Extension operators for type-2 fuzzy sets derived from overlap functions

Jia, Zihang; Qiao, Junsheng

doi:10.1016/j.fss.2022.10.015

Cited by 9 publications

(2 citation statements)

References 45 publications

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“…On the other end of the spectrum, aggregation theory of real numbers has an imperative effect both in actual applications and theory [14][15][16]. Hence, the aggregation function of real numbers is widely generalized to type-2 fuzzy set [17][18][19]. More specifically, Gera and Dombi [20] introduced the extended t-norm and t-conorm on fuzzy truth value by pointwise formulas.…”

Section: Introductionmentioning

confidence: 99%

The distributivity of extended semi-t-operators over extended S-uninorms on fuzzy truth values

Yang,

Li,

Liu

et al. 2024

Soft Comput

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Inspired by the thought of distributivity between semi-t-operator and S-uninorm, this paper primarily explores the distributivity between extended semi-t-operator and extended S-uninorm on fuzzy truth value. Firstly, Zadeh-extended semi-t-operator and S-uninorm are proposed on fuzzy truth value and some results of extended semi-operator are studied under special fuzzy truth values. Then, it concentrates on the sufficient condition about left and right distributivity of extended semi-t-operator over extended S-uninorm under the condition that semi-t-operator is left and right distributive over S-uninorm, respectively. Finally, when parameters satisfy different cases, sufficient conditions for the distributivity between extended semi-t-operator and extended S-uninorm are given under the condition that semi-t-operator satisfies distributivity or conditional distributivity over S-uninorm.

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Section: Introductionmentioning

confidence: 99%

The distributivity of extended semi-t-operators over extended S-uninorms on fuzzy truth values

Yang,

Li,

Liu

et al. 2024

Soft Comput

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“…Therefore, OFs can provide more flexibility in these issues (Bustince et al, 2021). Currently, OFs has been successfully applied in fuzzy rough set models (Jiang and Hu, 2023;Zhang et al, 2023c;Qi et al, 2023b), decisionmaking (Qi et al, 2023a;Jia and Qiao, 2020), fuzzy reasoning (Zhang et al, 2022), fuzzy mathematical morphology (Zhang et al, 2023a), and clustering (Jia et al, 2023). Meanwhile, OF and its dual aggregation function, i.e., grouping functions (GFs) have been used to construct FIs, such as (G, N )-implications (Dimuro et al, 2014), residual implications (Dimuro and Bedregal, 2015), QL-implications (Dimuro et al, 2017) and D-implications (Dimuro et al, 2019a,b).…”

Section: Introductionmentioning

confidence: 99%

On fuzzy implications derived from multiplicative generator pair of overlap functions

Jia,

Qiao,

Chen

2024

Preprint

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Fuzzy implications are widely used in approximate reasoning. Since there is no fuzzy implication satisfying all algebraic properties, it is necessary to construct fuzzy implications for different applications. One of the main construction methods of fuzzy implications is based on the generator of aggregation functions. Meanwhile, overlap functions are a class of extensively used aggregation functions. Moreover, one of classes of multiplicative generator pairs of overlap functions has only a few weaker conditions in its definition. Therefore, for approximate reasoning, this article introduces a novel class of fuzzy implications called MO-implications based on a class of multiplicative generator pairs of overlap functions. Furthermore, we study the basic properties of MO-implications and some classical tautologies related to MO-implications. The results show that (1) MO-implications are a novel class of fuzzy implications, which are distinct from some other classes of overlap functions-related fuzzy implications; (2) MO-implications always satisfy some useful algebraic properties, such as left neutrality property and consequent boundary; (3) Some classical tautologies related to MO-implications hold in many cases, including T-conditionality law, O-conditionality law and contraction law, such that MO-implications can be used in approximate reasoning.

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A novel deep belief network architecture with interval type-2 fuzzy set based uncertain parameters towards enhanced learning

Shukla,

Muhuri

2024

Fuzzy Sets and Systems

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Extension operators for type-2 fuzzy sets derived from overlap functions

Cited by 9 publications

References 45 publications

The distributivity of extended semi-t-operators over extended S-uninorms on fuzzy truth values

The distributivity of extended semi-t-operators over extended S-uninorms on fuzzy truth values

On fuzzy implications derived from multiplicative generator pair of overlap functions

A novel deep belief network architecture with interval type-2 fuzzy set based uncertain parameters towards enhanced learning

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