In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutro...

In this paper we consider compound conditionals, Fr\'echet-Hoeffding bounds and the probabilistic interpretation of Frank t-norms. By studying solvability suitable linear systems, show under logical independence sharpness for prevision conjunctions disjunctions $n$ conditional events. We study set all coherent assessments on a family containing events their conjunction, by verifying that it is ...

The Aczel-Alsina t-norms ware proposed by Aczel and Alsina in 1982, which are a very effective dominant technique used the construction of any kind aggregation operators. Moreover, Algebraic special case because parameter $$0<p<+\infty$$ . Additionally, complex intuitionistic fuzzy (COIF) set is an essential valuable part to handle vague awkward situations many real-life problems. Motivated abo...

In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper propose prioritized aggregation operators (AOs) for intuitionistic (IF) information. These AOs are symmetric nature based on the novel Aczel–Alsina t-norm t-conorm. Herein, we ...

As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the speciic roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norm...

We introduce the notion of interval-valued linear Diophantine fuzzy set, which is a generalized model for providing more accurate information, particularly in emergency decision-making, with help intervals membership grades and non-membership grades, as well reference parameters that provide freedom to decision makers analyze multiple objects alternatives universe. The accuracy numbers analyzed...

The confidence levels can reduce the influence of unreasonable evaluation value that was given by decision-maker on decision-making results. Archimedean t-norm and t-conorm (ATS) also have many advantages for processing uncertain data. Under this environment, q-rung orthopair fuzzy aggregation operator based ATS is one most successful extensions numbers in which we decrease deviation caused sub...

In classical (two-valued) logic, CNF and DNF forms of each propositional formula are equivalent to each other. In fuzzy logic, CNF and DNF forms are not equivalent, they form an interval that contains the fuzzy values of all classically equivalent propositional formulas. If we want to select a single value from this interval, then it is natural to select a linear combination of the interval's e...