200 research outputs found
Interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras
We introduce the concept of quasi-coincidence of a fuzzy interval value with
an interval valued fuzzy set. By using this new idea, we introduce the notions
of interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras and
investigate some of their related properties. Some characterization theorems of
these generalized interval valued fuzzy filters are derived. The relationship
among these generalized interval valued fuzzy filters of pseudo -algebras
is considered. Finally, we consider the concept of implication-based interval
valued fuzzy implicative filters of pseudo -algebras, in particular, the
implication operators in Lukasiewicz system of continuous-valued logic are
discussed
Toward a probability theory for product logic: states, integral representation and reasoning
The aim of this paper is to extend probability theory from the classical to
the product t-norm fuzzy logic setting. More precisely, we axiomatize a
generalized notion of finitely additive probability for product logic formulas,
called state, and show that every state is the Lebesgue integral with respect
to a unique regular Borel probability measure. Furthermore, the relation
between states and measures is shown to be one-one. In addition, we study
geometrical properties of the convex set of states and show that extremal
states, i.e., the extremal points of the state space, are the same as the
truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal
logic for probabilistic reasoning on product logic events and prove soundness
and completeness with respect to probabilistic spaces, where the algebra is a
free product algebra and the measure is a state in the above sense.Comment: 27 pages, 1 figur
Some properties of state filters in state residuated lattices
summary:We consider properties of state filters of state residuated lattices and prove that for every state filter of a state residuated lattice : \begin {itemize} \item [(1)] is obstinate ; \item [(2)] is primary is a state local residuated lattice; \end {itemize} and that every g-state residuated lattice is a subdirect product of , where is a prime state filter of . \endgraf Moreover, we show that the quotient MTL-algebra of a state residuated lattice by a state prime filter is not always totally ordered, although the quotient MTL-algebra by a prime filter is totally ordered
Algebraic Models for Qualified Aggregation in General Rough Sets, and Reasoning Bias Discovery
In the context of general rough sets, the act of combining two things to form
another is not straightforward. The situation is similar for other theories
that concern uncertainty and vagueness. Such acts can be endowed with
additional meaning that go beyond structural conjunction and disjunction as in
the theory of -norms and associated implications over -fuzzy sets. In the
present research, algebraic models of acts of combining things in generalized
rough sets over lattices with approximation operators (called rough convenience
lattices) is invented. The investigation is strongly motivated by the desire to
model skeptical or pessimistic, and optimistic or possibilistic aggregation in
human reasoning, and the choice of operations is constrained by the
perspective. Fundamental results on the weak negations and implications
afforded by the minimal models are proved. In addition, the model is suitable
for the study of discriminatory/toxic behavior in human reasoning, and of ML
algorithms learning such behavior.Comment: 15 Pages. Accepted. IJCRS-202
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