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 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 Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hong-yu Zhang ◽  
Jian-qiang Wang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
The Real ◽  
Comparison Approach ◽  
Interval 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. 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.

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 Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1012
Author(s):  
Subhadip Roy ◽  
Jeong-Gon Lee ◽  
Anita Pal ◽  
Syamal Kumar Samanta
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measures ◽  
Distance Measures ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Decision Making Problem ◽  
Definition Of ◽  
Bipolar Fuzzy Sets

In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.

scholarly journals Hybrid MCDM Based on VIKOR and Cross Entropy under Rough Neutrosophic Set Theory

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1334
Author(s):  
Katarina Rogulj ◽  
Jelena Kilić Kilić Pamuković ◽  
Majda Ivić
Keyword(s):  
Decision Making ◽  
Strategic Planning ◽  
Set Theory ◽  
Real Life ◽  
Multicriteria Decision Making ◽  
Strategic Decision ◽  
Cross Entropy ◽  
Neutrosophic Set ◽  
Multicriteria Decision ◽  
Pedestrian Bridges

Problems in real life usually involve uncertain, inconsistent and incomplete information. An example of such problems is strategic decision making with respect to remediation planning of historic pedestrian bridges. The multiple decision makers and experts, as well as the various mutually conflicting criteria, unknown criteria weights, and vagueness and duality in final decisions, provide motivation to develop a methodology that is able to resist the challenges implicit in this problem. Therefore, the aim of this research was to propose an algorithm based on the theory of rough neutrosophic sets in order to solve the problem of strategic planning with respect to the remediation of historic pedestrian bridges. A new multicriteria decision-making model is developed that is a fusion of rough set and neutrosophic set theory. A new cross entropy is proposed under a rough neutrosophic environment that does not possess the shortcomings of asymmetrical character and unknown occurrences. Additionally, a weighted rough neutrosophic symmetric cross entropy is proposed. Furthermore, a rough neutrosophic VIKOR method is introduced, with which the values of the utility measure, regret measure and VIKOR index are obtained. These values, as well as the weighted rough neutrosophic symmetric cross entropy measure, are used to provide a ranking of historic pedestrian bridges favorable to remediation. Finally, an illustrative example of the strategic planning of remediation for historic pedestrian bridges is solved and compared to other research, demonstrating the robustness, feasibility and efficacy of the model when dealing with complex multicriteria decision-making processes.

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.

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