Hesitant fuzzy prefilters and filters of EQ-algebras

Abstract

Application of hesitant fuzzy sets to EQ-algebras is discussed. The notions of hesitant fuzzy prefilters (filters) and positive implicative hesitant fuzzy prefilters (filters) of EQ-algebras are introduced, and several properties are investigated. Characterizations of hesitant fuzzy prefilters (filters) and positive implicative hesitant fuzzy prefilters (filters) are considered, and conditions for a hesitant fuzzy filter to be a positive implicative hesitant fuzzy filter are investigated. Finally, the extension property for a positive implicative hesitant fuzzy filter is established.

New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

“…In fact, type-2 inclusion relation is based on the following order relation on D* (see [5], and it is called a type-2 order relation in this paper):…”

“…Most of them are vague than precise, and uncertainty is a common research topic of many branches of science (economics, engineering, environment, management science, medical science, and so on). However, uncertainty is an unintelligible expression without a straightforward description, and many theories were established, such as probability theory, fuzzy set theory [1][2][3], intuitionistic fuzzy set theory [4], hesitant fuzzy set theory [5][6][7][8], soft set theory [9][10][11][12], rough set theory [13][14][15][16][17], granular computing [18][19][20][21][22][23][24][25][26][27], et al…”

Single–valued neutrosophic filters in EQ–algebras

“…This basic structure in fuzzy logic is ordering, represented by ∧-semilattice, with maximal element "1". Further materials regarding EQalgebras are available in the literature too [6,7,9,12]. Algebras including EQ-algebras have played an important role in recent years and have had its comprehensive applications in many aspects including dynam-* Corresponding author.…”

New types of hesitant fuzzy sets on UP-algebras

“…Jun and Song [6] introduced the concepts of (Boolean, prime, ultra, good) hesitant fuzzy filters and hesitant fuzzy MVfilters of MTL-algebras. In 2015, Jun and Song [7] introduced the concepts of hesitant fuzzy prefilters (resp., filters) and positive implicative hesitant fuzzy prefilters (resp., filters) of EQ-algebras. In 2016, Jun and Ahn [4] introduced the concepts of hesitant fuzzy subalgebras and hesitant fuzzy ideals of BCK/BCI-algebras.…”