Abstract
In this article, a new hybrid model named linear Diophantine fuzzy rough set (LDFRS) is proposed to magnify the notion of rough set (RS) and linear Diophantine fuzzy set (LDFS). Concerning the proposed model of LDFRS, it is more efficient to discuss the fuzziness and roughness in terms of linear Diophantine fuzzy approximation spaces (LDFA spaces); it plays a vital role in information analysis, data analysis, and computational intelligence. The concept of (<p,p′>,<q,q′>)-indiscernibility of a linear Diophantine fuzzy relation (LDF relation) is used for the construction of an LDFRS. Certain properties of LDFA spaces are explored and related results are developed. Moreover, a decision-making technique is developed for modeling uncertainties in decision-making (DM) problems and a practical application of fuzziness and roughness of the proposed model is established for medical diagnosis.
Highlights
IntroductionSome of the remarkable applications of linear Diophantine fuzzy set (LDFS) concerning algebraic structures, soft rough sets model, binary relations, and q-linear Diophantine fuzzy are found in [16–18]
Academic Editor: José Carlos R.Due to the growing interest in the development of computational intelligence techniques, classical set theory has been generalized to many beneficial theories and models.Some of the worthwhile set theoretic models are fuzzy sets (FSs) [1], intuitionistic fuzzy sets (IFSs) [2,3], bipolar fuzzy sets (BFSs) [4], rough sets (RSs) [5,6], soft sets (SSs) [7], etc.In 1965, Zadeh [1] introduced the conceptualization of FSs, one of the most successful extensions among the above-mentioned theories
The main objective of this article is to magnify the notion of linear Diophantine fuzzy set (LDFS) and RS for intelligent information processing
Summary
Some of the remarkable applications of LDFSs concerning algebraic structures, soft rough sets model, binary relations, and q-linear Diophantine fuzzy are found in [16–18]. In the information systems, where attribute values are not numerical, an excessive number of vibrant mathematicians investigated hybridization of FSs and RSs. Cock et al [37] proposed an innovative model of fuzzy rough sets and developed some forgotten step of roughness. Akram et al [44] suggested a novel hybrid decision-making approach based on intuitionistic fuzzy N-soft rough sets. Zhang et al [51] introduced novel classes of fuzzy soft β-covering-based fuzzy rough sets with applications to MCDM. They developed some results for two different fuzzy soft β-coverings having the same upper (lower) approximation operators.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
