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Register a new userConsensus and Consistency Level Optimization of Fuzzy Preference Relation: A Soft Computing Approach
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Added by
Sujit Das
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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In group decision making (GDM) problems fuzzy preference relations (FPR) are widely used for representing decision makers opinions on the set of alternatives. In order to avoid misleading solutions, the study of consistency and consensus has become a very important aspect. This article presents a simulated annealing (SA) based soft computing approach to optimize the consistency/consensus level (CCL) of a complete fuzzy preference relation in order to solve a GDM problem. Consistency level indicates as experts preference quality and consensus level measures the degree of agreement among experts opinions. This study also suggests the set of experts for the necessary modifications in their prescribed preference structures without intervention of any moderator.
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The concept of fuzzy soft set was introduced for the first time by Maji et al. in 2002, and was considered sharply from applicable aspects to theoretical aspects by a wide range of researchers. In this paper the concept of fuzzy soft norm over fuzzy soft spaces has been considered and some properties of fuzzy soft normed spaces are studied. We also study the fuzzy soft topology over a crisp set by using the fuzzy soft subsets of it and the relationship between fuzzy soft topology and general topology is investigated. Fuzzy soft linear operator over fuzzy soft spaces is introduced and continuity of such operators is considered.
Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors introduced by todays quantum computers, hybrid algorithms combining classical and quantum computers are used. In this paper we tackle the multiple query optimization problem (MQO) which is an important NP-hard problem in the area of data-intensive problems. We propose a novel hybrid classical-quantum algorithm to solve the MQO on a gate-based quantum computer. We perform a detailed experimental evaluation of our algorithm and compare its performance against a competing approach that employs a quantum annealer -- another type of quantum computer. Our experimental results demonstrate that our algorithm currently can only handle small problem sizes due to the limited number of qubits available on a gate-based quantum computer compared to a quantum computer based on quantum annealing. However, our algorithm shows a qubit efficiency of close to 99% which is almost a factor of 2 higher compared to the state of the art implementation. Finally, we analyze how our algorithm scales with larger problem sizes and conclude that our approach shows promising results for near-term quantum computers.
How to measure the degree of uncertainty of a given frame of discernment has been a hot topic for years. A lot of meaningful works have provided some effective methods to measure the degree properly. However, a crucial factor, sequence of propositions, is missing in the definition of traditional frame of discernment. In this paper, a detailed definition of ordinal frame of discernment has been provided. Besides, an innovative method utilizing a concept of computer vision to combine the order of propositions and the mass of them is proposed to better manifest relationships between the two important element of the frame of discernment. More than that, a specially designed method covering some powerful tools in indicating the degree of uncertainty of a traditional frame of discernment is also offered to give an indicator of level of uncertainty of an ordinal frame of discernment on the level of vector.
Preference orderings are orderings of a set of items according to the preferences (of judges). Such orderings arise in a variety of domains, including group decision making, consumer marketing, voting and machine learning. Measuring the mutual information and extracting the common patterns in a set of preference orderings are key to these areas. In this paper we deal with the representation of sets of preference orderings, the quantification of the degree to which judges agree on their ordering of the items (i.e. the concordance), and the efficient, meaningful description of such sets. We propose to represent the orderings in a subsequence-based feature space and present a new algorithm to calculate the size of the set of all common subsequences - the basis of a quantification of concordance, not only for pairs of orderings but also for sets of orderings. The new algorithm is fast and storage efficient with a time complexity of only $O(Nn^2)$ for the orderings of $n$ items by $N$ judges and a space complexity of only $O(min{Nn,n^2})$. Also, we propose to represent the set of all $N$ orderings through a smallest set of covering preferences and present an algorithm to construct this smallest covering set. The source code for the algorithms is available at https://github.com/zhiweiuu/secs
A ranking is an ordered sequence of items, in which an item with higher ranking score is more preferred than the items with lower ranking scores. In many information systems, rankings are widely used to represent the preferences over a set of items or candidates. The consensus measure of rankings is the problem of how to evaluate the degree to which the rankings agree. The consensus measure can be used to evaluate rankings in many information systems, as quite often there is not ground truth available for evaluation. This paper introduces a novel approach for consensus measure of rankings by using graph representation, in which the vertices or nodes are the items and the edges are the relationship of items in the rankings. Such representation leads to various algorithms for consensus measure in terms of different aspects of rankings, including the number of common patterns, the number of common patterns with fixed length and the length of the longest common patterns. The proposed measure can be adopted for various types of rankings, such as full rankings, partial rankings and rankings with ties. This paper demonstrates how the proposed approaches can be used to evaluate the quality of rank aggregation and the quality of top-$k$ rankings from Google and Bing search engines.
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