Residual operations of monotone binary operations over complete lattices

Sun, Feng; Wang, Xueping; Qu, Xiaobo; Shu, Qian-yu; Zhang, Xiao­hong

doi:10.1016/j.ijar.2019.04.005

Cited by 7 publications

(1 citation statement)

References 42 publications

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“…Proof. By Theorem 4.1 in [34] (or Theorem 3.1 in [35]), we get that the conditions (1) ∼ (4) are equivalent. By Theorem 4.2 in [34], we get that the conditions (1') ∼ (4') are equivalent.…”

Section: O and R (2)mentioning

confidence: 91%

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

Zhang

Liang

Bustince

et al. 2022

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Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability.

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Section: O and R (2)mentioning

confidence: 91%

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

Zhang

Liang

Bustince

et al. 2022

Axioms

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$$R_{\mathscr {O}}$$-implications induced from $$C_L$$-overlap functions on complete lattices

Qiao

2022

Soft Comput

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Characterizations of residual implications derived from uni-nullnorms

Sun

Huang

2020

Comp. Appl. Math.

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Uni-nullnorms generalize both uninorms and nullnorms. In this paper, residual implications derived from uni-nullnorms are investigated. First, properties of residual implications derived from uni-nullnorms and left-continuous uni-nullnorms are studied. Then, it is characterized for which uni-nullnorms the residuated operations are fuzzy implications. Finally, an axiomatic characterization of residual implications derived from left-continuous uninullnorms is given and the mutual independence of the properties in this characterization is investigated.

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Residual operations of monotone binary operations over complete lattices

Cited by 7 publications

References 42 publications

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications

$$R_{\mathscr {O}}$$-implications induced from $$C_L$$-overlap functions on complete lattices

Characterizations of residual implications derived from uni-nullnorms

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