On the bounded quasi‐degrees of c.e. sets

We study the degree structure of bQ‐reducibility and we prove that for any noncomputable c.e. incomplete bQ‐degree a, there exists a nonspeedable bQ‐degree incomparable with it. The structure $\mathcal {D}_{\mbox{bs}}$ of the $\mbox{bs}$‐degrees is not elementary equivalent neither to the structure of the $\mbox{be}$‐degrees nor to the structure of the $\mbox{e}$‐degrees. If c.e. degrees a and b form a minimal pair in the c.e. bQ‐degrees, then a and b form a minimal pair in the bQ‐degrees. Also, for every simple set S there is a noncomputable nonspeedable set A which is bQ‐incomparable with S and bQ‐degrees of S and A does not form a minimal pair.     

Representations of Finite Posets Over Discrete Valuation Rings

Given a discrete valuation ring R, a non-negative integer m, and a finite partially ordered set S, the representation type of a category rep(S*, R, m) of finite rank free R-module representations of S is characterized in terms of S and m. As an application, representation types of some categories of torsion-free abelian groups of finite rank are determined.     

On isocline lines for functions and convex stratifications of two variables

Let the isoclines of a function u be the level lines of the function θ = arg(Du). Formulas for the curvature and the length of isocline lines in terms of the curvatures k, j of the level curves and of the steepest descent lines of u are given. The special case when all isoclines are straight lines is studied: in this case the steepest descent lines bend proportionally to the level lines; the support function of the level lines is linear function on the isoclines parameterized by the level values, possibly changing them. This characterization gives a new proof of a property of the developable surfaces found in [A. Fialkow, Geometric characterization of invariant partial differential equations, Amer. J. Math. 59(4) (1937), pp. 833–844]. When u is in the class of quasi convex functions, the L _p norm of the length function I _θ of the isoclines has minimizers with isoclines straight lines; the same occurs for other functionals on u depending on k, j. For a strictly regular quasi convex function isoclines may have arbitrarily large length and arbitrarily large L ₁ norm of I _θ.     

Multi-objective multi-item solid transportation problem in fuzzy environment

A multi-objective multi-item solid transportation problem with fuzzy coefficients for the objectives and constraints, is modeled and then solved by two different methods. A defuzzification method based on fuzzy linear programming is applied for fuzzy supplies, demands and conveyance capacities, including the condition that both total supply and conveyance capacity must not fall below the total demand. First, expected values of the fuzzy objective functions are considered to derive crisp values. Another method based on the concept of “minimum of fuzzy number” is applied for the objective functions that yields fuzzy values instead of particular crisp values for the fuzzy objectives. Fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives. A numerical example is solved using above mentioned methods and corresponding results are compared.     

Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making

The purpose of this paper is to present a generalized hesitant fuzzy synergetic weighted distance (GHFSWD) measure, which is based on the generalized hesitant fuzzy weighted distance (GHFWD) measure and the generalized hesitant fuzzy ordered weighted distance (GHFOWD) measure proposed by Xu and Xia [Z. Xu, M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inf. Sci. 181 (2011) 2128–2138.], and investigate its some desirable properties and special cases. The GHFSWD measure not only generalizes both the GHFWD and GHFOWD measures as well as the common hesitant fuzzy distance measures, but also reflects the importance degrees of both the given individual distances and their ordered positions. Then, based on the defined notions of positive ideal hesitant fuzzy set and negative ideal hesitant fuzzy set, we utilize the proposed GHFSWD measure to develop a method for multiple criteria decision making with hesitant fuzzy information. The method is flexible because it allows decision makers to provide preference with hesitancy and determine different decision results by choosing different decision strategies. Finally, a numerical example is provided to illustrate the feasibility and practicality of the proposed method.     

Set-valued cooperative games with fuzzy payoffs. The fuzzy assignment game

In this paper we study cooperative games with fuzzy payoffs. The main advantage of the approach presented is the incorporation into the analysis of the problem of ambiguity inherent in many real-world collective decision situations. We propose extensions of core concepts which maintain the fuzzy nature of allocations, and lead to a more satisfactory study of the problem within the fuzzy context. Finally, we illustrate the extended core concepts and the approach to obtain the corresponding allocations through the analysis of assignment games with uncertain profits.