The existing expert weight determination method for multi-attribute decision making based on the Pythagorean fuzzy number approach does not make sufficient use of hesitation involved with information, which may cause biased assignment. Therefore, to address issue unknown weights and attribute evaluation numbers in group decision-making problems, a is proposed that improves treatment sets. First...

since the rate of return on different opportunities for investment is random, the optimal distribution of ones capital is put foreward as a stochastic control problem. in this paper, using modem techniques in the theory of random functions and the stochsatic calculus, the problem is discussed for the case when the information possessed by the different investors, as well as their probability be...

The objective of this study is to present the test results of variable air volume (VAV) air conditioning system optimized by two objective genetic algorithm (GA). The objective functions are energy savings and thermal comfort. The optimal set points for fuzzy logic controller (FLC) are the supply air temperature (Ts), the supply duct static pressure (Ps), the chilled water temperature (Tw), and...

This paper deals with the stock portfolio selection problem involved trapezoidal fuzzy number returns and multiple mental accounts. A behavioral decision model is proposed to maximize possibilistic mean value of return ensure each account exceeding given minimum aspiration level a probability. Then, some programming models are designed solve optimal strategy. Finally, one numerical example illu...

Real estate investments are typically characterized by high degrees of leverage and long loan tenures. In perfect capital markets, leverage has no impact on the investment decision apart from tax considerations. However, the mortgage financing market is imperfect in many countries. In the presence of market imperfections, an optimal holding period exists for real property investments. We provid...

It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coefficients in any number of variables is sufficient, but that there exists a parametrization of Pythagorean triples by a single triple of integer-valued polynomials. The second author has recently studied polynomial pa...

We address the question of the “partition regularity” of the Pythagorean equation a+b = c; in particular, can the natural numbers be assigned a 2-coloring, so that no Pythagorean triple (i.e., a solution to the equation) is monochromatic? We prove that the hypergraph of Pythagorean triples can contain no Steiner triple systems, a natural obstruction to 2-colorability. Then, after transforming t...

Does the world really need another article about Pythagorean triples? Here is why we think so. The set of Pythagorean triples has a lot of interesting structure, which has intrigued both amateur and professional mathematicians. It is the topic of an extensive mathematical literature, almost all of which relies on an enumeration of primitive Pythagorean triples that has been known since ancient ...

The coordination of two-echelons supply chain by buyback contract under the imperfect product quality and fuzzy demand environment is investigated in this paper. The mathematical models are built based on credibility theory, and the optimal parameters of buyback contract are obtained. In addition, the influence of the imperfect product rate on the parameters of buyback contract is analyzed. Fin...

and Applied Analysis 3 A α , A β are matrices that will be updated adaptively with the following updating laws: ?̇? α (t) = −Q −1 ⋅ z ⋅ ξ T α ⋅ es, ?̇? β (t) = −Q −1 ⋅ z ⋅ ξ T β ⋅ es ⋅ u (t) (12) and finally the control law is described as follows: u (t) = 1 β (t) + β (x) (− [α (t) + ?̂? (x)] + v (t)) . (13) 2.2. Direct Adaptive Fuzzy Controller (DAFC). Control law u(t) in feedback linearization m...