Fuzzy Multi-Criteria Assignment Problems Using Two-Dimensional Fuzzy Soft Set Theory

Author(s):  
Shyamal Kumar Mondal

In this chapter, author has introduced a new concept of two-dimensional fuzzy soft sets together with various operations, properties and theorems on them. Then, an algorithm named 2-DFS has been developed for solving fuzzy multi-criteria assignment problems with multiple decision makers. The performance of this newly proposed method is verified by the popular Hungarian Method in case of solving fuzzy assignment problems with single criterion and single decision maker. By Hungarian Method, one may only solve fuzzy assignment problems with single criterion and single decision maker, in the contrary the advantage of our 2-DFS Algorithm is that by it, any fuzzy assignment problem with any number of criteria and any number of decision makers can be solved effectively. At last,2- DFS Algorithm is applied for solving fuzzy multi-criteria assignment problems in medical science to evaluate the effectiveness of different modalities of treatment of a disease.

Author(s):  
Orhan Dalkiliç

AbstractWith the generalization of the concept of set, more comprehensive structures could be constructed in topological spaces. In this way, it is easier to express many relationships on existing mathematical models in a more comprehensive way. In this paper, the topological structure of virtual fuzzy parametrized fuzzy soft sets is analyzed by considering the virtual fuzzy parametrized fuzzy soft set theory, which is a hybrid set model that offers very practical approaches in expressing the membership degrees of decision makers, which has been introduced to the literature in recent years. Thus, it is aimed to contribute to the development of virtual fuzzy parametrized fuzzy soft set theory. To construct a topological structure on virtual fuzzy parametrized fuzzy soft sets, the concepts of point, quasi-coincident and mapping are first defined for this set theory and some of its characteristic properties are investigated. Then, virtual fuzzy parametrized fuzzy soft topological spaces are defined and concepts such as open, closed, closure, Q-neighborhood, interior, base, continuous, cover and compact are given. In addition, some related properties of these concepts are analyzed. Finally, many examples are given to make the paper easier to understand.


2020 ◽  
Vol 30 (1) ◽  
pp. 59-70
Author(s):  
Shehu Mohammed ◽  
Akbar Azam

The notion of soft set theory was initiated as a general mathematical tool for handling ambiguities. Decision making is viewed as a cognitive-based human activity for selecting the best alternative. In the present time, decision making techniques based on fuzzy soft sets have gained enormous attentions. On this development, this paper proposes a new algorithm for decision making in fuzzy soft set environment by hybridizing some existing techniques. The first novelty is the idea of absolute scores. The second concerns the concept of priority table in group decision making problems. The advantages of our approach herein are stronger power of objects discrimination and a well-determined inference.


2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
B. Ahmad ◽  
Athar Kharal

We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.


2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Anubha Taneja Mukherjee

Decision making is an inherently complicated procedure, which by its very nature requires the decision-maker to co-opt all the stakeholders concerned. The procedure of decision-making may vary from country to country, depending on its size, culture, history and special demographic circumstances. Around the world, key decision-makers include the executive, the legislature and the judiciary. While the distribution of powers between these three may vary in tandem with their relation to each other, their roles remain the same. While the legislature enacts laws for its citizens, the executive, popularly known as the government, implements these laws and while doing so promulgates policies that are in alignment with the said laws. Mostly, the executive is also authorised to promulgate some laws of its own. The judiciary, on the other hand, comes into the picture when there is a dispute with regard to such laws. It also steps in on its own at times. While settling such disputes, the judiciary also ends up setting what we know as precedents, which also become a part of the legal fabric of a society. In a nutshell, these three are the key decision makers in any country. As mentioned above, while making decisions, these authorities are mostly required to co-opt all the stakeholders concerned, thereby making decision making a consultative process. These stakeholders include think tanks, research bodies, media and most importantly the affected party. The reason for having such a consultative procedure in place is that the decision makers are not experts in every subject or issue that comes their way. For instance, when a need to promulgate a national policy on thalassemia presents itself to a certain government, whether it be owing to media reportage or representations from the civil society, the decision makers will look towards people considered to be the experts in the subject to come forward and be a part of the policy making. One could say that this sounds like an ideal situation where the government actually invites people concerned with thalassemia to come forward and share views about it for the purpose of policy making. It is, however, true! It is as true for India as it is for any developed country. What we must ensure then is that the government or the decision maker considers us, the patients, as the experts. While it does sound obvious that those impacted with the disorder would be the ones with the first-hand knowledge about the disorder, the very fact that there is a topic in this conference on the role of patients in decision making speaks volumes about the distance that remains to be covered by the patients of thalassemia as far as participation in decision-making is concerned. With the massive strides in the field of medical science and the unflinching support of organisations like Thalassemia International Federation (TIF), we have now reached the stage where we must step out of the victim mode and represent ourselves before the decision-makers, whether by forming Patients Advocacy Groups or otherwise. One may take cue from various associations around the world. Global HD Organisations are a good example. They are known to have got together to give patients a voice in clinical research. The most popular strategy for reaching out to the decision makers is to unite, engage, and partner both in private meetings and consultative fora like events, task forces and projects. “Unite, Engage & Partner” can therefore be the most successful mantra for engaging with the decision makers. Talking of examples of advocacy and participation by patients, while there are numerous examples in Europe and North America of the power of patient advocacy so much so that patients are on the same level as doctors when it comes to voicing opinions in policy making, TIF on an international level has created since 2009 the Expert Patients Programme, and is now moving forward in giving patients a voice through its educational platform. Recently, India also launched its first Thalassemia Patients Advocacy Group (PAG) in the august presence of the Deputy Chief Minister of the capital of the country. The India PAG has seven patients from the fields of law, psychology, education and IT. The Group is already involved with the government on the formulation of the National Thalassemia Policy. This is a great start and this should give enough and more encouragement to thalassemics across the world to UNITE, ENGAGE AND PARTNER in the process that impacts them the most – decision-making!


