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

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

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world.

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Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decision making method. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

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Interval neutrosophic sets and their application in multicriteria decision making problems.

In this paper, a novel outranking approach for multi-criteria decision-making (MCDM) problems is proposed to address situations where there is a set of numbers in the real unit interval and not just a specific number with a neutrosophic set. Firstly, the operations of interval neutrosophic sets and their related properties are introduced. Then some outranking relations for interval neutrosophic numbers (INNs) are defined based on ELECTRE IV, and the properties of the outranking relations are further discussed in detail. Additionally, based on the outranking relations of INNs, 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 examples is also conducted.

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

Interval valued q-rung orthopair fuzzy sets and their properties

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

The concept of q‐rung orthopair fuzzy set (q‐ROFS) is the extension of intuitionistic fuzzy set (IFS) in which the sum of the qth power of the support for and the qth power of the support against is bounded by one. Therefore, the q‐ROFSs are an important way to express uncertain information in broader space, and they are superior to the IFSs and the Pythagorean fuzzy sets. In this paper, the familiarity degree of the experts with the evaluated objects is incorporated to the initial assessments under q‐rung orthopair fuzzy environment. For this, some aggregation operators are proposed to combine these two types of information. Their some important properties are also well proved. Furthermore, these developed operators are utilized in a multicriteria decision‐making approach and demonstrated with a real life problem of customers' choice. Then, the experimental results are compared with other existing methods to show its superiority over recent research works.

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Confidence levels q-rung orthopair fuzzy aggregation operators and its applications to MCDM problems

Intuitionistic fuzzy sets introduced by Atanassov are generalization of fuzzy sets as they also handle the non-determinacy which is caused by degree of hesitation of decision maker. The present study proposes a computational method of forecasting for fuzzy time series. In the proposed method the notion of intuitionistic fuzzy set is used in fuzzy time series forecasting with simplified computational approach. The developed model has been tested on the movement of share market prices of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India. Further the method has been implemented for forecasting SENSEX of BSE. The suitability of the developed model has also been examined by comparing it with the other existing models to show its superiority.

Fuzzy Time Series Model Based on Intuitionistic Fuzzy Sets for Empirical Research in Stock Market

Present study proposes a method for fuzzy time series forecasting based on difference parameters. The developed method has been presented in a form of simple computational algorithm. It utilizes various difference parameters being implemented on current state for forecasting the next state values to accommodate the possible vagueness in the data in an efficient way. The developed model has been simulated on the historical student enrollments data of University of Alabama and the obtained forecasted values have been compared with the existing methods to show its superiority. Further, the developed model has also been implemented in forecasting the movement of market prices of share of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India.

Bhagawati Prasad Joshi

Papers

Interval valued q-rung orthopair fuzzy sets and their properties

Intuitionistic fuzzy sets based method for fuzzy time series forecasting

Confidence levels q-rung orthopair fuzzy aggregation operators and its applications to MCDM problems

Fuzzy Time Series Model Based on Intuitionistic Fuzzy Sets for Empirical Research in Stock Market

A computational method for fuzzy time series forecasting based on difference parameters