scholarly journals Linear Diophantine Fuzzy Soft Rough Sets for the Selection of Sustainable Material Handling Equipment

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1215
Author(s):  
Muhammad Riaz ◽  
Masooma Raza Hashmi ◽  
Humaira Kalsoom ◽  
Dragan Pamucar ◽  
Yu-Ming Chu
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Material Handling ◽  
Optimal Decision ◽  
Soft Sets ◽  
Sustainable Material ◽  
Material Handling Equipment ◽  
Core Set ◽  
Modeling Uncertainties ◽  
Selection Of

The concept of linear Diophantine fuzzy sets (LDFSs) is a new approach for modeling uncertainties in decision analysis. Due to the addition of reference or control parameters with membership and non-membership grades, LDFS is more flexible and reliable than existing concepts of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs). In this paper, the notions of linear Diophantine fuzzy soft rough sets (LDFSRSs) and soft rough linear Diophantine fuzzy sets (SRLDFSs) are proposed as new hybrid models of soft sets, rough sets, and LDFS. The suggested models of LDFSRSs and SRLDFSs are more flexible to discuss fuzziness and roughness in terms of upper and lower approximation operators. Certain operations on LDFSRSs and SRLDFSs have been established to discuss robust multi-criteria decision making (MCDM) for the selection of sustainable material handling equipment. For these objectives, some algorithms are developed for the ranking of feasible alternatives and deriving an optimal decision. Meanwhile, the ideas of the upper reduct, lower reduct, and core set are defined as key factors in the proposed MCDM technique. An application of MCDM is illustrated by a numerical example, and the final ranking in the selection of sustainable material handling equipment is computed by the proposed algorithms. Finally, a comparison analysis is given to justify the feasibility, reliability, and superiority of the proposed models.

Intuitionistic Fuzzy Soft Ideals

2020 ◽  
pp. 91-104
Author(s):  
Shuker Khalil
Keyword(s):  
Social Science ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Sets ◽  
Real Life ◽  
Soft Sets ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Sets Theory

The basic notions of soft sets theory are introduced by Molodtsov to deal with uncertainties when solving problems in practice as in engineering, social science, environment, and economics. This notion is convenient and easy to apply as it is free from the difficulties that appear when using other mathematical tools as theory of theory of fuzzy sets, rough sets, and theory of vague sets. The soft set theory has recently gaining significance for finding rational and logical solutions to various real-life problems, which involve uncertainty, impreciseness, and vagueness. The concepts of intuitionistic fuzzy soft left almost semigroups and the intuitionistic fuzzy soft ideal are introduced in this chapter, and some of their basic properties are studied.

Soft Sets and Its Applications

2016 ◽  
pp. 65-85 ◽  
Author(s):  
B. K. Tripathy ◽  
K. R. Arun
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Practical Applications ◽  
Set Operations ◽  
New Models ◽  
Pros And Cons

Uncertainty is an inherent characteristic of modern day databases. In order to handle such databases with uncertainty, several new models have been introduced in the literature. Some new models like fuzzy sets introduced by Zadeh (1965), rough sets invented by Z. Pawlak (1982) and intuitionistic fuzzy sets extended by K.T. Atanassov (1986). All these models have their own pros and cons. However, one of the major problems with these models is the lack of sufficient number of parameters to deal with uncertainty. In order to add adequate number of parameters, soft set theory was introduced by Molodtsov in 1999. Since then the theoretical developments on soft set theory has attracted the attention of researchers. However, the practical applications of any theory are of enough importance to make use of it. In this chapter, the basic definitions of soft set, operations and properties are discussed. Also, the aim in this chapter is to discuss on the different applications of soft sets; like decision making, parameter reduction, data clustering and data dealing with incompleteness.

On Theory of Multisets and Applications

2016 ◽  
pp. 1-22
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Rough Sets ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Current Status ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Mathematics ◽  
Basic Sets

Although multiple occurrences of elements are immaterial in sets, in real life situations repetition of elements is useful. So, the notion of multisets (also called as bags) was introduced, where repetition of elements is taken into account. Fuzzy set, intuitionistic (a misnomer here as intuitionistic mathematics has nothing to do with its fuzzy counterpart) fuzzy sets, rough sets and soft sets are extensions of the basic notion of sets as they model uncertainty in data. Following this multisets have been extended to fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Many properties of basic sets have been extended to the context of multisets, fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Several applications of different multisets mentioned above are found in literature. In this chapter, it is our aim to introduce the different concepts of multisets, their properties, current status and highlight their applications.

A Multi Attribute Selection of Mobile Robot using AHP/M-GRA Technique

2020 ◽  
pp. 262-284
Author(s):  
Surinder Kumar ◽  
Tilak Raj
Keyword(s):  
Mobile Robot ◽  
Flexible Manufacturing ◽  
Material Handling ◽  
Attribute Selection ◽  
Material Handling Equipment ◽  
Utility Index ◽  
Automated Material Handling ◽  
Grey Relational ◽  
Robot Selection ◽  
Selection Of

Today's highly competitive environment and volatile market conditions at national and international level are forcing the manufacturing concerns and its management to adopt the advance automated material handling equipment like mobile robots in a flexible manufacturing system (FMS) to meet the customers' demand regarding quality and variety of product at minimal cost. Selection of a robot is one of the most difficult problems in today's manufacturing environment. The problem has become more challenging due to increasing specifications and complexity of the robot. The main aim of this paper is to develop and implement an integrated methodology based on AHP (Analytical Hierarchy Process) and M-GRA (Modified Grey Relational Analysis) for the selection of a mobile robot for material handling in FMS environment. In this methodology, AHP technique has been used to assign the relative importance between mobile robot selection attributes and M-GRA technique is applied to determine mobile robot selection utility index. The proposed AHP/M – GRA technique is more suitable for the decision making in the presence of vagueness. The methodology is illustrated by means of an example. The ranking and evaluation of this process will provide a good guidance to the decision maker/user to select the appropriate material handling equipment on the basis of attributes. This is the novel effort in the area of robot selection.

A Multi Attribute Selection of Mobile Robot using AHP/M-GRA Technique

2016 ◽  
Vol 7 (4) ◽  
pp. 94-114
Author(s):  
Surinder Kumar ◽  
Tilak Raj
Keyword(s):  
Mobile Robot ◽  
Flexible Manufacturing ◽  
Material Handling ◽  
Attribute Selection ◽  
Material Handling Equipment ◽  
Utility Index ◽  
Automated Material Handling ◽  
Grey Relational ◽  
Robot Selection ◽  
Selection Of

Today's highly competitive environment and volatile market conditions at national and international level are forcing the manufacturing concerns and its management to adopt the advance automated material handling equipment like mobile robots in a flexible manufacturing system (FMS) to meet the customers' demand regarding quality and variety of product at minimal cost. Selection of a robot is one of the most difficult problems in today's manufacturing environment. The problem has become more challenging due to increasing specifications and complexity of the robot. The main aim of this paper is to develop and implement an integrated methodology based on AHP (Analytical Hierarchy Process) and M-GRA (Modified Grey Relational Analysis) for the selection of a mobile robot for material handling in FMS environment. In this methodology, AHP technique has been used to assign the relative importance between mobile robot selection attributes and M-GRA technique is applied to determine mobile robot selection utility index. The proposed AHP/M – GRA technique is more suitable for the decision making in the presence of vagueness. The methodology is illustrated by means of an example. The ranking and evaluation of this process will provide a good guidance to the decision maker/user to select the appropriate material handling equipment on the basis of attributes. This is the novel effort in the area of robot selection.

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