The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems proved by authors in 2017. In this study, homomorphism between algebras is defined, function examined then congruence relations are defined algebra. First third isomorphism introduced.

Fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. In this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. We focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. At last, fuzzy completecongruen...

In this paper we develop the method of diagrams for fuzzy predicate logics and give a characterization of different kinds of preserving mappings in terms of diagrams. Our work is a contribution to the modeltheoretic study of equality-free fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts bei...

By using a special t-level relation U(μ, t) = {(x, y) ∈ S × S|(μ(x) ∧ μ(y)) ∨ IdS(x, y) ≥ t} based on a fuzzy ideal μ of a semigroup S, which is a congruence relation, we study the roughness of soft semigroups under this special ideal of S, such as rough soft subsemigroups, rough soft ideals and rough soft prime ideals.

Today most research related to manufacturing strategy development concentrates on descriptive processes and conceptual models, and therefore lacks the capability of assessing the supportive degree of manufacturing strategy to competitive priorities, and is also difficult to assess the congruence among various decisions of the manufacturing strategy. This paper proposes an approach for manufactu...

An important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic, is that of a filter. Filters can be used, amongst others, to define congruence relations. Specific kinds of filters include Boolean filters and prime filters. In this paper, we define several different filters of residuated lattices and triangle algebras and examine their mutual...

This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals) from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R) is isom...