Pseudo General Overlap Functions and Weak Inflationary Pseudo BL-Algebras

Liang, Rong; Zhang, Xiao­hong

doi:10.3390/math10163007

Cited by 12 publications

(4 citation statements)

References 27 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, POFs and PGFs have a wide adaptability and application value. There are still many theoretical and applied problems to be studied in terms of pseudo overlap functions and fuzzy logic (see [42][43][44][45][46][47]).…”

Section: Discussionmentioning

confidence: 99%

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

Zhang

Liang

Bustince

et al. 2022

Axioms

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

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

Zhang

Liang

Bustince

et al. 2022

Axioms

Self Cite

View full text Add to dashboard Cite

show abstract

“…Secondly, we will continue to deeply study the application scenarios such as video detection of bus traffic roads and vehicle or pedestrian tracking. Thirdly, we will consider fusing overlap functions and fuzzy (rough) sets (see [45][46][47][48][49]) to design fog-attention-module. To provide convenience for researchers, all codes will be available at http://github.com/mendy-2013.…”

Section: Discussionmentioning

confidence: 99%

Joint Semantic Deep Learning Algorithm for Object Detection under Foggy Road Conditions

Fan

et al. 2022

Mathematics

View full text Add to dashboard Cite

Current mainstream deep learning methods for object detection are generally trained on high-quality datasets, which might have inferior performances under bad weather conditions. In the paper, a joint semantic deep learning algorithm is proposed to address object detection under foggy road conditions, which is constructed by embedding three attention modules and a 4-layer UNet multi-scale decoding module in the feature extraction module of the backbone network Faster RCNN. The algorithm differs from other object detection methods in that it is designed to solve low- and high-level joint tasks, including dehazing and object detection through end-to-end training. Furthermore, the location of the fog is learned by these attention modules to assist image recovery, the image quality is recovered by UNet decoding module for dehazing, and then the feature representations of the original image and the recovered image are fused and fed into the FPN (Feature Pyramid Network) module to achieve joint semantic learning. The joint semantic features are leveraged to push the subsequent network modules ability, and therefore make the proposed algorithm work better for the object detection task under foggy conditions in the real world. Moreover, this method and Faster RCNN have the same testing time due to the weight sharing in the feature extraction module. Extensive experiments confirm that the average accuracy of our algorithm outperforms the typical object detection algorithms and the state-of-the-art joint low- and high-level tasks algorithms for the object detection of seven kinds of objects on road traffics under normal weather or foggy conditions. All codes will be available at github.com/mendy-2013.

show abstract

“…At the end of this part, we look back at the conception of inflationary pseudo-general residuated lattices proposed in [23], as well as a few properties they satisfy and the definition of a special class of weak inflationary pseudo-BL-algebras they contain.…”

Section: Definition 8 ([9]mentioning

confidence: 99%

“…Therefore, we further generalize it, provide the new concept of weak inflationary BL-algebras (briefly weak IBL-algebra), and elaborate the one-to-one correspondence between inflationary general overlap functions and weak IBL-algebras. Then, some properties of weak IBL-algebra and some filters of inflationary (pseudo-) general residuated lattices are discussed (some of the latest studies on overlap functions, pseudo overlap functions, and residuated lattices that we refer to are contained in [18][19][20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices

Zhang

Liang²,

Bedregal³

2022

Mathematics

Self Cite

View full text Add to dashboard Cite

After the research on naBL-algebras gained by the non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of non-associative generalization of BL-algebras, which can be obtained by general overlap functions. In this paper, we show that not every inflationary general overlap function can induce an inflationary BL-algebra by a counterexample and thus propose the new concept of weak inflationary BL-algebras. We prove that each inflationary general overlap function corresponds to a weak inflationary BL-algebra; therefore, two mistaken results in the previous paper are revised. In addition, some properties satisfied by weak inflationary BL-algebras are discussed, and the relationships among some non-classical logic algebras are analyzed. Finally, we establish the theory of filters and quotient algebras of inflationary general residuated lattice (IGRL) and inflationary pseudo-general residuated lattice (IPGRL), and characterize the properties of some kinds of IGRLs and IPGRLs by naBL-filters, (weak) inflationary BL-filters, and weak inflationary pseudo-BL-filters.

show abstract

Pseudo General Overlap Functions and Weak Inflationary Pseudo BL-Algebras

Cited by 12 publications

References 27 publications

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

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

Joint Semantic Deep Learning Algorithm for Object Detection under Foggy Road Conditions

Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices

Contact Info

Product

Resources

About