Author(s):  
Samsiah Abdul Razak ◽  
Daud Mohamad

The introduction of soft set theory by Molodstov has gained attention by many as it is useful in dealing with uncertain data. It is advantageous to use due to its parameterization form of data. This concept has been used in solving many decision making problems and has been generalized in various aspects in particular to fuzzy soft set (FSS) theory. In decision making using FSS, the objective is to select an object from a set of objects with respect to a set of choice parameter using fuzzy values. Although FSS theory has been extensively used in many applications, the importance of weight of parameters has not been highlighted and thus is not incorporated in the calculation. As it depends on one’s perception or opinion, the importance of the parameters may differ from one decision maker to another. Besides, existing methods in FSS only consider one or two decision makers to select the alternatives. In reality, group decision making normally involves more than two decision makers. In this paper we present a method for solving group decision making problems that involves more than two decision makers based on fuzzy soft set by taking into consideration the weight of parameters. The method of lambda – max which frequently utilize in fuzzy analytic hierarchy process (FAHP) has been applied to determine the weight of parameters and an algorithm for solving decision making problems is presented. Finally we illustrate the effectiveness of our method with a numerical example.


2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao

Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. In this paper, by introducing a generalization parameter, which itself is trapezoidal fuzzy, we define generalized trapezoidal fuzzy soft sets and then study some of their properties. Finally, applications of generalized trapezoidal fuzzy soft sets in a decision making problem and medical diagnosis problem are shown.


Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1575
Author(s):  
Mabruka Ali ◽  
Adem Kiliçman ◽  
Azadeh Zahedi Khameneh

Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the literature. However, these algorithms are not able to overcome the issue of comparable alternatives and, in fact, might be ignored due to the lack of a comprehensive priority approach. In order to provide a partial solution to this problem, we present a group decision-making solution which is based on a preference relationship of interval-valued fuzzy soft information. Further, corresponding to each parameter, two crisp topological spaces, namely, lower topology and upper topology, are introduced based on the interval-valued fuzzy soft topology. Then, using the preorder relation on a topological space, a score function-based ranking system is also defined to design an adjustable multi-steps algorithm. Finally, some illustrative examples are given to compare the effectiveness of the present approach with some existing methods.


Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 621 ◽  
Author(s):  
Majdoleen Qamar ◽  
Nasruddin Hassan

Neutrosophic triplet structure yields a symmetric property of truth membership on the left, indeterminacy membership in the centre and false membership on the right, as do points of object, centre and image of reflection. As an extension of a neutrosophic set, the Q-neutrosophic set was introduced to handle two-dimensional uncertain and inconsistent situations. We extend the soft expert set to generalized Q-neutrosophic soft expert set by incorporating the idea of soft expert set to the concept of Q-neutrosophic set and attaching the parameter of fuzzy set while defining a Q-neutrosophic soft expert set. This pattern carries the benefits of Q-neutrosophic sets and soft sets, enabling decision makers to recognize the views of specialists with no requirement for extra lumbering tasks, thus making it exceedingly reasonable for use in decision-making issues that include imprecise, indeterminate and inconsistent two-dimensional data. Some essential operations namely subset, equal, complement, union, intersection, AND and OR operations and additionally several properties relating to the notion of generalized Q-neutrosophic soft expert set are characterized. Finally, an algorithm on generalized Q-neutrosophic soft expert set is proposed and applied to a real-life example to show the efficiency of this notion in handling such problems.


2021 ◽  
pp. 1-17
Author(s):  
Hanchuan Lu ◽  
Ahmed Mostafa Khalil ◽  
W. Alharbi ◽  
M. A. El-Gayar

 In this article, we propose a novel concept of the generalized picture fuzzy soft set by combining the picture fuzzy soft set and the fuzzy parameter set. For possible applications, we explain five kinds of operations (e.g., subset, equal, union, intersection, and complement) based on generalized picture fuzzy soft sets. Then, we establish several theoretical operations of generalized picture fuzzy soft sets. In addition, we present the new type by using the AND operation of the generalized picture fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. Finally, we give a comparison between the picture fuzzy soft set theory and the generalized picture fuzzy soft set theory. It is shown that our proposed (i.e., generalized picture fuzzy soft set theory) is viable and provide decision makers a more mathematical insight before making decisions on their options.


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