Solving interval-valued transportation problem using a new ranking function for octagonal fuzzy numbers

In this paper, we introduce a new method to solve Interval-Valued Transportation Problem (IVTP) to deal with those problems of transportation wherein the information available is imprecise. First, a newly proposed fuzzification method is used to convert the IVTP to octagonal fuzzy transportation problem and then with the help of ranking function proposed in this paper, the fuzzy transportation problem is converted into crisp transportation problem. Lastly, Initial Basic Feasible Solution (IBFS) of this problem is obtained using Vogel’s Approximation Method and the solution is improved using Modified Distribution (MODI) method. A numerical example with interval data is solved using the proposed algorithm to make comparison of the solution with some other methods. Also, a numerical example with parameters in the form of octagonal fuzzy numbers is illustrated to compare the effectiveness of the proposed ranking technique. The proposed fuzzification and ranking technique can be used in the other fields of decision making dealing with the data in the same form as considered in this paper.

The Ranking Function for Solving the Fuzzy Hotelling T2 Test

A multivariate control chart is measured by many variables that are correlated in production, using the quality characteristics in any product. In this paper, statistical procedures were employed to find the multivariate quality control chart by utilizing fuzzy Hotelling test. The procedure utilizes the triangular membership function to treat the real data, which were collected from Baghdad Soft Drinks Company in Iraq. The quality of production was evaluated by using a new method of the ranking function.

Controlling Fairness and Bias in Dynamic Learning-to-Rank (Extended Abstract)

Rankings are the primary interface through which many online platforms match users to items (e.g. news, products, music, video). In these two-sided markets, not only do the users draw utility from the rankings, but the rankings also determine the utility (e.g. exposure, revenue) for the item providers (e.g. publishers, sellers, artists, studios). It has already been noted that myopically optimizing utility to the users -- as done by virtually all learning-to-rank algorithms -- can be unfair to the item providers. We, therefore, present a learning-to-rank approach for explicitly enforcing merit-based fairness guarantees to groups of items (e.g. articles by the same publisher, tracks by the same artist). In particular, we propose a learning algorithm that ensures notions of amortized group fairness, while simultaneously learning the ranking function from implicit feedback data. The algorithm takes the form of a controller that integrates unbiased estimators for both fairness and utility, dynamically adapting both as more data becomes available. In addition to its rigorous theoretical foundation and convergence guarantees, we find empirically that the algorithm is highly practical and robust.

Beyond equi-joins

We study theta-joins in general and join predicates with conjunctions and disjunctions of inequalities in particular, focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking function. Our approach achieves strong time and space complexity properties: with n denoting the number of tuples in the database, we guarantee for acyclic full join queries with inequality conditions that for every value of k , the k top-ranked answers are returned in O ( n polylog n + k log k ) time. This is within a polylogarithmic factor of O ( n + k log k ), i.e., the best known complexity for equi-joins, and even of O ( n + k ), i.e., the time it takes to look at the input and return k answers in any order. Our guarantees extend to join queries with selections and many types of projections (namely those called "free-connex" queries and those that use bag semantics). Remarkably, they hold even when the number of join results is n ℓ for a join of ℓ relations. The key ingredient is a novel O ( n polylog n )-size factorized representation of the query output , which is constructed on-the-fly for a given query and database. In addition to providing the first nontrivial theoretical guarantees beyond equi-joins, we show in an experimental study that our ranked-enumeration approach is also memory-efficient and fast in practice, beating the running time of state-of-the-art database systems by orders of magnitude.

Dhouib-Matrix-TSP1 Method to Optimize Octagonal Fuzzy Travelling Salesman Problem Using α-Cut Technique

This paper proposes the optimization of the fuzzy travel salesman problem by using the α-Cut technique as a ranking function and the Dhouib-Matrix-TSP1 as an approximation method. This method is enhanced by the standard deviation metric and obtains a minimal tour in fuzzy environment where all parameters are octagonal fuzzy numbers. Fuzzy numbers are converted into a crisp number thanks to the ranking function α-Cut. The proposed approach in details is discussed and illustrated by a numerical example. This method helps in designing successfully the tour to a salesman on navigation through the distance matrix so that it minimizes the total fuzzy distance.

Graph-based entity-oriented search

Entity-oriented search has revolutionized search engines. In the era of Google Knowledge Graph and Microsoft Satori, users demand an effortless process of search. Whether they express an information need through a keyword query, expecting documents and entities, or through a clicked entity, expecting related entities, there is an inherent need for the combination of corpora and knowledge bases to obtain an answer. Such integration frequently relies on independent signals extracted from inverted indexes, and from quad indexes indirectly accessed through queries to a triplestore. However, relying on two separate representation models inhibits the effective cross-referencing of information, discarding otherwise available relations that could lead to a better ranking. Moreover, different retrieval tasks often demand separate implementations, although the problem is, at its core, the same. With the goal of harnessing all available information to optimize retrieval, we explore joint representation models of documents and entities, while taking a step towards the definition of a more general retrieval approach. Specifically, we propose that graphs should be used to incorporate explicit and implicit information derived from the relations between text found in corpora and entities found in knowledge bases. We also take advantage of this framework to elaborate a general model for entity-oriented search, proposing a universal ranking function for the tasks of ad hoc document retrieval (leveraging entities), ad hoc entity retrieval, and entity list completion. At a conceptual stage, we begin by proposing the graph-of-entity, based on the relations between combinations of term and entity nodes. We introduce the entity weight as the corresponding ranking function, relying on the idea of seed nodes for representing the query, either directly through term nodes, or based on the expansion to adjacent entity nodes. The score is computed based on a series of geodesic distances to the remaining nodes, providing a ranking for the documents (or entities) in the graph. In order to improve on the low scalability of the graph-of-entity, we then redesigned this model in a way that reduced the number of edges in relation to the number of nodes, by relying on the hypergraph data structure. The resulting model, which we called hypergraph-of-entity, is the main contribution of this thesis. The obtained reduction was achieved by replacing binary edges with n -ary relations based on sets of nodes and entities (undirected document hyperedges), sets of entities (undirected hyperedges, either based on cooccurrence or a grouping by semantic subject), and pairs of a set of terms and a set of one entity (directed hyperedges, mapping text to an object). We introduce the random walk score as the corresponding ranking function, relying on the same idea of seed nodes, similar to the entity weight in the graph-of-entity. Scoring based on this function is highly reliant on the structure of the hypergraph, which we call representation-driven retrieval. As such, we explore several extensions of the hypergraph-of-entity, including relations of synonymy, or contextual similarity, as well as different weighting functions per node and hyperedge type. We also propose TF-bins as a discretization for representing term frequency in the hypergraph-of-entity. For the random walk score, we propose and explore several parameters, including length and repeats, with or without seed node expansion, direction, or weights, and with or without a certain degree of node and/or hyperedge fatigue, a concept that we also propose. For evaluation, we took advantage of TREC 2017 OpenSearch track, which relied on an online evaluation process based on the Living Labs API, and we also participated in TREC 2018 Common Core track, which was based on the newly introduced TREC Washington Post Corpus. Our main experiments were supported on the INEX 2009 Wikipedia collection, which proved to be a fundamental test collection for assessing retrieval effectiveness across multiple tasks. At first, our experiments solely focused on ad hoc document retrieval, ensuring that the model performed adequately for a classical task. We then expanded the work to cover all three entity-oriented search tasks. Results supported the viability of a general retrieval model, opening novel challenges in information retrieval, and proposing a new path towards generality in this area.