An Algorithm for Producing Fuzzy Negations via Conical Sections

Abstract

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.

An Algorithm for Fuzzy Negations Based-Intuitionistic Fuzzy Copula Aggregation Operators in Multiple Attribute Decision Making

“…In the future our aim is to combine the proposed operations with fuzzy negations via conic sections [36], in order to produce modified families of aggregator operations of IFVs. Furthermore, we are willing to adapt the proposed operations, following the appropriate transformation, in other types of fuzzy sets, such as hesitant fuzzy sets [37], and unbalanced linguistic term sets [38] and neutrosophic sets [39], in order to construct algorithms for multiple attribute decision making and multiple attribute group decision making.…”

Fuzzy implications based on quasi-copula and fuzzy negations

“…In the theory of fuzzy logic as well as in classical logic, negation plays a decisive role, and the following definition is given. [2]) and [20]).…”

Generator of Fuzzy Implications

“…Krol [19] dealt with some functions of fuzzy implication within the laws of propositional calculus, leading to new fuzzy implications. Souliotis and Papadopoulos [20] discovered simple mathematical and computational procedures as well as strong fuzzy implications with the help of geometric concepts such as ellipticity and hyperbola.…”