track the irregularities in them as medical imaging plays a substantial part in the treatment, therapy and diagnosis of various organs, tumors and various abnormalities. It favors the patient with more speedy and decisive disease controlling with lesser side effects. The geometrical shape, the tumor's size and tissue's abnormal growth can be calculated by the segmentation of that particular image. It is still a great challenge for the researchers to tackle with an automatic segmentation in the medical imaging. Based on the texture analysis, different images are processed by optimization of level set segmentation. Traditionally, optimization was manual for every image where each parameter is selected one after another. By applying fuzzy logic, the segmentation of image is correlated based on texture features, to make it automatic and more effective. There is no initialization of parameters and it works like an intelligent system. It segments the different MRI images without tuning the level set parameters and give optimized results for all MRI's. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a new method for the ranking of triangular type-2 fuzzy sets. In this method crucial measurements such as expectation value of centroid, transfer coefficient between the centroid of secondary membership function and left, right deviation of footprint of uncertainty, of primary membership function have been taken into account. The method also satisfies the reasonable properties for the ordering of fuzzy quantities. Further, some related properties such as robustness of the ranking function have been studied. The utility of the raking function have been tested in multicriteria decision making problem. [ABSTRACT FROM AUTHOR]

Dual hesitant fuzzy set, first proposed by Zhu et al. (Dual hesitant fuzzy sets, J Appl Math, 1-13, 2012) as an extension of hesitant fuzzy sets, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as a special case. Dual hesitant fuzzy sets consist of two parts, that is, the membership and nonmembership degrees, which are represented by two sets of possible values. Therefore, in accordance with the practical demand, these sets are more flexible than the existing fuzzy sets, and provide much more information about the situation. In this paper, the axiom definition of distance and similarity measures between dual hesitant fuzzy sets is introduced. Some new distance and similarity measures based on the geometric distance model, the set-theoretic approach, and the matching functions are proposed. The proposed distance measures are then applied to the multiple-attribute decision making under dual hesitant fuzzy environments. Through the distance measure between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, a practical example of investment alternatives is given to demonstrate the effectiveness of the developed measures. The advantages of the proposed distance measure over existing measures have been presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the variational method for geometric contours which helps the level set function remain close to the sign distance function, therefor it remove the need of expensive re-initialization procedure and thus, level set method is applied on magnetic resonance images (MRI) to track the irregularities in them as medical imaging plays a substantial part in the treatment, therapy and diagnosis of various organs, tumors and various abnormalities. It favors the patient with more speedy and decisive disease controlling with lesser side effects. The geometrical shape, the tumor's size and tissue's abnormal growth can be calculated by the segmentation of that particular image. It is still a great challenge for the researchers to tackle with an automatic segmentation in the medical imaging. Based on the texture analysis, different images are processed by optimization of level set segmentation. Traditionally, optimization was manual for every image where each parameter is selected one after another. By applying fuzzy logic, the segmentation of image is correlated based on texture features, to make it automatic and more effective. There is no initialization of parameters and it works like an intelligent system. It segments the different MRI images without tuning the level set parameters and give optimized results for all MRI's. [ABSTRACT FROM AUTHOR]

The natural rivers in developing countries have not been meeting their desirable water quality objectives due to discharge of untreated wastewater from domestic and industrial sources for a long time; and thus need to implement rational water quality management (WQM) plans. Overall sustainability of proposed WQM options should not be overlooked during the planning phase due to lack or absence of data. In this research, a framework is proposed for the evaluation of different WQM options to meet the water quality objectives of natural rivers. Five main sustainability criteria (SSC) are considered, including cost (capital, land and operational), land requirements, operation and maintenance issues, environmental impacts, and socio-economic impacts. In addition, several sub-criteria (impacts) have also been included to rationally justify the assessment of SSC by the decision makers (DM). The values of cost and land requirement criteria are calculated; whereas, the other SSC are subjective in nature. However, both types possess uncertainties associated with calculation errors, inherent assumptions, and the differences in DM's opinions. Further, due to data limitations in developing countries, the ranking order of WQM options established by the DM should be preferred. To deal with such uncertainties and the DM preferences, the Fuzzy UTASTAR multicriteria analysis method (based on linear programing) has been used for sustainability evaluation. To appraise the practicality of the proposed framework, it has been applied to the WQM of the Ravi River in Pakistan. The minimal difference between the DM's top ranked options affirms the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of different proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable properties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Limitations of existing ranking methods have been studied. Further for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Syst Appl 36:6833-6842, ) is incorrect. The main aim of this paper is to propose a new approach for the ranking of L- R type generalized fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as RM approach. The main advantage of the proposed approach is that it provides the correct ordering of generalized and normal fuzzy numbers and it is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets Syst 118:375-385, ). [ABSTRACT FROM AUTHOR]