Fuzzy Implications Generating from Fuzzy Negations

Souliotis, Georgios; Papadopoulos, Basil K.

doi:10.1007/978-3-030-01418-6_72

Cited by 5 publications

(8 citation statements)

References 8 publications

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“…The last developments in the theory of fuzzy implications (if…X…then…Y…) indicate that fuzzy negation is enough to generate an algorithmic process of production for fuzzy implications, (c.f. [2,3]). For example, supposing that in the context of an application, the fuzzy implication Yager is selected, which is generated in the following way:…”

Section: Discussionmentioning

confidence: 99%

“…indicate that fuzzy negation is enough to generate an algorithmic process of production for fuzzy implications, (c.f. [2,3]). For example, supposing that in the context of an application, the fuzzy implication Yager is selected, which is generated in the following way: I(x, y) = f −1 (x• f (y)), where f is a decreasing function; if f is replaced by a fuzzy negation, then an algorithm for producing fuzzy implications is automatically generated.…”

Section: Discussionmentioning

confidence: 99%

“…It should be noticed that Proposition 3 in paragraph 3 Main Results and particularly Equation 14, constitute new results that might be used in the production of implications, merely from negations (c.f. [2,3]), and by extension in reaching conclusions. In general, the algorithmic approach of negations is virtually non-existent in the applications of fuzzy sets and implications, without any reasons explaining such a gap.…”

Section: Introductionmentioning

confidence: 92%

“…Fuzzy negations play a crucial role in the creation of De Morgan triples and also in the construction of fuzzy implications (c.f. [1][2][3]). As a general admission, the construction of fuzzy negations is the foundation stone of the triples De Morgan construction and fuzzy implications.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Algorithm for Producing Fuzzy Negations via Conical Sections

Souliotis

Papadopoulos

2019

Algorithms

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In this paper we introduced a new class of strong negations, which were generated via conical sections. This paper focuses on the fact that simple mathematical and computational processes generate new strong fuzzy negations, through purely geometrical concepts such as the ellipse and the hyperbola. Well-known negations like the classical negation, Sugeno negation, etc., were produced via the suggested conical sections. The strong negations were a structural element in the production of fuzzy implications. Thus, we have a machine for producing fuzzy implications, which can be useful in many areas, as in artificial intelligence, neural networks, etc. Strong Fuzzy Negations refers to the discrepancy between the degree of difficulty of the effort and the significance of its results. Innovative results may, therefore, derive for use in literature in the specific field of mathematics. These data are, moreover, generated in an effortless, concise, as well as self-evident manner.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Algorithm for Producing Fuzzy Negations via Conical Sections

Souliotis

Papadopoulos

2019

Algorithms

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“…ere are fuzzy implications that are constructed by function generators with specific properties [4,[9][10][11][12]. Moreover, there are generation methods of fuzzy implications from known fuzzy implications [4,13].…”

Section: Introductionmentioning

confidence: 99%

An Application of Classical Logic’s Laws in Formulas of Fuzzy Implications

Grammatikopoulos

Papadopoulos

2020

Journal of Mathematics

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The crucial role that fuzzy implications play in many applicable areas was our motivation to revisit the topic of them. In this paper, we apply classical logic’s laws such as De Morgan’s laws and the classical law of double negation in known formulas of fuzzy implications. These applications lead to new families of fuzzy implications. Although a duality in properties of the preliminary and induced families is expected, we will prove that this does not hold, in general. Moreover, we will prove that it is not ensured that these applications lead us to fuzzy implications, in general, without restrictions. We generate and study three induced families, the so-called D ′ -implications, QL ′ -implications, and R ′ -implications. Each family is the “closest” to its preliminary-“creator” family, and they both are simulating the same (or a similar) way of classical thinking.

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Generator of Fuzzy Implications

Daniilidou,

Konguetsof,

Souliotis

et al. 2023

Preprint

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In this research paper an algorithm for the derivation of methods based on theorems and axioms of fuzzy logic is presented, analyzed and applied. This new proposed procedure generates fuzzy methods and evaluates the value of fuzzy propositions through fuzzy implication. The new implications of the family should satisfy a number of axioms. Also, we denote the conditions in order to satisfy the maximum number of axioms. Moreover, authors state and prove theorems focusing on fuzzy implication, observing the rule: the fuzzy function of fuzzy implication is strong and that lead to fuzzy negation. In addition, the optimal number of repetitions is calculated according to the expected truth value. The formulas produced are verified through the use of temperature and humidity values over a certain period of time and in a certain geographical area in Greece. The basic steps of the methodology are the fuzzification of the data given using four membership degree functions and the application of the membership degrees of temperature and humidity values on a new type of fuzzy implication. Finally, we observed that the isosceles trapezium gave the best results and the type of fuzzy implication can be effectively applied.

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Fuzzy Implications Generating from Fuzzy Negations

Cited by 5 publications

References 8 publications

An Algorithm for Producing Fuzzy Negations via Conical Sections

An Algorithm for Producing Fuzzy Negations via Conical Sections

An Application of Classical Logic’s Laws in Formulas of Fuzzy Implications

Generator of Fuzzy Implications

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