scholarly journals The Parameter Reduction of Fuzzy Soft Sets Based on Soft Fuzzy Rough Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Zhiming Zhang
Keyword(s):  
Set Theory ◽  
Rough Sets ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Fuzzy Rough Sets ◽  
Soft Sets ◽  
Parameter Reduction ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Soft Sets

Fuzzy set theory, rough set theory, and soft set theory are three effective mathematical tools for dealing with uncertainties and have many wide applications both in theory and practise. Meng et al. (2011) introduced the notion of soft fuzzy rough sets by combining fuzzy sets, rough sets, and soft sets all together. The aim of this paper is to study the parameter reduction of fuzzy soft sets based on soft fuzzy rough approximation operators. We propose some concepts and conditions for two fuzzy soft sets to generate the same lower soft fuzzy rough approximation operators and the same upper soft fuzzy rough approximation operators. The concept of reduct of a fuzzy soft set is introduced and the procedure to find a reduct for a fuzzy soft set is given. Furthermore, the concept of exclusion of a fuzzy soft set is introduced and the procedure to find an exclusion for a fuzzy soft set is given.

scholarly journals Soft Rough Approximation Operators and Related Results

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Zhaowen Li ◽  
Bin Qin ◽  
Zhangyong Cai
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Generalized Rough Set ◽  
Special Case

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.

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 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 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 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 Parameter reduction analysis under interval-valued m-polar fuzzy soft information

2021 ◽  
Author(s):  
Muhammad Akram ◽  
Ghous Ali ◽  
José Carlos R. Alcantud
Keyword(s):  
Set Theory ◽  
Optimal Choice ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Parameter Reduction ◽  
Fuzzy Methods ◽  
Interval Representations ◽  
Interval Valued ◽  
Selection Of

AbstractThis paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.

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