Generalized trapezoidal fuzzy numbers (GTFNs) have been widely applied in uncertain decision-making problems. The similarity between GTFNs plays an important part in solving such problems, while there are some limitations in existing similarity measure methods. Thus, based on the cosine similarity, a novel similarity measure of GTFNs is developed which is combined with the concepts of geometric...

Propositional dynamic logic (PDL) provides a natural setting for semantics of means-end relations involving non-determinism, but such models do not include probabilistic features common to much practical reasoning involving means and ends. We alter the semantics for PDL by adding probabilities to the transition systems and interpreting dynamic formulas 〈α〉φ as fuzzy predicates about the reliabi...

We propose an additive "semantic measure" theory based on the model of a perception based fuzzy truthoods in analogy to probability measure. Probability measure, which is the subject of the probability theory, is a special case of the fuzzy measure in the Dempster-Shafer theory when the focal sets are singletons. In the literature, the fuzzy measure is considered an extension of the probability...

One of the generalizations of the Wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. The Reliability Wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. Closed expressions are derived for t...

The Supply Chain is considered a necessity for the success of organizations seeking the most economic, environmental and social impacts. In addition, the implementation and suitable execution of this supply chain seems to be necessary. Considering the importance of the social impacts of this supply chain, a fuzzy multi-objective mathematical model is provided such that, in addition to consideri...

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...