scholarly journals On topological structures of virtual fuzzy parametrized fuzzy soft sets

2021 ◽  
Author(s):  
Orhan Dalkiliç
Keyword(s):  
Mathematical Models ◽  
Set Theory ◽  
Topological Structure ◽  
Soft Set ◽  
Decision Makers ◽  
Topological Spaces ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Topological Structures ◽  
Fuzzy Soft Sets

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.

scholarly journals An algorithm for fuzzy soft set based decision making approach

2020 ◽  
Vol 30 (1) ◽  
pp. 59-70
Author(s):  
Shehu Mohammed ◽  
Akbar Azam
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Group Decision Making ◽  
Group Decision ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Priority Table

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.

scholarly journals On Fuzzy Soft Sets

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
B. Ahmad ◽  
Athar Kharal
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

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.

scholarly journals A Decision Making Method using Fuzzy Soft Sets

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Samsiah Abdul Razak ◽  
Daud Mohamad
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Uncertain Data ◽  
Soft Set ◽  
Decision Makers ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Analytic Hierarchy ◽  
Fuzzy Soft Sets

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.

scholarly journals Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

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.

A new type of generalized picture fuzzy soft set and its application in decision making

2021 ◽  
pp. 1-17
Author(s):  
Hanchuan Lu ◽  
Ahmed Mostafa Khalil ◽  
W. Alharbi ◽  
M. A. El-Gayar
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
New Type ◽  
Fuzzy Soft Sets ◽  
Novel Concept ◽  
Fuzzy Parameter

 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.

scholarly journals On Generalised Interval-Valued Fuzzy Soft Sets

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaoqiang Zhou ◽  
Qingguo Li ◽  
Lankun Guo
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Lattice Structures ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
New Approach ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application of the new approach in decision making based on generalised interval-valued fuzzy soft set is developed.

scholarly journals Similarity Measure of Lattice Ordered Multi-Fuzzy Soft Sets Based on Set Theoretic Approach and Its Application in Decision Making

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1255 ◽  
Author(s):  
Sabeena Begam S ◽  
Vimala J ◽  
Ganeshsree Selvachandran ◽  
Tran Thi Ngan ◽  
Rohit Sharma
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Similarity Measure ◽  
Real Life ◽  
Soft Set ◽  
Theoretic Approach ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov’s soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set (LMFSS) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of LMFSS is proposed to calculate the similarity between two LMFSSs. Moreover, some of its properties are introduced and proved. Finally, an application of LMFSS in decision making using similarity measure is analysed.

scholarly journals Representation and application of Fuzzy soft sets in type-2 environment

2021 ◽  
Author(s):  
Biplab Paik ◽  
Shyamal Kumar Mondal
Keyword(s):  
Fuzzy Set ◽  
Decision Procedure ◽  
Soft Set ◽  
Decision Makers ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Weighted Type

AbstractThis paper has represented a soft-set in the type-2 environment by its simplest form as an augmentation to soft-set theories. Furthermore, we have applied the type-2 fuzzy soft set(T2FSS) by using our most straightforward representation to find the solution of a decision-making-problem (DMP) based-on T2FSS as well as weighted type-2 fuzzy soft set (WT2FSS). We have proposed two definitions, namely, Mid-$$\alpha $$ α -threshold fuzzy-set of a T2FSS and Mid-$$\lambda $$ λ -threshold fuzzy-set of a T2FSS. Furthermore, we have presented the definition, namely, level fuzzy-soft-set(LFSS) of a T2FSS. Using this concept, we have prepared two algorithms to select one object in T2FSS as well as WT2FSS based on DMP, which take regret disinclination and expectation preference of decision-makers into consideration in the decision procedure. Also, we have presented two numerical examples at the end.

scholarly journals HIMPUNAN LEMBUT KABUR HESITANT DAN APLIKASINYA DALAM PENGAMBILAN KEPUTUSAN

2017 ◽  
Vol 6 (3) ◽  
pp. 23
Author(s):  
Sri Delvia Oriza ◽  
Nova Noliza Bakar
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Mathematical Theory ◽  
Soft Set ◽  
Hesitant Fuzzy Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Level Soft Set

Abstract. Molodstov's soft set theory is a newly emerging mathematical tool to handleuncertainty. The soft set theory can be combined with other mathematical theory like asfuzzy set theory. This paper aims to extend hesitant fuzzy set to hesitant fuzzy soft sets.Then, the complement, "AND", "OR", union, intersection operations and De Morgan'slaw are dened on hesitant fuzzy soft sets. Finally, with the help of level soft set, thehesitant fuzzy soft sets are applied to a decision making problem.Kata Kunci: Soft set, Fuzzy set, Hesitant fuzzy set, Hesitant fuzzy soft set, Level softset

scholarly journals Possibility Pythagorean bipolar fuzzy soft sets and its application

2021 ◽  
Vol 4 (2) ◽  
pp. 17-29
Author(s):  
M. Palanikumar ◽  
◽  
K. Arulmozhi ◽  
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

We interact the theory of possibility Pythagorean bipolar fuzzy soft sets, possibility bipolar fuzzy soft sets and define complementation, union, intersection, AND and OR. The possibility Pythagorean bipolar fuzzy soft sets are presented as a generalization of soft sets. Notably, we tend to showed De Morgan’s laws, associate laws and distributive laws that are holds in possibility Pythagorean bipolar fuzzy soft set theory. Also, we advocate an algorithm to solve the decision making problem primarily based on soft set model.

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