Abstract In this paper, we first obtain an identity for differentiable mappings. Then, establish some new generalized inequalities convex functions involving parameters and fractional integrals. We show that these results reduce to several Simpson-, midpoint- trapezoid-type inequalities. The given in study are the generalizations of proved earlier papers.

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

Several algorithms exist to determine the shortest path in a network for the crisp case where the weights are real numbers. In the real world, these weights represent parameters like cost, packet arrival time, link capacity etc which are not naturally precise. To model the uncertainty involved, for the first time we use the Gaussian fuzzy numbers as weights and a method has been presented in th...

Recently, Flores-Franulič et al. [A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 208 (2008) 55-59] proved the Stolarsky’s inequality for the Sugeno integral on the special class of continuous and strictly monotone functions. This result can be generalized to a general class of fuzzy convex functions in this paper. We also give a fuzzy integral inequal...

In this work, we address and explore the concept of generalized \(m\)-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate current initiated idea. Furthermore, prove latest variant Hermite-Hadamard type inequality employing proposed definition preinvexity. We also derive severa...

In the present paper, using novel generalizations of the Hukuhara di¤erence for fuzzy sets, we introduce and study new generalized di¤erentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy di¤erentiabilities …nding connections between them. Characterization and relatively simple expressions are provided f...

A new technique for adaptation of fuzzy membership functions in a fuzzy inference system is proposed. The pointer technique relies upon the isolation of the specific membership functions that contributed to the final decision, followed by the updating of these functions’ parameters using steepest descent. The error measure used is thus backpropagated from output to input, through the min and ma...