JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (9): 36-42.doi: 10.6040/j.issn.1671-9352.0.2018.560

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Distributivity of fuzzy implications over additively generated overlap and grouping functions

ZHANG Ting-hai, QIN Feng   

  1. College of Mathematics and Informatics, Jiangxi Normal University, Nanchang 330022, Jiangxi, China
  • Online:2019-09-20 Published:2019-07-30

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Abstract: Among the researches of the fuzzy system, the distributivity between fuzzy implications and some special aggregation functions(e.g. t-norms, t-conorms, uninorms, t-operators, semi-uninorms and semi-t-operators)has been studied by many authors. Overlap functions and grouping functions have been followed with interest for their applications in image processing, classification problems and decision making based on fuzzy preference relations. In this paper, we give necessary and sufficient conditions for two distributivity equations I(O(x,y),z)=G(I(x,z),I(y,z)) and I(x,G1(y,z))=G2(I(x,y),I(x,z)), where O is an additively generated overlap function, G1 and G2 are additively generated grouping functions and I is a binary function satisfying boundary conditions.

Key words: fuzzy implication, overlap function, grouping function, Cauchy function equation, distributivity

CLC Number: 

  • O159
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