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 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 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 Multicriteria Decision Making Method Based on the Higher Order Hesitant Fuzzy Soft Set

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
B. Farhadinia
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Multicriteria Decision Making ◽  
Higher Order ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Soft Set ◽  
Multicriteria Decision ◽  
Special Cases

The main goal of this contribution is to introduce the concept of higher order hesitant fuzzy soft set as an extension of fuzzy soft set that encompasses most of the existing extensions of fuzzy soft set as special cases. Furthermore, this new concept provides us with a method for dealing with multicriteria fuzzy decision making problems which are difficult to explain in other existing extensions of fuzzy soft set theory, especially when problems involve parameters with different-dimensional levels.

scholarly journals Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

2020 ◽  
Author(s):  
Shigui Du ◽  
Jun Ye ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Multicriteria Decision Making ◽  
Neutrosophic Set ◽  
Human Knowledge ◽  
Multicriteria Decision ◽  
Business Partners ◽  
Weighted Arithmetic ◽  
New Framework

Abstract As the generalization of the classical fuzzy number, the concept of Z-number introduced by Zadeh indicates more ability to depict the human knowledge and judgments of both restraint and reliability as an order pair of fuzzy numbers. In indeterminacy and inconsistent environment, a neutrosophic set is described by the truth, falsity, and indeterminacy degrees, but they lack measures related to reliability. To describe the hybrid information of combining the truth, falsity and indeterminacy degrees with their corresponding reliability degrees, this paper first proposes the concept of a neutrosophic Z-number (NZN) set, which is a new framework of neutrosophic values combined with the neutrosophic measures of reliability, as the generalization of the Z-number and the neutrosophic set. Then, we define the operations of neutrosophic Z-numbers (NZNs) and a score function for ranking NZNs. Next, we present NZN weighted arithmetic averaging (NZNWAA) and NZN weighted geometric averaging (NZNWGA) operators to aggregate NZN information and investigate their properties. Regarding the NZNWAA and NZNWGA operators and the score function, a multicriteria decision making (MDM) approach is developed in the NZN environment. Finally, an illustrative example about the selection problem of business partners is given to demonstrate the applicability and effectiveness of the developed MDM approach in NZN setting.

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