This paper deals with the problem of looking for the set of defuzzification method features allowing us to generate the most accurate fuzzy models in combination with each fuzzy implication operator. Hence, we try to find fuzzy inference engines that are appropriate from the practical engineering point of view. To do so, the three basic properties for fuzzy implication operators presented in [C...

in this paper, we investigate duality of modular g-riesz bases and g-riesz basesin hilbert c*-modules. first we give some characterization of g-riesz bases in hilbert c*-modules, by using properties of operator theory. next, we characterize the duals of a giveng-riesz basis in hilbert c*-module. in addition, we obtain sucient and necessary conditionfor a dual of a g-riesz basis to be again a g...

Three-way fuzzy inference is the theoretical basis of three-way control. The proposed TCRI method based on a Mamdani implication operator and uses one simple composition operation. In order to effectively improve method, this paper proposes full triple I algorithm for gives solution TFMP problem. emphasis our research R0 Go¨del solution, which related residual implication, as well Zadeh’s Mamda...

The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are descri...

This paper analyzes the performance of some fuzzy implications proposed in the bibliography together with the operators needed for their definition and for the fuzzy inference process, Examining the specialized literature, it is clear that the selection of the best fuzzy implication operator has become one of the main question in the design of a fuzzy system, being occasionally contradictory (a...

In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, ...

A new family of fuzzy implications, motivated by classic Sheffer stroke operator, is introduced. Sheffer stroke, which is a negation of a conjunction and is called NAND as well, is one of the two operators that can be used by itself, without any other logical operators, to constitute a logical formal system. Classical implication can be presented just by Sheffer stroke operator in two ways whic...

This paper deals with the problem of searching basic properties for robust implication operators in fuzzy control. We use the word “robust” in the sense of good average behavior in different applications and in combination with different defuzzification methods. We study the behavior of the two main families of implication operators in the fuzzy control inference process. These two families are...

In our previous study, we defined the semantics of modal μ-calculus on minplus algebra N∞ and developed a model-checking algorithm. N∞ is the set of all natural numbers and infinity (∞), and has two operations min and plus. In the semantics, disjunctions are interpreted by min and conjunctions by plus. This semantics allows interesting properties of a Kripke structure, such as the shortest path...