Classification by ordinal sums of conjunctive and disjunctive functions for explainable AI and interpretable machine learning solutions

Hudec, Miroslav; Mináriková, Erika; Mesiar, Radko; Saranti, Anna; Holzinger, Andreas

doi:10.1016/j.knosys.2021.106916

Cited by 42 publications

(28 citation statements)

References 38 publications

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“…and adjusting value 0.5 to edges of subintervals, we can observe that for two attributes (n = 2) this aggregation behaves as [15]…”

Section: łUkasiewicz T-norm Its Dual łUkasiewicz T-conorm and Arithmetic Meanmentioning

confidence: 97%

“…The proposed classification is beneficial when users search for transparent and explainable classification, but are not able to provide clear requirements. The comparison with other classification approaches is discussed in [15]. The next section explores ordinal sums for solving this demand.…”

Section: Classification Into Three Classesmentioning

confidence: 99%

“…In order to keep the expected value on edges of subintervals [0, a] 2 and [a, 1] 2 , when a = 0.5, the product t-norm on [0, 0.5] is expressed as [15]…”

Section: Product T-norm Its Dual Probabilistic Sum T-conorm and Variations Of Averaging Functionsmentioning

confidence: 99%

“…Hence, aggregation functions of mixed behaviour should be considered. This work evaluates the recently proposed theoretical work on classification by ordinal sums of conjunctive and disjunctive functions [15] on examples and proposes a further theoretical extension.…”

Section: Introductionmentioning

confidence: 99%

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Applicability of Ordinal Sums of Conjunctive and Disjunctive Functions in Classification

Hudec

Mesiar

Mináriková

2021

Atlantis Studies in Uncertainty Modelling

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Classification relies on the rules expressed by domain experts, or on the labeled attribute explaining the output classes. However, such information is not always available. In this work, we explore classification according to aggregation functions of mixed behaviour by the variability in ordinal sums of conjunctive and disjunctive functions. By this approach, entities are classified into three classes: yes, no and maybe including inclination to the classes yes and no. By the proposed approach, domain experts (or ordinal users) explain classification linguistically, without stating IF-THEN rules and labeled output. The applicability is illustrated by two examples. The discussion of the results and further research activities conclude the paper.

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“…and adjusting value 0.5 to edges of subintervals, we can observe that for two attributes (n = 2) this aggregation behaves as [15]…”

Section: łUkasiewicz T-norm Its Dual łUkasiewicz T-conorm and Arithmetic Meanmentioning

confidence: 97%

Section: Classification Into Three Classesmentioning

confidence: 99%

“…In order to keep the expected value on edges of subintervals [0, a] 2 and [a, 1] 2 , when a = 0.5, the product t-norm on [0, 0.5] is expressed as [15]…”

Section: Product T-norm Its Dual Probabilistic Sum T-conorm and Variations Of Averaging Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Applicability of Ordinal Sums of Conjunctive and Disjunctive Functions in Classification

Hudec

Mesiar

Mináriková

2021

Atlantis Studies in Uncertainty Modelling

Self Cite

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“…The researchers are working on various parameterized models including: decision-making based on FS sets [34], fuzzy partition based on fuzzy hypergraphs [35], Hebbian structures based on fuzzy hypergraphs [36], decision-making based on intuitionistic FS sets [37], extensions of fuzzy hypergraphs [38], and bipolar fuzzy competition graphs [39]. For more terminologies and concepts, we refer the reader to [40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Decision-making methods based on fuzzy soft competition hypergraphs

Akram

Shahzadi

Rasool

et al. 2022

Complex Intell. Syst.

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Fuzzy soft set theory is an effective framework that is utilized to determine the uncertainty and plays a major role to identify vague objects in a parametric manner. The existing methods to discuss the competitive relations among objects have some limitations due to the existence of different types of uncertainties in a single mathematical structure. In this research article, we define a novel framework of fuzzy soft hypergraphs that export the qualities of fuzzy soft sets to hypergraphs. The effectiveness of competition methods is enhanced with the novel notion of fuzzy soft competition hypergraphs. We study certain types of fuzzy soft competition hypergraphs to illustrate different relations in a directed fuzzy soft network using the concepts of height, depth, union, and intersection simultaneously. We introduce the notions of fuzzy soft k-competition hypergraphs and fuzzy soft neighborhood hypergraphs. We design certain algorithms to compute the strength of competition in fuzzy soft directed graphs that reduce the calculation complexity of existing fuzzy-based non-parameterized models. We analyze the significance of our proposed theory with a decision-making problem. Finally, we present graphical, numerical, as well as theoretical comparison analysis with existing methods that endorse the applicability and advantages of our proposed approach.

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