Parametric Fuzzy Implications Produced via Fuzzy Negations with a Case Study in Environmental Variables

Souliotis, Georgios; Papadopoulos, Basil K.

doi:10.3390/sym13030509

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…Furthermore, the discovery made in this paper opens the possibility of using numerical analysis as a potential tool in the study of fuzzy logic. Moreover, it is important to point out the fact that the generalized fuzzy connectives that were created by this paper are a very powerful and useful asset to the researchers that are active in fields like decision-making, artificial intelligence, and even environmental study like [29,30]. It is important also to mention that the use of second-degree polynomials in the process of generalization saved valuable processing resources and significantly reduced the complexity of the whole procedure, helping its widespread adoption.…”

Section: Discussionmentioning

confidence: 94%

Generation of Polynomial Automorphisms Appropriate for the Generalization of Fuzzy Connectives

Makariadis,

Konguetsof

et al. 2023

Symmetry

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Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field.

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Section: Discussionmentioning

confidence: 94%

Generation of Polynomial Automorphisms Appropriate for the Generalization of Fuzzy Connectives

Makariadis,

Konguetsof

et al. 2023

Symmetry

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“…Makariadis et al [2] presented the form of an implication using fuzzy negations constructed with the help of conic sections. The relation was applied to real temperature and humidity data of E.M.Y with full applications.…”

Section: Literature Review-related Workmentioning

confidence: 99%

Generator of Fuzzy Implications

Daniilidou,

Konguetsof,

Souliotis

et al. 2023

Algorithms

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In this research paper, a generator of fuzzy methods based on theorems and axioms of fuzzy logic is derived, analyzed and applied. The family presented generates fuzzy implications according to the value of a selected parameter. The obtained fuzzy implications should satisfy a number of axioms, and the conditions of satisfying the maximum number of axioms are denoted. New theorems are stated and proven based on the rule that the fuzzy function of fuzzy implication, which is strong, leads to fuzzy negation. In this work, the data taken were fuzzified for the application of the new formulae. The fuzzification of the data was undertaken using four kinds of membership degree functions. The new fuzzy functions were compared based on the results obtained after a number of repetitions. The new proposed methodology presents a new family of fuzzy implications, and also an algorithm is shown that produces fuzzy implications so as to be able to select the optimal method of the generator according to the value of a free parameter.

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“…Example 6. Consider the overlap function O(x, y) = xy, the grouping function G(x, y) = 1 − (1 − x) 2 (1 − y) 2 and the fuzzy negation N given by Equation (9). Then, for all x, y ∈ [0, 1], one has that:…”

Section: Go *mentioning

confidence: 99%

“…In recent years, a plethora of fuzzy implication functions have been proposed in the literature [1][2][3][4]. These functions have been investigated from a more theoretical point of view [2,5,6] to the one involving practical applications [7][8][9]. They can be used in various fields such as approximate reasoning [10][11][12][13], decision making [14], image processing [15], and fuzzy mathematical morphology [16].…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Implications Derived from General Overlap Functions and Their Relation to Other Classes

Pinheiro

Santos

Dimuro

et al. 2022

Axioms

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There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO,N)-implication functions. We also investigate their properties, the aggregation of (GO,N)-implication functions, their characterization and the intersections with other classes of fuzzy implication functions.

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Parametric Fuzzy Implications Produced via Fuzzy Negations with a Case Study in Environmental Variables

Cited by 7 publications

References 14 publications

Generation of Polynomial Automorphisms Appropriate for the Generalization of Fuzzy Connectives

Generation of Polynomial Automorphisms Appropriate for the Generalization of Fuzzy Connectives

Generator of Fuzzy Implications

On Fuzzy Implications Derived from General Overlap Functions and Their Relation to Other Classes

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