Definition and selection of fuzzy sets in genetic‐fuzzy systems using the concept of fuzzimetric arcs

Kybernetes ◽  
2008 ◽  
Vol 37 (1) ◽  
pp. 166-181 ◽  
Author(s):  
Issam Kouatli
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Systems ◽  
Genetic Fuzzy Systems ◽  
Selection Of

Genetic Fuzzy Systems Applied to Ports and Coasts Engineering

2011 ◽  
pp. 759-766
Author(s):  
Óscar Ibáñez ◽  
Alberte Castro
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Fuzzy Systems ◽  
Optimal Solution ◽  
Rule Based ◽  
Genetic Fuzzy Systems ◽  
Search Spaces ◽  
To Come ◽  
Complex Search Spaces ◽  
Rule Based Systems

Fuzzy Logic (FL) and fuzzy sets in a wide interpretation of FL (in terms in which fuzzy logic is coextensive with the theory of fuzzy sets, that is, classes of objects in which the transition from membership to non membership is gradual rather than abrupt) have placed modelling into a new and broader perspective by providing innovative tools to cope with complex and ill-defined systems. The area of fuzzy sets has emerged following some pioneering works of Zadeh (Zadeh, 1965 and 1973) where the first fundamentals of fuzzy systems were established. Rule based systems have been successfully used to model human problem-solving activity and adaptive behaviour. The conventional approaches to knowledge representation are based on bivalent logic. A serious shortcoming of such approaches is their inability to come to grips with the issue of uncertainty and imprecision. As a consequence, the conventional approaches do not provide an adequate model for modes of reasoning. Unfortunately, all commonsense reasoning falls into this category. The application of FL to rule based systems leads us to fuzzy systems. The main role of fuzzy sets is representing Knowledge about the problem or to model the interactions and relationships among the system variables. There are two essential advantages for the design of rule-based systems with fuzzy sets and logic: • The key features of knowledge captured by fuzzy sets involve handling uncertainty. • Inference methods become more robust and flexible with approximate reasoning methods of fuzzy logic. Genetic Algorithms (GAS) are a stochastic optimization technique that mimics natural selection (Holland, 1975). GAs are intrinsically robust and capable of determining a near global optimal solution. The use of GAS is usually recommended for optimization in high-dimensional, multimodal complex search spaces where deterministic methods normally fail. GAs explore a population of solutions in parallel. The GA is a searching process based on the laws of natural selections and genetics. Generally, a simple GA contains three basic operations: selection, genetic operations and replacement. A typical GA cycle is shown in Fig. 1. In this paper it is shown how a genetic algorithm can be used in order to optimize a fuzzy system which is used in wave reflection analysis at submerged breakwaters.

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.

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