Novel classes of coverings based multigranulation fuzzy rough sets and corresponding applications to multiple attribute
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Novel classes of coverings based multigranulation fuzzy rough sets and corresponding applications to multiple attribute group decision‑making Xueling Ma1 · Jianming Zhan1 · Bingzhen Sun2 · José Carlos R. Alcantud3
© Springer Nature B.V. 2020
Abstract The notion of covering based multigranulation fuzzy rough set (CMGFRS) models is a generalization of both granular computing and covering based fuzzy rough sets. Therefore it has become a powerful tool for coping with vague and multigranular information in cognition. In this paper we introduce three kinds of CMGFRS models by means of fuzzy β-neighborhoods and fuzzy complementary β-neighborhoods, and we investigate their axiomatic properties. We investigate three respective types of coverings based CMGFRS models, namely, optimistic, pessimistic and variable precision setups. In particular, by using multigranulation fuzzy measure degrees and multigranulation fuzzy complementary measure degrees, we derive three types of coverings based γ-optimistic (γ-pessimistic) CMGFRSs and E (F, G)-optimistic and E (F, G)-pessimistic CMGFRSs, respectively. We discuss the interrelationships among these three types of CMGFRS models and covering based Zhan-CMGFRS models. In view of the theoretical analysis for these three types of CMGFRS models, we put forward a novel methodology to multiple attribute group decision-making problem with evaluation of fuzzy information. An effective example is fully developed, hence concluding the applicability of the proposed methodology. Keywords MGRS · Covering based (optimistic · pessimistic and variable precision) MGFRS · Fuzzy (complementary) β-neighborhood · Multigranulation fuzzy (complementary) measure degree · MAGDM with fuzzy information * Jianming Zhan [email protected] Xueling Ma [email protected] Bingzhen Sun [email protected] José Carlos R. Alcantud [email protected] 1
Department of Mathematics, Hubei Minzu University, Enshi 445000, China
2
School of Economics and Management, Xidian University, Xi’an 710071, China
3
BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain
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1 Introduction In this paper, we unify some attractive components of various noteworthy approaches to formal theories of imprecise, uncertain and inexact cognition. The most prominent seed is rough set theory, which has already benefitted from successful blendings with multigranulation, fuzziness, or covering-based structures. Due to its generality, our general model will enable us to put forward suitable multiple attribute group decision-making solutions that apply to a wide array of situations. Before stating our research objectives, we proceed to review some chief ideas from the primary branches we are concerned with.
1.1 A brief review on the development of rough set theory After Pawlak (1982) set forth rough set theory (briefly, RST), this tool and its generalizations have become attractive to researchers that have popularized this subject. It has bee
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