Multi-attribute group decision making method under 2-dimension uncertain linguistic variables

A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.

A Proxy Signature Scheme as Secure as Decisional Diffie-Hellman Problem

Based on decisional Difiie-Hcllman problem, we propose a simpleproxy-protected signature scheme In the random oracle model, we also carry out the strict securityproof for the proposed scheme. The security of the proposed scheme is not loosely related to thediscrete logarithm assumption hut tightly related to the decisional Diffie-Hellman assumption in therandom oracle model.

THE SPECTRALITY DECISION PROBLEM

An efficient algorithm for deciding whether a given integer vector is the spectrum of some Boolean function is presented. The algorithm performs a step-by-step spectral decomposition of the input vector and checks at each step a set of necessary conditions for spectrality for the resulting vectors. The algorithm concludes that the input vector cannot lead to a valid Boolean function as soon as a vector not satisfying the conditions is found, which, as proved in the paper, for almost all cases happens after the first step of the decomposition.

Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of differ- ent proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable prop- erties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Lim- itations of existing ranking methods have been studied. Fur- ther for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.

A Measure of the Structured Degree for Decision Problems

Analysis on the taxonomy of decision problems is made and some fundamental views on decision problems are stated in this paper. Based upon understanding of decision problem and its structure in depth, a measure of the structured degree for decision problems is obtained by constructing a monotonic mapping. The corresponding relation between the measure value and division of the structured degree for decision problems is given in quantity and theories of decision support are enlarged.

Reinforcement Learning Algorithm for Solving Load Commitment Problem Considering a General Load Model

Under the smart grid paradigm, in the near future all consumers will be exposed to variable pricing schemes introduced by utilities. Hence, there is a need to develop algorithms which could be used by the consumers to schedule their loads. In this paper, load scheduling problem is formulated as a LCP （load commitment problem）. The load model is general and can model atomic and non-atomic loads. Furthermore, it can also take into consideration the relative discomfort caused by delay in scheduling any load. For this purpose, a single parameter ＂uric＂ is introduced in the load model which captures the relative discomfort caused by delay in scheduling a particular load. Guidelines for choosing this parameter are given. All the other parameters of the proposed load model can be easily specified by the consumer. The paper shows that the general LCP can be viewed as multi-stage decision making problem or a MDP （Markov decision problem）. RL （reinforcement learning） based algorithm is developed to solve this problem. The efficacy of the algorithm is investigated when the price of electricity is available in advance as well as for the case when it is random. The scalability of the approach is also investigated.

ON THE DECISION PROBLEM OF THE CENTER OR FOCUS FOR A CLASS OF PLANAR POLYNOMIAL FIELDS

In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any order derivative of h(x) at x=0 and obtain the focus value of each order. The new method in this paper avoids the recurence operation and reduces the work in calculating the focus value.

Complexities of Homomorphism and Isomorphism for Definite Logic Programs

A homomorphism φ of logic programs from P to P＇ is a function mapping Atoms（P） to Atoms（P＇） and it preserves complements and program clauses. For each definite program clause a ← a1,...,an ∈ P it implies that φ（a） ←- φ（a1）,...,φ（an） is a program clause of P＇. A homomorphism φis an isomorphism if φ is a bijection. In this paper, the complexity of the decision problems on homomorphism and isomorphism for definite logic programs is studied. It is shown that the homomorphism problem （HOM-LP） for definite logic programs is NP-complete, and the isomorphism problem （ISO-LP） is equivalent to the graph isomorphism problem （GI）.

Secure Proxy Re-Encryption from CBE to IBE

In this paper, an efficient hybrid proxy re-encryption scheme that allows the transformation of the ciphertexts in a traditional public key cryptosystem into the ciphertexts in an identity-based system is proposed. The scheme is non-interactive, unidirectional and collude ＂safe＂. Furthermore, it is compatible with current IBE （identity-based encryption） deployments. The scheme has chosen ciphertext security in the random oracle model assuming the hardness of the Decisional Bilinear Diffie-Hellman problem.

Parameterized Algorithmics for Computational Social Choice:Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science,and Social Science on the one side, and Mathematics and Computer Science（including Artificial Intelligence and Multiagent Systems） on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. This work is dedicated to Jianer Chen, one of the strongest problem solvers in the history of parameterized algorithmics,on the occasion of his 60 th birthday.