This paper presents the study of algebraic structures equipped with inverted associativity axiom. Initially, definition left and right almost-groups is introduced afterwards, focused on more general structures, which are almost-hypergroups their enumeration in cases order 2 3. The outcomes these enumerations compared corresponding hypergroups reveal interesting results. Next, fundamental proper...

In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings.

The issues relating fuzzy sets definition are under consideration including the analogue for separation axiom, statistical interpretation and membership function representation by the conditional Probabilities.

Graph theory has an important role in the area of applications of networks and clustering‎. ‎In the case of dealing with uncertain data‎, ‎we must utilize ambiguous data such as fuzzy value‎, ‎fuzzy interval value or values of fuzzy number‎. ‎In this study‎, ‎values of fuzzy number were used‎. ‎Initially‎, ‎we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value f...

We address the problem of aggregating demand across a group of consumers, who are identical in terms of wealth and face identical price vectors, but vary in their chosen consumption bundles. We show that, when a stochastic demand function is constructed to aggregate a number of deterministic demand functions, satisfaction of the weak axiom of stochastic revealed preference by this stochastic de...

I consider an extension of the Borda count to case when individuals can have weak preferences, and show that it satisfies several normatively appealing axioms. The first axiom is preferences Modified Independence Irrelevant Alternatives in Maskin (2020a). second a new which call Up–Down Symmetry. remaining axioms are more standard. • allows for preferences. this One Alternatives. Another called

Our work is a contribution to the model-theoretic 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 being studied are the Leibniz congruence and the relative relation. On the one hand, the Leibniz congruence of a model identifies the elements that are indistinguishable...

In two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation. The s...

In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0 (weak weak König’s