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

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets

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.

/pdf/interval-neutrosophic-sets-and-their-application-in-apox56c6cy.pdf

Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

Topology vs generalized rough sets

Highlights? A new approach to solve multi-attribute decision making problems in intuitionistic fuzzy environment. ? The same alternative with different attributes are considered as one unified entity. ? A revised score function and a revised accuracy function of intuitionistic fuzzy sets based on human intuition. ? The degree of membership, the degree of nonmembership and the degree of hesitation are with various importance. ? An optimization model is established to estimate the relative degree of importance. In this paper we present a new approach to solve multi-attribute decision making problems in intuitionistic fuzzy environment. This approach is based on a new ranking method of intuitionistic fuzzy sets, in which the evaluated values (in the form of intervals) of the same alternative with different attributes are considered as one unified entity. According to people's intuition, the ranking method proposed in this paper is mainly grounded on a revised score function and a revised accuracy function of intuitionistic fuzzy sets. Different from the traditional methods, in this new approach, the degree of membership, the degree of nonmembership and the degree of hesitation are considered with various importance in reflecting the true image of the respective alternative. Furthermore, an optimization model is established to estimate the relative degree of importance of each quantity. Finally, two practical examples are provided to illustrate our approach.

A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets

Rational decision making models with incomplete weight information for production line assessment

Graphical abstractThese figures demonstrate the areas where the extended fuzzy TOPSIS method cannot manage to differentiate the alternatives. The TOPSIS method is based on the ratio formula (11), various λ values can cause the shape to change dramatically. Display Omitted HighlightsThe ranking ambiguity of the extended fuzzy TOPSIS method in MADM is revealed.Graphical interpretations are demonstrated to fully stress the ranking inadequacy.Two supplemental indexes are formulated to assist the extended fuzzy TOPSIS method.The sufficiency of the two indexes plus the original fuzzy TOPSIS method is proved.Impacts caused by the factors such as alternative quantity are discussed. The TOPSIS method, commonly known as the technique for order preference by similarity to ideal solutions, is one of the most popular approaches used in multi-attribute decision making (MADM). The fundamental procedure of the traditional TOPSIS method is rather straightforward, the ranking position of an alternative depends on its relative closeness to the positive ideal solution and the negative ideal solution, respectively. In order to encompass uncertain and ambiguous decision elements, an extension of the original TOPSIS method has been coined. With the help of fuzzy sets based TOPSIS, an overwhelming trend of fuzzy decision making applications has been witnessed. In the present work, however, it is found that the extended fuzzy TOPSIS method is unable to distinguish all the different alternatives under linguistic environment. Moreover, the undistinguishable alternatives are countless in quantity, and they have formed specific patterns with respect to the parameters of TOPSIS methods. To dampen this ranking ambiguity, we designed a set of supplemental methods to construct a revised TOPSIS approach with linguistic evaluations. Correspondingly, the sufficiency of the revised TOPSIS method to guarantee total orders has been proven. Furthermore, a numerical example concerning the production line improvement of a manufacturing company is demonstrated to validate the feasibility and supremacy of the proposed method. Finally, a series of further discussions are performed to shed some lights on the impacts caused by the changes of the alternative quantity, the attribute quantity, and the type of linguistic term.

A note on the TOPSIS method in MADM problems with linguistic evaluations

A new form of fuzzy variable, the intuitionistic fuzzy variable, is introduced.A three level fuzzy dominance model is developed with a sufficiency proof.Two distance based methods are proposed to apply the TOPSIS method.The proposed methods are analyzed via consistency and sensitivity. The present paper aims at advancing the well-recognized uncertainty theory built upon the credibility measure. In face of the increasing level of uncertainty embedded within the real world problem solving, it is discovered that the fuzzy variables defined in the credibility space are far from adequate to reflect the hesitance incurred during decision making. Although more complex fuzzy quantities are introduced, such as the fuzzy possibility space based type-2 fuzzy variables, the area of intuitionistic fuzzy variables is still a largely unexplored territory. Therefore, a novel concept of intuitionistic fuzzy variable is introduced hereby as an attempt to extend the uncertainty theory, which possesses a decent self-dual property compared with the fuzzy set theory. Unlike the intuitionistic fuzzy set theory, which has been widely implemented in various application fields, the intuitionistic fuzzy variables have hardly been employed in practices, especially the decision making sector. To bridge the gap, three outranking methods are developed to help evaluate intuitionistic fuzzy variables. The sufficient conditions of the three methods in distinguishing different fuzzy variables are also proved in the present work. The benefits of ranking with the three methods include the minimum amount of defuzzification, which prevents the information loss to a significant extent. Furthermore, in order to validate the proposed methods, a numerical study is performed. And the consistency of the ranking outputs from the three proposed methods is analyzed afterward. Besides, several managerial insights are presented regarding the sensitivity analysis of each ranking method.

Zhi Pei

Papers

Topology vs generalized rough sets

A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets

Rational decision making models with incomplete weight information for production line assessment

A note on the TOPSIS method in MADM problems with linguistic evaluations

Intuitionistic fuzzy variables