Constructing strict left (right)-disjunctive left (right) semi-uninorms and coimplications satisfying the order property
| Autor: | Zhudeng Wang, Meixia Niu, Xiaoying Hao, Yuan Wang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Property (philosophy) Logic 010102 general mathematics 02 engineering and technology Lower approximation 01 natural sciences Combinatorics Fuzzy connective Complete lattice Artificial Intelligence Binary operation 0202 electrical engineering electronic engineering information engineering Order (group theory) 020201 artificial intelligence & image processing 0101 mathematics Modus ponens Upper approximation Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 323:79-93 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2016.12.006 |
| Popis: | In this paper, we further study the constructions of left (right) semi-uninorms and coimplications on a complete lattice. We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-disjunctive left (right) semi-uninorms of a binary operation. Then, we lay out the formulas for calculating the upper and lower approximation coimplications, which satisfy the order property, of a binary operation. Finally, we investigate the relationships between the lower approximation strict left (right)-disjunctive left (right) arbitrary ∧-distributive left (right) semi-uninorms and upper approximation right arbitrary ∨-distributive coimplications which satisfy the order property, and give some conditions such that the upper approximation strict left (right)-disjunctive left (right) semi-uninorms of a binary operation and lower approximation coimplication, which satisfies the order property, of the left (right) deresiduum of the binary operation satisfy the generalized dual modus ponens rule. |
| Databáze: | OpenAIRE |
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