scholarly journals Markov chain based on neutrosophic numbers in decision making

2021 ◽  
Vol 48 (4) ◽  
Author(s):  
Kuppuswami Govindan ◽  
◽  
Sujatha Ramalingam ◽  
Nagarajan Deivanayagampillai ◽  
Said Broumi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Markov Chain ◽  
Stochastic Model ◽  
Uncertain Information ◽  
New Approach ◽  
Fuzzy Environment ◽  
Future Behavior ◽  
Construction Type ◽  
Fuzzy Probabilities

Markov chain is a stochastic model for estimating the equilibrium of any system. It is a unique mathematical model in which the future behavior of the system depends only on the present. Often biased possibilities can be used over biased probabilities, for handling uncertain information to define Markov chain using fuzzy environment. Indeterminacy is different from randomness due to its construction type where the items involved in the space are true and false in the same time. In this context as an extension of conventional and fuzzy probabilities neutrosophic probability (NP) was introduced. These neutrosophic probabilities can be captured as neutrosophic numbers. In this paper, Markov chain based on neutrosophic numbers is introduced and a new approach to the ergoticity for the traffic states in the neutrosophic Markov chain based on neutrosophic numbers is verified. The proposed approach is applied to decision-making in the prediction of traffic volume.

Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems

2018 ◽  
Vol 29 (1) ◽  
pp. 154-171 ◽  
Author(s):  
Muhammad Sajjad Ali Khan ◽  
Saleem Abdullah ◽  
Asad Ali ◽  
Khaista Rahman
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Information Aggregation ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Fuzzy Environment ◽  
Multidimensional Evaluation

Abstract In this paper, we introduce the concept of the Pythagorean hesitant fuzzy set (PHFS), which is the generalization of the intuitionistic hesitant fuzzy set under the restriction that the square sum of its membership degrees is ≤1. In decision making with PHFSs, aggregation operators play a key role because they can be used to synthesize multidimensional evaluation values represented as Pythagorean hesitant fuzzy values into collective values. Under PHFS environments, Pythagorean hesitant fuzzy ordered weighted averaging and Pythagorean fuzzy ordered weighted geometric operators are used to aggregate the Pythagorean hesitant fuzzy values. The main advantage of these operators is that they provide more accurate and valuable results. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean hesitant fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, we compare the proposed approach to the existing methods.

scholarly journals Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 468 ◽  
Author(s):  
Jiahuan He ◽  
Xindi Wang ◽  
Runtong Zhang ◽  
Li Li
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Project Assessment ◽  
Fuzzy Environment ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs). Second, we propose some new aggregation operators of q-RPFNs based on the newly-developed operations, i.e., the q-rung picture fuzzy Dombi Hamy mean (q-RPFDHM) operator, the q-rung picture fuzzy Dombi weighted Hamy mean (q-RPFDWHM) operator, the q-rung picture fuzzy Dombi dual Hamy mean (q-RPFDDHM) operator, and the q-rung picture fuzzy Dombi weighted dual Hamy mean (q-RPFDWDHM) operator. Properties of these operators are also discussed. Third, a new q-rung picture fuzzy MAGDM method is proposed with the help of the proposed operators. Finally, a best project selection example is provided to demonstrate the practicality and effectiveness of the new method. The superiorities of the proposed method are illustrated through comparative analysis.

The multiple attribute decision model of grey targets based on grey potential degree

2017 ◽  
Vol 7 (3) ◽  
pp. 365-375 ◽  
Author(s):  
Aiqing Ruan ◽  
Yinao Wang
Keyword(s):  
Decision Making ◽  
Decision Model ◽  
Uncertain Information ◽  
New Approach ◽  
Content Type ◽  
Actual Application ◽  
Multiple Attribute ◽  
Decision Making Problem ◽  
Resource Data ◽  
Multiple Resource

Purpose Grey target decision making is one of the important problems of decision-making theory. It is critical to express uncertain information effectively and depose them in a reasonable and simple way. The purpose of this paper is to solve the grey target problem by the grey potential degree method without whiten value and without distribution function. Furthermore, this new approach has an advantage of realizing both comparing and standardization work during the process of treating the data. Design/methodology/approach First, this paper makes a brief overview of the existing method for grey target decision. Then, the conception of a grey potential degree system is introduced and the conception of standard grey potential degree is build up, and a new grey potential-based method based on the grey target multiple attribute decision method is proposed. At the same time, the standard grey potential and its application in multiple resource data are studied. Findings At the same time the standard grey potential and its application in multiple resource data are studied. Standard grey potential is presented by means of three examples together with the comparison with the existing method to demonstrate that the grey potential-based method could be used to solve the problem of grey target decision conveniently and effectively. Originality/value It is very important to compare grey numbers to obtain scientific and reasonable results for a grey target decision-making problem. However, in the actual application of grey numbers, it is difficult to find out the probability density function or the whiten function of grey numbers. When grey numbers are compared and deposed through the whiten value, much information regarding grey numbers will be lost and, at the same time, the value of grey numbers in uncertainty is partly lost. The method discussed in this paper is reasonable and feasible.

scholarly journals Hierarchical Decision-making using a New Mathematical Model based on the Best-worst Method

