NeutroAlgebras and particularly NeutroGroups are novel algebraic structures where at least one of the classical axioms is satisfied by not all the elements of the set. In the theoretical literature consulted by the authors, most of the NeutroGroups examples are obtained from the well known Z_n groups endowed with either product or sum operations. This chapter aims to propose a method for the generation of NeutroGroups in a simple and automatic way from uninorms, with special interest in uninorms based on combining functions in both Mycin and Prospector expert systems. The use of theses uninorms suggests the possible application of NeutroGroups in fields such as decision making as can be found in the consulted literature, as well as for Expert Systems, among others. NeutroGroups of finite or infinite cardinality will be generated, where the axioms of NeutroAsociativity or NeutroInverse are fulfilled, and also indeterminacy is symbolically included within this theory. One family of non-commutative NeutroGroups is proposed.
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Neutrosophy is the branch of philosophy that treats neutralities. F. Smarandache introduced this theory, where if <A> denotes a concept, idea, theory and so on, a triad (<A>, < neutA >, < AntiA >) could be defined, such that < AntiA > represents what is opposed to <A>, while <NeutA > represents what is neither <A> or <AntiA>, (Smarandache, 2005). Recently, the same author defined the NeutroAlgebras as new algebraic structures arising in the theory of Neutrosophy, so classical structures formed by elements well defined based on always true axioms are generalized to others that may be false or undefined in some cases, (Smarandache, 2020a; Smarandache, 2020b; Smarandache, 2020c). Specifically, in NeutroAlgebras, it is essential that the axioms of algebraic structures are not fulfilled for all elements of the structure, although at least one element must fulfill it. A Partial or Classical Algebra fulfills all the axioms, while the AntiAlgebra is defined such that at least one axiom is not fulfilled at all.
Among the most studied classical algebraic structures are groups, defined as a nonempty set of elements with an operator such that it is internal, which satisfies the associativity axiom, the existence of a neutral element and that each element of the set has an inverse (Isaacs, 2008). In the case of NeutroGroups, these axioms are not fulfilled by all the elements of the set, (Agboola, 2020a).
Classical group theory constitutes an important pillar in mathematical modeling within Physics, Chemistry and cryptography, (Isaacs, 2008). The NeutroAlgebras have been applied to resolve Decision Making problems, (Silva-Jiménez et al., 2021).
One of the purposes argued by F. Smarandache to extend the classical algebraic theory is that in the real world not all axioms are always fulfilled, nor are the operations always well defined.
Apart from these arguments, some well-known results from mathematics and physics indicate the need to include indeterminacy in these sciences that are based on mathematical logic. Some examples are the Uncertainty Principle of Heisenberg and the Gödel's theorems of incompleteness. These ideas suggest the relevance of developing a group theory where indeterminacy is part of the algebraic structure.
The main objective of this chapter is to propose the generation of NeutroGroups from uninorms, (Fodor et al., 1997). The uninorms are defined as the generalization of t-norms and t-conorms where the axioms of commutativity, associativity, increasing and existence of a neutral element are preserved, although in uninorms the neutral element may be a value in the range (0, 1), not 1 as in t- norms, nor 0 as in t-conorms. This aggregation operator was originally defined in the theory of fuzzy sets to intervals [0, 1], then it was extended to other frameworks like the intuitionistic fuzzy sets (Deschrijver & Kerre, 2004), neutrosophic sets (González-Caballero et al.,), and neutrosophic offsets (González-Caballero et al., 2019).
The advantage of what is proposed in this chapter is the automatic generation in a simple way of NeutroGroups of finite or infinite cardinality. The examples that are usually proposed in the literature are based on the groups 
(Kandasamy et al., 2020) endowed with the sum or product operation, in this chapter this universe of NeuroGroups is expanded. In addition, some generating uninorms use the aggregation functions in Mycin medical expert and Prospector mining expert systems, (Kaufmann et al., 1981; Shortliffe, 1976). These last uninorms suggest the possible application of these NeutroAlgebras in expert systems and decision making.
These functions can be extended to a more general field of elements where indeterminacy represented symbolically with the letter “I” is included. This is an advantage for these functions based on experts' evaluations and evidence, e.g., for aggregating totally opposite values, if it is believed that there is both, evidence totally against and evidence totally in favor of a hypothesis, sometimes the combined value is defined as 0, however, it is better to assess it as a contradiction and therefore an indeterminacy in an explicit way.