Spherical fuzzy sets and spherical fuzzy TOPSIS method

Multicriteria decision-making (MCDM) refers to making decisions in the presence of multiple and usually conflicting criteria. Fuzzy decision-making is used where vague and incomplete data exist for the solution. Fuzzy multicriteria decision-making is one of the most popular problems handled by the researchers in the literature. In this paper, we survey the latest status of fuzzy multicriteria decision-making methods and classify these methods dividing into two parts: fuzzy multiattribute decision-making (MADM) and fuzzy multiobjective decision-making (MODM). Most of the publications are on fuzzy MADM since there are a plenty of classical multiattribute decision-making methods in the literature. Tabular and graphical illustrations for each method are given.

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Fuzzy Multicriteria Decision-Making: A Literature Review

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets SNSs have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers SNNs and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making MCGDM problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.

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Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

In recent years several previous scholars made attempts to develop, extend, propose and apply Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for solving problems in decision making issues Indeed, there are questions, how TOPSIS can help for solving these problems? Or does TOPSIS solved decision making problems in the real world? Therefore, this study shows the recent developments of TOPSIS approach which are presented by previous scholars To achieve this objective, there are 105 reviewed papers which developed, extended, proposed and presented TOPSIS approach for solving DM problems The results of the study indicated that 49 scholars have extended or developed TOPSIS technique and 56 scholars have proposed or presented new modifications for problems solution related to TOPSIS technique from 2000 to 2015 In addition, results of this study indicated that, previous studies have modifications related to this technique in 2011 more than other years

Development of TOPSIS Method to Solve Complicated Decision-Making Problems — An Overview on Developments from 2000 to 2015

The novel operations of simplified neutrophic numbers (SNNs) and relational properties are developed.Some outranking relations for SNNs are defined based on ELECTRE, and properties among the outranking relations are further discussed in detail.Based on the outranking relations of SNNs, the ranking approach is developed to handle MCDM problems. In this paper, a new outranking approach for multi-criteria decision-making (MCDM) problems is developed in the context of a simplified neutrosophic environment, where the truth-membership degree, indeterminacy-membership degree and falsity-membership degree for each element are singleton subsets in 0,1. Firstly, the novel operations of simplified neutrosophic sets (SNSs) and relational properties are developed. Then some outranking relations for simplified neutrosophic number (SNNs) are defined, based on ELECTRE, and the properties within the outranking relations are further discussed in detail. Additionally, based on the outranking relations of SNNs, a ranking approach is developed in order to solve MCDM problems. Finally, two practical examples are provided to illustrate the practicality and effectiveness of the proposed approach. Moreover, a comparison analysis based on the same example is also conducted.

An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets

Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making

Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making

We propose a fuzzy time series forecasting method using hesitant fuzzy sets.An aggregation operator is also proposed to aggregate hesitant fuzzy elements.Hesitancy is introduced by using multiple fuzzification methods.University of Alabama enrollments and SBI share prices are forecasted.Performance of method is measured in terms of MSE and AFER. This study proposes a fuzzy time series forecasting method based on hesitant fuzzy sets for forecasting in the environment of hesitant information. The proposed method addresses the problem of establishing a common membership grade for the situation when multiple fuzzification methods are available to fuzzify time series data. An aggregation operator for aggregating hesitant information is also proposed in the study. The proposed method is implemented to forecast enrollment at University of Alabama and price of state bank of India (SBI) share at Bombay stock exchange (BSE), India. In both time series data are fuzzified with triangular fuzzy sets constructed using intervals of equal and unequal length. The performance of the proposed method in forecasting student enrollments and SBI share price is measured in terms of root mean square and average forecasting errors. Statistical validation and performance analysis is also carried out to validate the proposed forecasting method.

Fuzzy time series forecasting method based on hesitant fuzzy sets

Fuzzy time series models are of great interest in forecasting when the information is imprecise and vague. However, the major problem in fuzzy time series forecasting is the accuracy of the forecasted values. In the present study we propose a hybrid method of forecasting based on fuzzy time series and intuitionistic fuzzy sets. The proposed model is a simplified computational approach that uses the degree of nondeterminacy to establish fuzzy logical relations on time series data. The developed model was implemented on the historical enrollment data for the University of Alabama and the forecasted values were compared with the results of existing methods to show its superiority. The suitability of the proposed method was also examined in forecasting market share prices of the State Bank of India on the Bombay Stock Exchange, India.

Intuitionistic fuzzy sets based method for fuzzy time series forecasting

Atanassov introduced the notion of intuitionistic fuzzy set as generalization of the fuzzy set, which has been proved to be very useful tool in handling nondeterminacy (hesitation) in the system. In the implementation of fuzzy time series forecasting, nondeterminacy is always neglected without any reason. In this paper, we give the notion of intuitionistic fuzzy time series to handle the nondeterminism in time series forecasting. An intuitionistic fuzzy time series forecasting model is also proposed. The proposed intuitionistic fuzzy time series forecasting method uses intuitionistic fuzzy logical relations on time series data. Performance of the proposed method is verified by applying it on two time series data. The effectiveness of the proposed intuitionistic fuzzy time series forecasting method is verified by comparing the forecasted output with other intuitionistic-fuzzy-set-based fuzzy time series forecasting methods using root-mean-square error and average forecasting error.

Sanjay Kumar

Papers

Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making

Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making

Fuzzy time series forecasting method based on hesitant fuzzy sets

Intuitionistic fuzzy sets based method for fuzzy time series forecasting

Intuitionistic Fuzzy Time Series: An Approach for Handling Nondeterminism in Time Series Forecasting