2019 ◽  
Vol 14 (6) ◽  
pp. 710-725 ◽  
Author(s):  
Mohammad Hashemi Tabatabaei ◽  
Maghsoud Amiri ◽  
Mohammad Ghahremanloo ◽  
Mehdi Keshavarz-Ghorabaee ◽  
Edmundas Kazimieras Zavadskas ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Evaluation Methodology ◽  
Hierarchical Decision Making ◽  
New Approach ◽  
Multi Criteria Evaluation ◽  
Proposed Model ◽  
Hierarchical Decision ◽  
Decision Making Processes ◽  
Best Worst Method

Decision-making processes in different organizations often have a hierarchical and multilevel structure with various criteria and sub-criteria. The application of hierarchical decision-making has been increased in recent years in many different areas. Researchers have used different hierarchical decision-making methods through mathematical modeling. The best-worst method (BWM) is a multi-criteria evaluation methodology based on pairwise comparisons. In this paper, we introduce a new hierarchical BWM (HBWM) which consists of seven steps. In this new approach, the weights of the criteria and sub-criteria are obtained by using a novel integrated mathematical model. To analyze the proposed model, two numerical examples are provided. To show the performance of the introduced approach, a comparison is also made between the results of the HBWM and BWM methodologies. The analysis demonstrates that HBWM can effectively determine the weights of criteria and sub-criteria through an integrated model.

Multiple-attribute decision making method based on power generalized maclaurin symmetric mean operators under normal wiggly hesitant fuzzy environment

2021 ◽  
pp. 1-26
Author(s):  
Peide Liu ◽  
Pei Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Hesitant Fuzzy Set ◽  
Uncertain Information ◽  
Fuzzy Environment ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Special Cases ◽  
The Impact

A normal wiggly hesitant fuzzy set is a very useful tool to mine the potential uncertain information given by decision makers, which is considered as an extension of hesitant fuzzy set and can improve the effectiveness of decision making. Power average operator can relieve the impact on decision result of unreasonable data, and the generalized Maclaurin symmetric mean operator (GMSM) is an extension of Maclaurin symmetric mean operator with wider range of applications, which can consider the relationship among decision attributes. By integrating the advantages of them, in this paper, we develop the normal wiggly hesitant fuzzy power GMSM (NWHFPGMSM) operator and its weighted form based on the distance measure of two normal wiggly hesitant fuzzy elements, then we further discuss their properties and some special cases. Thus, a new multi-attribute decision making method based on the NWHFPGMSM operator under normal wiggly hesitant fuzzy environment is proposed. Finally, we select some examples to illustrate the effectiveness and superiority of the proposed method in this paper through comparison and analysis with other methods.

scholarly journals STOCHASTIC MODEL OF RISK MANAGEMENT OPTIMIZATION

2021 ◽  
Author(s):  
Iryna Debela
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Risk Management ◽  
Stochastic Model ◽  
Human Factor ◽  
New Technologies ◽  
Mathematical Formulation ◽  
Markov Property ◽  
Management Decision ◽  
Economic Risk

Economic activity of economic entities is associated with the constant search for effective management solutions: the optimal option for the allocation of resources, promising areas of development, the feasibility of introducing new technologies and developing new markets. Complications of internal and external relationships, the presence of a large number of unpredictable indicators limit the activities of an individual enterprise, do not allow to form an optimal strategy for the development of economic objects without the use of specific management methods and models. The basis for modeling management systems, including modeling of priority areas of agricultural sector, is to build a mathematical model. An adequate mathematical model must take into account the dynamics, stochastic uncertainty and unstructured management processes of economic objects, which is quite difficult to implement. In addition, the task of management and decision-making always contains a group of non-material, qualitative factors that are difficult to formalize, describe in quantitative terms, but which certainly have a decisive influence on the quality of the decision. Such "factors of influence" include the human factor. The result of human behavior can nullify any optimal solution, based on any adequate mathematical model. Accordingly, the mathematical model should also take into account the risk impact of the human factor, in the context of the entire management decision-making process. For management system models, there are a number of unresolved formalization and risk considerations. Mathematical formulation of the problem of optimizing economic risk management, as a rule, begins with the formalization of input parameters, qualitative and quantitative estimates of model variables, selection of mathematical tools. The information base of optimization models is the preliminary analytical and statistical indicators of the dynamics of the studied economic object. The article investigates the stochastic model of economic risk management. The set of implementations of random processes is considered as a limited set of random variables with a Markov property, which formalizes the problem of risk management, as a random process of obtaining the predicted benefit.

Uncertainty evaluations through interval-valued Pythagorean hesitant fuzzy Archimedean aggregation operators in multicriteria decision making

2021 ◽  
pp. 1-29
Author(s):  
Arun Sarkar ◽  
Nayana Deb ◽  
Animesh Biswas
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Uncertain Information ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Multicriteria Decision ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Interval Valued

In many cases, use of Pythagorean hesitant fuzzy sets may not be sufficient to characterize uncertain information associated with decision making problems. From that view point the concept of interval-valued Pythagorean hesitant fuzzy sets are introduced in this paper. Considering the flexibility with the general parameters, Archimedean t-conorms and t-norms are applied to develop several operational laws in interval-valued Pythagorean hesitant fuzzy environment. Some characteristics of the developed operators are presented. The newly developed operators are used to derive a methodology for solving multicriteria decision making problems with interval-valued Pythagorean hesitant fuzzy information. Finally, two illustrative examples are provided to establish the validity of the proposed approach and are compared with the existing technique to exhibit its flexibility and effectiveness.

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