On aggregation operators of transitive similarity and dissimilarity relations

Similarity and dissimilarity are widely used concepts. One of the most studied matters is their combination or aggregation. However, transitivity property is often ignored when aggregating despite being a highly important property, studied by many authors but from different points of view. We collect here some results in preserving transitivity when aggregating, intending to clarify the relationship between aggregation and transitivity and making it useful to design aggregation operators that keep transitivity property. Some examples of the utility of the results are also shown.Peer ReviewedPostprint (published version

An approach for uncertainty aggregation using generalised conjunction/disjunction aggregators

Decision Support Systems are often used in the area of system evaluation. The quality of the output of such a system is only as good as the quality of the data that is used as input. Uncertainty on data, if not taken into account, can lead to evaluation results that are not representative. In this paper, we propose a technique to extend Generalised Con- junction/Disjunction aggregators to deal with un- certainty in Decision Support Systems. We first de- fine the logic properties of uncertainty aggregation through reasoning on strict aggregators and after- wards extend this logic to partial aggregators

An Abstract Approach to Consequence Relations

We generalise the Blok-J\'onsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\'onsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariably aggregated via set-theoretical union. Our approach is more general in that non-idempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. In their abstract form, thus, deductive relations are defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods, and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic

Treatment of imprecision in data repositories with the aid of KNOLAP

Traditional data repositories introduced for the needs of business processing, typically focus on the storage and querying of crisp domains of data. As a result, current commercial data repositories have no facilities for either storing or querying imprecise/ approximate data. No significant attempt has been made for a generic and applicationindependent representation of value imprecision mainly as a property of axes of analysis and also as part of dynamic environment, where potential users may wish to define their “own” axes of analysis for querying either precise or imprecise facts. In such cases, measured values and facts are characterised by descriptive values drawn from a number of dimensions, whereas values of a dimension are organised as hierarchical levels. A solution named H-IFS is presented that allows the representation of flexible hierarchies as part of the dimension structures. An extended multidimensional model named IF-Cube is put forward, which allows the representation of imprecision in facts and dimensions and answering of queries based on imprecise hierarchical preferences. Based on the H-IFS and IF-Cube concepts, a post relational OLAP environment is delivered, the implementation of which is DBMS independent and its performance solely dependent on the underlying DBMS engine

Pythagorean fuzzy combinative distance-based assessment with pure linguistic information and its application to financial strategies of multi-national companies

This article addresses the issue of selecting Financial Strategies in Multi-National companies (F.S.M.). The F.S.M. typically has to consider multiple factors involving multiple stakeholders and, hence, can be handled by applying an appropriate Multi-Criteria Group Decision-Making (M.C.G.D.M.) approach. To address this issue, we develop an M.C.G.D.M. framework to tackle the F.S.M. problem. To handle inherent uncertainty in business decisions as reflected by linguistic reasoning, we embark on constructing a Linguistic Pythagorean Fuzzy (L.P.F.) M.C.G.D.M. framework that is capable of tackling both uncertain decision information and linguistic variables. The proposed approach extends the combinative distancebased assessment (C.O.D.A.S.) method into the L.P.F. environment, and processes decision input expressed as Pythagorean fuzzy sets (P.F.S.) and pure linguistic variables (rather than converting linguistic information into fuzzy numbers). The developed L.P.F.- C.O.D.A.S. technique aggregates the L.P.F. information and is applied to the F.S.M. problem with uncertain linguistic information. A comparative analysis is carried out to compare the results obtained from the proposed L.P.F.-C.O.D.A.S. approach with those from other extensions of C.O.D.A.S. Furthermore, a sensitivity analysis is conducted to check the impact of changes in a distance threshold parameter on the ranking results

Fuzzy Aggregators - an Overview

The article deals with mathematical formalism of the process of combining several inputs into a single output in fuzzy inteligent systems, the process known as aggregation. We are interested in logic aggregation operators. Such aggregators are present in most decision problems and in fuzzy expert systems. Fuzzy inteligent systems are equipped with aggregation operators (aggregators) with which reasoning models adapt well to human reasoning. A brief overview of the field of fuzzy aggregators is given. Attention is devoted to so called graded logic aggregators.. The role of fuzzy agregators in modelling reasoning and the way they are chosen in modelling are pointed out. The conclusions are given and research in the field is pointed out