The neutrosophic set (NS) can be better to express the incomplete, indeterminate and inconsistent information, and Hamacher aggregation operators extended the Algebraic and Einstein aggregation operators and the generalized aggregation operators can generalize the arithmetic, geometric, and quadratic aggregation operators. In this paper, we combined Hamacher operations and generalized aggregati...

In this article, Hamacher operations of Picture Fuzzy Matrices are proposed, which direct extensions Intuitionistic Matrices. By using these scalar multiplication and exponentiation constructed for a picture fuzzy matrix certain new relations established

As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. Some new hesitant fuzzy operational rules are introduced based on the Hamacher t-conorm and t-norm, whereby we present a multi attribute decision making method under hesitan...

In this paper, we investigate the probabilistic decision making problems with hesitant fuzzy information, some new probabilistic decision making analysis methods are developed. Then, we have developed some new probability aggregation operators with hesitant fuzzy information: probability hesitant fuzzy Hamacher weighted average(P-HFHWA) operator, immediate probability hesitant fuzzy Hamacher or...

A general functional connective generator is proposed for the Hamacher family in this short study. The connective generator generates a variety of different families in which the original Hamacher family can be observed as a special case. Although the original additive connective generator that was proposed by Dombi is also capable of generating Hamacher norms, we show that there is yet another...

Domination is a relation between general operations defined on a poset. The old open problem is whether domination is transitive on the set of all t-norms. In this paper we contribute partially by inspection of domination in the family of Frank and Hamacher tnorms. We show that between two different t-norms from the same family, the domination occurs iff at least one of the t-norms involved is ...

delivery of cancer radiation treatment using multileaf collimators Davaasteren Baatar, Natashia Boland, Robert Johnston Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia, {[email protected], [email protected], , [email protected]} Horst W. Hamacher Department of Mathematics, University of Kaiserslautern, 67653 Kaiserslautern, Germany,...

This paper proposed a novel adaptive neuro-fuzzy inference system (ANFIS), which combines subtract clustering, employs adaptive Hamacher T-norm and improves the prediction ability of ANFIS. The expression of multiinput Hamacher T-norm and its relative feather has been originally given, which supports the operation of the proposed system. Empirical study has testified that the proposed model ove...

The definition of t-norms and t-conorms of the class of Hamacher with multilayer feedforward artificial neural networks is achieved in this work. This fact lets to insert fuzzy knowledge into neural network before its training.