Browsing by Author "Surendra Singh Gautam"

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A modified weighted method of time series forecasting in intuitionistic fuzzy environment
(Springer, 2020) Surendra Singh Gautam; Abhishekh; S.R. Singh
In this paper, we present a modified weighted method of time series forecasting using intuitionistic fuzzy sets. The proposed weighted method provides a better approach to extent of the accuracy in forecasted outputs. As it is established that the length of interval plays a crucial role in forecasting the historical time series data, so a new technique is proposed to define the length of interval and the partition of the universe of discourse into unequal length of intervals. Further, triangular fuzzy sets are defined and obtain membership grades of each datum in historical time series data to their respective triangular fuzzy sets. Based on the score and accuracy function of intuitionistic fuzzy number, the historical time series data is intuitionistic fuzzified and assigned the weight for intuitionistic fuzzy logical relationship groups. Defuzzification technique is based on the defined intuitionistic fuzzy logical relationship groups and provides better forecasting accuracy rate. The proposed method is implemented to forecast the enrollment data at the University of Alabama and market share price of SBI at BSE India. The results obtained have been compared with other existing methods in terms of root mean square error and average forecasting error to show the suitability of the proposed method. © 2020, Operational Research Society of India.
A New High-Order Approach for Forecasting Fuzzy Time Series Data
(World Scientific Publishing Co., 2018) Surendra Singh Gautam; Abhishekh; S.R. Singh
In forecasting the fuzzy time series data, several authors took grades of membership 1, 0.5 and 0 for linguistic interval corresponding to fuzzy set. In this paper, we have proposed high-order approach for forecasting the fuzzy time series data by using the grade of membership value defined for each datum corresponding to triangular fuzzy sets and fuzzify the historical data by triangular fuzzy sets which have their maximum membership values. Also, we establish high-order fuzzy logical relationship groups and give a new technique for defuzzification process, by which we can compute the forecasted value in a more efficient way with lower value of MSE. For verifying the suitability of proposed method, we illustrate time series data of student enrollments at the University of Alabama, USA, and crop (Lahi) production of Pantnagar farm, G. B. Pant University of Agriculture and Technology, Pantnagar, India. The forecasting accuracy rate of proposed high-order forecasting method is better than those of existing methods and the forecasted production is much closer to the actual production. © 2018 World Scientific Publishing Europe Ltd.
A new method of time series forecasting using intuitionistic fuzzy set based on average-length
(Taylor and Francis Ltd., 2020) Abhishekh; Surendra Singh Gautam; S.R. Singh
The major problem in the field of fuzzy time series (FTS) is the accuracy rate in the forecasted values. To overcome this problem here, we propose a model for intuitionistic FTS forecasting based on average-length of interval, which enhances the forecasting result. The proposed model is focused on how to fuzzify the historical time series data. Here, the fuzzification of each observation is intuitionistic fuzzification, which is based on the maximum degree of score function and also establishes intuitionistic fuzzy logical relationships (IFLR) among all intuitionistic fuzzified data set. Here, we use simple arithmetic computations in defuzzification process with measuring the frequency of IFLR. An illustrative example of enrollments at the University of Alabama is used to verify the effectiveness of the proposed model and comparison in terms of RMSE and AFE with some of the existing forecasting models to show its superiority. © 2020, © 2020 Chinese Institute of Industrial Engineers.
A New Type 2 Fuzzy Time Series Forecasting Model Based on Three-Factors Fuzzy Logical Relationships
(World Scientific, 2019) Abhishekh; Surendra Singh Gautam; Shiva Raj Singh
The study of fuzzy time series models have been extensively used to improve the accuracy rates in forecasting problems. In this paper, we present a new type 2 fuzzy time series forecasting model based on three-factors fuzzy logical relationship groups. The proposed method uses a new technique to define partitions the universe of discourse into different length of intervals for different factors. Also, the proposed method fuzzifies the historical data sets of the main factors, second factors and third factors to their maximum membership grades obtained by their corresponding triangular fuzzy sets and construct the fuzzy logical relationship groups which is based on the three-factors to enhance in the forecasting accuracy rates. This paper introduces a new defuzzification technique based on their frequency occurrences of fuzzy logical relationships in fuzzy logical relationship groups. The fitness of the propose method is verified in the forecasting of Bombay Stock Exchange (BSE) Sensex historical data and compare in terms of root mean square and average forecasting errors which indicates that the proposed method produce more accurate forecasted output over the existing models in fuzzy time series. © 2019 World Scientific Publishing Company.
