Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1]. So, we can apply techniques of interval-valued fuzzy sets to fuzzy automata. In particular, we prove that Atanassov’s Kα operators allow us to retrieve the information given by the transition functions of...

Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. first give definition and some properties interval integral that are naturally investigated as an extension nabla delta integrals. With help integral, we present variants Jensen inequalities convex concave functions on arbitrary scale. Moreover, Hölder’s Minkowski’s proved. Also, severa...

In recent years, the theory of convexity has influenced every field mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements have been introduced, one them is set-valued convexity. Interval-valued convex mappings are a special type maps. These close relationship with symmetry analysis. One important aspects between symmetric analysis ability work on a...

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and...

Overlap functions are a class of aggregation that measure the overlapping degree between two values. They have been successfully applied as fuzzy conjunction operation in several problems which associativity is not required, such image processing and classification. Interval-valued overlap were defined an extension to express interval-valued data, they usually when there uncertainty regarding a...

In this paper, a new soft computing group decision method based on the concept of compromise ratio is introduced for determining decision makers (DMs)' weights through the group decision process under uncertainty. In this method, preferences and judgments of the DMs or experts are expressed by linguistic terms for rating the industrial alternatives among selected criteria as well as the relativ...

Abstract In this paper, we introduce $(h_{1},h_{2})$ ( h 1 , 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex functions by using Riemann–Liouville fracti...

Abstract In the preset study, we introduce new class of convex fuzzy-interval-valued functions which is called log- h -convex (log- FIVFs) by means fuzzy order relation. We have also investigated some properties FIVFs. Using this class, present Jensen and Hermite–Hadamard inequalities (HH-inequalities). Moreover, useful examples are presented to verify HH-inequalities for Several known special ...

Abstract In this study, we introduce the new concept of $$h$$ h -convex fuzzy-interval-valued functions. Under concept, present versions Hermite–Hadamard inequalities (H–H inequalities) are called fuzzy-interval type for functions ( FIVF) by means fuzzy order relation. This relation is defined level wise thro...