Monthly Average Rainfall Forecasting Based On An Adaptive Neuro-Fuzzy Inference System in Upper Brahmani Basin, Odisha, India

Floods disrupt human activities, resulting in the loss of lives and property of a region. Excessive rainfall is one of the reasons for flooding, especially in the downstream areas of a catchment. Because of its complexity, understanding and forecasting rainfall is incredibly a challenge. This study investigates the use of an Adaptive Neuro-Fuzzy Inference System (ANFIS) in predicting rainfall using several surface weather parameters as predictors. An ANFIS model is developed for forecasting rainfall over the Upper Brahmani Basin by using 30 years of climate data. A hybrid model with six membership functions gives the best forecast for an area. The suggested method blends neural network learning capabilities with language representations of fuzzy systems that are transparent. The application of ANFIS is to the upper Brahmani river basin is tried for the first time. The ANFIS model with various input structures and membership functions has been built, trained, and tested to evaluate the capability of the model. Statistical performance indices are used to evaluate the performance. Using the developed model, forecast is done for year 2021 – 2030.

Attributes Inequality in Multidimensional Poverty MeasuresFuzzy Modeling

Poverty is recently considered to be a multidimensional one. That is to say the poor can suffer multiple disadvantages at the same time. This paper aims to further develop and refine the multidimensional poverty measure using Fuzzy Sets Theory (FST). The application of FST starts with the choice of membership functions and the rules to manipulate to integrate attributes inequality in multidimensional poverty measure. An application based on individual well-being data from Tunisian households in 2015 is presented to illustrate use proposed concepts. JEL classification: P46; I32; D81; C00;

Rough sets in graphs using similarity relations

<abstract><p>In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $ \mathcal{G} $ preserve the indiscernibility partitions. Further, we prove that for any graph $ \mathcal{G} $ with $ k $ orbits, any reduct $ \mathcal{R} $ consists of one element from $ k-1 $ orbits of the graph. We also study the rough membership functions for paths, cycles, complete and complete bipartite graphs. Moreover, we introduce essential sets and discernibility matrices induced by orbits of graphs and study their relationship. We also prove that every essential set consists of union of any two orbits of the graph.</p></abstract>

Unification of imprecise data - translation of fuzzy to multi-valued knowledge over Y-axis

Inference systems are a well-defined technology derived from knowledge-based systems. Their main purpose is to model and manage knowledge as well as expert reasoning to insure a relevant decision making while getting close to human induction. Although handled knowledge are usually imperfect, they may be treated using a non classical logic as fuzzy logic or symbolic multi-valued logic. Nonetheless, it is required sometimes to consider both fuzzy and symbolic multi-valued knowledge within the same knowledge-based system. For that, we propose in this paper an approach that is able to standardize fuzzy and symbolic multi-valued knowledge. We intend to convert fuzzy knowledge into symbolic type by projecting them over the Y-axis of their membership functions. Consequently, it becomes feasible working under a symbolic multi-valued context. Our approach provides to the expert more flexibility in modeling their knowledge regardless of their type. A numerical study is provided to illustrate the potential application of the proposed methodology.

Properties of interval type-2 fuzzy sets in decision support systems

Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.

Implementasi Kendali Keseimbangan Gerak Two Wheels Self Balancing Robot Menggunakan Fuzzy Logic

Self balancing robot is a two-wheeled robot that only has two fulcrums so that this robot is an unbalanced system. Therefore, a control system that can maintain the stability of the robot is needed so that the robot can keep in standing position. This study aims to design a self-balancing robot and its control system which improves the robot's performance against the maximum angle of disturbance that can be overcome. The control system used is based on fuzzy logic with 9 membership functions and 81 rules. The control system is applied to the ESP-32 microcontroller with the MPU-6050 sensor as a feedback position of the robot and DC motor as an actuator. Complementary filters are added to the MPU-6050 sensor readings to reduce noise to obtain better robotic tilt angle readings. The improvement of this research compared to previous research based on fuzzy is the addition of the number of membership functions from 7 to 9 and the embedding of a complementary filter on the MPU-6050 sensor output reading. The result shows that the designed self balancing robot which has dimensions of 10cm x 18cm x 14.5cm can cope with the maximum disturbance angle up to 17.5⁰.

Optimization of Fuzzy Logic Based Virtual Pilot for Wargaming

This paper deals with the design of an autopilot based on a set of fuzzy controllers. The model of the aircraft that the autopilot controls is defined as a model with 6 degrees of freedom, where the inputs to this model are the settings of the engine thrust (DX), rudder rotation (Dl) and elevators (Dm and Dn). The fuzzy controllers are of the Mamdani type, where the set of parameters defining the controller allow the derivation of membership functions of the input variables and membership functions of the output variables. The parameters of fuzzy controllers are determined by the optimization process. For the purpose of optimization, a fitness function is defined, which derives the simulation parameters from its parameter (vector), and the simulation subsequently performed and evaluated determines whether it is a feasible solution in addition the value of this solution. By this optimization process, the sub-optimal solution is found and is then used to define the settings of the fuzzy controllers and, therefore, the autopilot. This paper contains a description of each step of the solution of the described problem, and with the help of the obtained results, it is determined that the presented procedure allows us to find an autopilot capable of controlling the defined model of the aircraft. In addition, there is a brief description regarding the misconceptions explored during the development of the experiment.

Development of algorithm for fuzzy art appraisal model

This paper presents an algorithm for a fuzzy art appraisal model, which is a hierarchical model based on a base price and the following adjustment. In the first step of the model, we determine the list of linguistic variables, their number, types of terms and types of membership functions for each term. Then, we analyze the subject area, process expert information and build a knowledge base containing 50 predicate rules of inference. The analysis shows that the model reflects a 4.37% error in a porcelain figurine appraisal. The paper also outlines recommendations on the implementation of the developed algorithm for fuzzy art appraisal model using Fuzzy Logic Toolbox for Matlab package and explains package limitations such as the need for strong authentication of art pieces, identification of mass artworks and a limited range of artwork that can be appraised.

Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2

In the paper, the inequality \frac{\mu^{\frac{1}{\nu}}}{\nu} + \frac{\nu^{\frac{1}{\mu}}}{\mu} \leq \frac{1}{2\mu\nu} - 1 is introduced and proved. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E.