A Novel Moving Average Forecasting Approach Using Fuzzy Time Series Data Set
(Springer New York LLC, 2019) Surendra Singh Gautam; Abhishekh
In this study, we develop a novel moving average forecasting approach based on fuzzy time series data set. The main objective of applying this moving average approach in develop method is to provide better results and enhance the accuracy in forecasted output by reducing the fluctuation in time series data set. The developed method is to define the universe of discourse and partition into equal length of intervals which is based on the average-length method. Further, triangular fuzzy sets are defined and obtain a membership grade of each moving average historical datum rather than actual datum of historical fuzzy time series data. Here, the fuzzification process of moving average historical data to their maximum membership grades obtained into corresponding triangular fuzzy sets. The general suitability of developed model has been examined by implementing in the forecast of student enrollments data at the University of Alabama. Further, the market price of State Bank of India share at Bombay Stock Exchange, India, has also been implemented in the forecast. The developed method of moving average fuzzy time series provides an improved forecasted output with least root mean square error and average forecasting errors which shows that our developed method is more superior than other existing models available in the literature based on fuzzy time series data. © 2019, Brazilian Society for Automatics--SBA.
A refined method of forecasting based on high-order intuitionistic fuzzy time series data
(Springer Verlag, 2018) Abhishekh; Surendra Singh Gautam; S.R. Singh
In this paper, we present a refined method of forecasting based on high-order intuitionistic fuzzy time series by transformed a historical fuzzy time series data into intuitionistic fuzzy time series data via defining their appropriate membership and non-membership function. The fuzzification of historical time series data is intuitionistic fuzzification which is based on their score and accuracy function. Also intuitionistic fuzzy logical relationship groups are defined and introduced a defuzzification process for high-order intuitionistic fuzzy time series. The aim of this paper is to propose an idea of high-order intuitionistic fuzzy time series which is generalization of fuzzy time series models and its experimental result shows that the proposed high-order intuitionistic fuzzy forecasting method gets better forecasting accuracy rates over the existing methods. The proposed method has been implemented on the historical enrollment data at the University of Alabama. The comparison result of these illustration shows that the proposed method has smaller forecasting accuracy rates in terms of MSE and MAPE over than the existing models in fuzzy time series. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
A refined weighted method for forecasting based on type 2 fuzzy time series
(Taylor and Francis Ltd., 2018) Abhishekh; Surendra Singh Gautam; S.R. Singh
In this paper, we proposed a method for type 2 fuzzy time series forecasting which is an extension of type 1 fuzzy time series model to enhance the accuracy in forecasts. The proposed method uses frequency distribution approach to define the appropriate length of intervals. High and low observations are used to define type 2 fuzzy time series and different fuzzy logical relationship groups (FLRGs) have been obtained for both high and low observations. Further, weight function are defined with the help of FLRGs to compute forecasted outputs by a simple arithmetic mean rather than complicated union and intersection operator of type 2 fuzzy sets. The proposed method has been applied for forecasting university enrollments and crop (wheat) production. It is shown that the proposed method has higher accuracy in terms of mean absolute percent error and root-mean-square error (RMSE) as compared to the other fuzzy time series methods. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series
(World Scientific Publishing Co. Pte Ltd, 2018) Abhishekh; Surendra Singh Gautam; S.R. Singh
Intuitionistic fuzzy set plays a vital role in data analysis and decision-making problems. In this paper, we propose an enhanced and versatile method of forecasting using the concept of intuitionistic fuzzy time series (FTS) based on their score function. The developed method has been presented in the form of simple computational steps of forecasting instead of complicated max-min compositions operator of intuitionistic fuzzy sets to compute the relational matrix R. Also, the proposed method is based on the maximum score and minimum accuracy function of intuitionistic fuzzy numbers (IFNs) to fuzzify the historical time series data. Further intuitionistic fuzzy logical relationship groups are defined and also provide a forecasted value and lies in an interval and is more appropriate rather than a crisp value. Furthermore, the proposed method has been implemented on the historical student enrollments data of University of Alabama and obtains the forecasted values which have been compared with the existing methods to show its superiority. The suitability of the proposed model has also been examined to forecast the movement of share market price of State Bank of India (SBI) at Bombay Stock Exchange (BSE). The results of the comparison of MSE and MAPE indicate that the proposed method produces more accurate forecasting results. © 2018 World Scientific Publishing Company.