Multicriteria Decision-Making Method Under a Single Valued Neutrosophic Environment

2017 ◽  
Vol 13 (4) ◽  
pp. 23-37 ◽  
Author(s):  
Shapu Ren
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
Ranking Order ◽  
Dice Similarity Measure

A single valued neutrosophic set (SVNS) is a subclass of neutrosophic sets, which generalizes fuzzy sets, interval valued fuzzy set, and intuitionistic fuzzy set. It can be used to easily express incomplete, indeterminate and inconsistent information. This paper introduces the Dice similarity measure of single valued neutrosophic numbers (SVNNs) for ranking SVNNs and a single valued neutrosophic prioritized weighted geometric (SVNPWG) operator for aggregating single valued neutrosophic information. Based on the SVNPWG operator and the Dice similarity measure for SVNNs, a multicriteria decision-making method with different priority levels in the criteria is established in which the evaluation values of alternatives with respective to criteria are represented in the form of SVNNs. The ranking order of alternatives is performed through the Dice measure and the best one(s) can be determined as well. Finally, an illustrative example shows the application of the proposed method.

scholarly journals An Extended EDAS Method for Multicriteria Decision-Making Based on Multivalued Neutrosophic Sets

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Lili Han ◽  
Cuiping Wei
Keyword(s):  
Decision Making ◽  
Belief Systems ◽  
Intuitionistic Fuzzy Set ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Parameter Analysis ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
Comprehensive Evaluations

Neutrosophic set (NS) is a generalization of intuitionistic fuzzy set (IFS). It depicts not only the incomplete information but also the indeterminate information and inconsistent information which exist commonly in belief systems. In this paper, the evaluation based on distance from average solution (EDAS) method is extended to handle multicriteria decision-making problems with multivalued neutrosophic numbers (MVNNs). The average solution under all the criteria is calculated by the proposed convex weighted average operator of MVNNs. Then, the positive distance and the negative distance from each solution to the average solution are calculated, and the comprehensive evaluations of alternatives are obtained by integrating two kinds of distance values to get the ranking result. Finally, the rationality and efficiency of the proposed method are shown by the parameter analysis and comparisons with some existing methods.

scholarly journals Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods

2015 ◽  
Vol 15 (4) ◽  
pp. 13-26 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Cross Entropy ◽  
Entropy Measure ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
Entropy Measures ◽  
The Cross ◽  
Ranking Order ◽  
Interval Neutrosophic Sets

Abstract Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued neutrosophic cross entropy indicates an asymmetrical phenomenon or may produce an undefined (unmeaningful) phenomenon in some situations. In order to overcome these disadvantages, this paper proposes an improved cross entropy measure of SVNSs and investigates its properties, and then extends it to a cross entropy measure between interval neutrosophic sets (INSs). Furthermore, the cross entropy measures are applied to multicriteria decision making problems with single valued neutrosophic information and interval neutrosophic information. In decision making methods, through the weighted cross entropy measure between each alternative and the the ideal alternative, one can obtain the ranking order of all alternatives and the best one. The decision-making methods using the proposed cross entropy measures can efficiently deal with decision making problems with incomplete, indeterminate and inconsistent information which exist usually in real situations. Finally, two illustrative examples are provided to demonstrate the application and efficiency of the developed decision making approaches under single valued neutrosophic and interval neutrosophic environments.

scholarly journals Distance Based Entropy Measure of Interval-Valued Intuitionistic Fuzzy Sets and Its Application in Multicriteria Decision Making

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Tabasam Rashid ◽  
Shahzad Faizi ◽  
Sohail Zafar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Fuzzy entropy means the measurement of fuzziness in a fuzzy set and therefore plays a vital role in solving the fuzzy multicriteria decision making (MCDM) and multicriteria group decision making (MCGDM) problems. In this study, the notion of the measure of distance based entropy for uncertain information in the context of interval-valued intuitionistic fuzzy set (IVIFS) is introduced. The arithmetic and geometric average operators are firstly used to aggregate the interval-valued intuitionistic fuzzy information provided by the decision makers (DMs) or experts corresponding to each alternative, and then the fuzzy entropy of each alternative is calculated based on proposed distance measure. Several numerical examples are solved to demonstrate the application to MCDM and MCGDM problems to show the effectiveness of the proposed approach.

Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy and Indeterminacy Based Cross Entropy

2016 ◽  
Vol 859 ◽  
pp. 129-143 ◽  
Author(s):  
Ilanthenral Kandasamy ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Cross Entropy ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
Inconsistent Information ◽  
Decision Making Problem ◽  
The Cross

Double Refined Indeterminacy Neutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache (2013), which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into two, based on membership; as indeterminacy leaning towards truth membership (IT) and indeterminacy leaning towards false membership (IF). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular case of the refined neutrosophic set (where each T, I, F can be refined into T1, T2, ...; I1, I2, ...; F1, F2, ...). DRINS is better equipped at dealing indeterminate and inconsistent information, with more accuracy than SVNS, which fuzzy sets and Intuitionistic Fuzzy Sets (IFS) are incapable of. Based on the cross entropy of neutrosophic sets, the cross entropy of DRINSs, known as Double Refined Indeterminacy neutrosophic cross entropy, is proposed in this paper. This proposed cross entropy is used for a multicriteria decision-making problem, where the criteria values for alternatives are considered under a DRINS environment. Similarly, an indeterminacy based cross entropy using DRINS is also proposed. The double valued neutrosophic weighted cross entropy and indeterminacy based cross entropy between the ideal alternative and an alternative is obtained and utilized to rank the alternatives corresponding to the cross entropy values. The most desirable one(s) in decision making process is selected. An illustrative example is provided to demonstrate the application of the proposed method. A brief comparison of the proposed method with the existing methods is carried out.

scholarly journals Generalized Weighted Exponential Similarity Measures of Single Valued Neutrosophic Sets

2019 ◽  
pp. 57-66
Author(s):  
Abhijit .. ◽  
◽  
◽  
Arnab Paul
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Fuzzy Set ◽  
Investment Decision ◽  
Uncertain Data ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Neutrosophic Set ◽  
Pythagorean Fuzzy Set ◽  
Neutrosophic Sets

A single valued neutrsophic set is one of the most successful extensions of the classical set, fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set and q-rung orthopair fuzzy set due to the fact that it can handle uncertain data in more wider way. In this paper, we introduce some new generalized weighted similarity measures based on the exponential functions defined on truth-membership function, indeterminacy membership function and falsity membership function of a single valued neutrosophic set to study the independent influences of the truth-membership function, indeterminacy membership function and falsity membership function. The salient features of these proposed similarity measures are studied in detail. Based on the proposed similarity measures, we propose a multi attribute decision making method. To show the feasibility and effectiveness of the proposed method, an investment decision making problem is demonstrated.

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