In this paper Hermite—Hadamard type inequalities for m-convex and (α,m)-convex functions for fuzzy integrals are given. Some examples are also given to illustrate the results.

Abstract In this paper, the convex nonsmooth optimization problem with fuzzy objective function and both inequality equality constraints is considered. The Karush–Kuhn–Tucker necessary optimality conditions are proved for such a extremum problem. Further, exact $$l_{1}$$ l 1 </mml:...

Given a monic linear pencil L in g variables, let PL = (PL(n))n∈N where PL(n) := { X ∈ Sn | L(X) 0 } , and Sn is the set of g-tuples of symmetric n × n matrices. Because L is a monic linear pencil, each PL(n) is convex with interior, and conversely it is known that convex bounded noncommutative semialgebraic sets with interior are all of the form PL. The main result of this paper establishes a ...

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets,...

High oxygen conductivities can be achieved in cation ordered LnxZrl_=O2_l x (Ln=Gd, Nd) solid solutions with pyrochlore (P) structure. High values of the pre-exponentlal factor °o are correlated with the degree of anion disorder in the 8b oxygen sublattice (neutron diffraction). The activation energy AH is lowered by cation ordering (F-P transition; effect of x) due to the occurence of a prefer...

Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy numbers. Fuzzy implication is proposed with the help of algebraic operations and a lattice stru...

Abstract In this paper, we introduce the non-convex interval-valued functions for fuzzy-interval-valued functions, which are called "Equation missing"-convex by means of fuzzy order relation. This relation is defined level-wise through Kulisch–Miranker given on interval space. By using -->-convexity concept, present fuzzy-interval Hermite–Hadamard inequali...

following the idea of $l$-fuzzy neighborhood system as introduced byfu-gui shi, and its generalization to $(l,m)$-fuzzy neighborhood system, the relationship between  $(l,m)$-fuzzy topology and $(l,m)$-fuzzy neighborhood system will be further studied. as an application of the obtained results, we will describe the initial structures of $(l,m)$-fuzzy neighborhood subspaces and $(l,m)$-fuzzy top...

In the field of nonlinear programming (in continuous variables) convex analysis [22, 23] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called " discrete convex analysis " [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid ...

Abstract: Classical cost efficiency (CE) measurement models require exact and accurate knowledge of the input and output values for each decision making unit (DMU). However, the observed values of the input and output data in real-world problems are often imprecise or vague. In recent years, fuzzy data envelopment analysis (DEA) has been successfully used to deal with imprecise or vague data in...