Hybrid Set Structures for Soft Computing

2014 ◽  
pp. 75-94
Author(s):  
Sunil Jacob John ◽  
Babitha KV
Keyword(s):  
Fuzzy Sets ◽  
Soft Computing ◽  
Rough Sets ◽  
Computational Techniques ◽  
Computational Problem ◽  
Significant Interest ◽  
Computational Systems

A Major problem in achieving an effective computational systems is the presence of inherent uncertainty in the computational problem itself. Among various techniques proposed to address this, the technique of soft computing is of significant interest. Further, Generalized set structures like fuzzy sets, rough sets, multisets etc. have already proven their role in the context of soft computing. The computational techniques based on one of these structures alone will not always yield the best results but a fusion of two or more of them can often give better results. Such structures are regarded as hybrid set structures. This chapter surveys an analysis of various hybrid set structures which are quite useful tools for soft computing and shows how this hybridization can help in improving modeling real situations.

ROUGH FUZZY SETS AND FUZZY ROUGH SETS*

1990 ◽  
Vol 17 (2-3) ◽  
pp. 191-209 ◽  
Author(s):  
DIDIER DUBOIS ◽  
HENRI PRADE
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Fuzzy Rough Sets

Rough Sets and Approximate Reasoning

2014 ◽  
pp. 180-228 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Approximate Reasoning ◽  
Human Reasoning ◽  
Intuitionistic Fuzzy ◽  
Application Point ◽  
Future Work

Several models have been introduced to capture impreciseness in data. Fuzzy sets introduced by Zadeh and Rough sets introduced by Pawlak are two of the most popular such models. In addition, the notion of intuitionistic fuzzy sets introduced by Atanassov and the hybrid models obtained thereof have been very fruitful from the application point of view. The introduction of fuzzy logic and the approximate reasoning obtained through it are more realistic as they are closer to human reasoning. Equality of sets in crisp mathematics is too restricted from the application point of view. Therefore, extending these concepts, three types of approximate equalities were introduced by Novotny and Pawlak using rough sets. These notions were found to be restrictive in the sense that they again boil down to equality of sets and also the lower approximate equality is artificial. Keeping these points in view, three other types of approximate equalities were introduced by Tripathy in several papers. These approximate equalities were further generalised to cover the approximate equalities of fuzzy sets and intuitionistic fuzzy sets by him. In addition, considering the generalisations of basic rough sets like the covering-based rough sets and multigranular rough sets, the study has been carried out further. In this chapter, the authors provide a comprehensive study of all these forms of approximate equalities and illustrate their applicability through several examples. In addition, they provide some problems for future work.

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.

Modal Logic, Rough Sets, and Fuzzy Sets

2000 ◽  
pp. 35-55
Author(s):  
Tetsuya Murai ◽  
Michinori Nakata ◽  
Masaru Shimbo
Keyword(s):  
Modal Logic ◽  
Fuzzy Sets ◽  
Rough Sets

Soft Computing for Evolutionary Information Systems — Potentials of Rough Sets

2000 ◽  
pp. 481-494 ◽  
Author(s):  
A. B. Patki ◽  
G. V. Raghunathan ◽  
Soumik Ghosh ◽  
S. Sivasubramanian ◽  
Azar Khurshid
Keyword(s):  
Information Systems ◽  
Soft Computing ◽  
Rough Sets ◽  
Evolutionary Information
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