OWA-based fuzzy m-ary adjacency relations in Social Network Analysis.

In this paper we propose an approach to Social Network Analysis (SNA) based on fuzzy m-ary adjacency relations. In particular, we show that the dimension of the analysis can naturally be increased and interesting results can be derived. Therefore, fuzzy m-ary adjacency relations can be computed starting from fuzzy binary relations and introducing OWA-based aggregations. The behavioral assumptions derived from the measure and the exam of individual propensity to connect with other suggest that OWA operators can be considered particularly suitable in characterizing such relationships.reciprocal relation; fuzzy preference relation; priority vector; normalization

The dynamics of consensus in group decision making: investigating the pairwise interactions between fuzzy preferences.

In this paper we present an overview of the soft consensus model in group decision making and we investigate the dynamical patterns generated by the fundamental pairwise preference interactions on which the model is based. The dynamical mechanism of the soft consensus model is driven by the minimization of a cost function combining a collective measure of dissensus with an individual mechanism of opinion changing aversion. The dissensus measure plays a key role in the model and induces a network of pairwise interactions between the individual preferences. The structure of fuzzy relations is present at both the individual and the collective levels of description of the soft consensus model: pairwise preference intensities between alternatives at the individual level, and pairwise interaction coefficients between decision makers at the collective level. The collective measure of dissensus is based on non linear scaling functions of the linguistic quantifier type and expresses the degree to which most of the decision makers disagree with respect to their preferences regarding the most relevant alternatives. The graded notion of consensus underlying the dissensus measure is central to the dynamical unfolding of the model. The original formulation of the soft consensus model in terms of standard numerical preferences has been recently extended in order to allow decision makers to express their preferences by means of triangular fuzzy numbers. An appropriate notion of distance between triangular fuzzy numbers has been chosen for the construction of the collective dissensus measure. In the extended formulation of the soft consensus model the extra degrees of freedom associated with the triangular fuzzy preferences, combined with non linear nature of the pairwise preference interactions, generate various interesting and suggestive dynamical patterns. In the present paper we investigate these dynamical patterns which are illustrated by means of a number of computer simulations.

Modelling fraud detection by attack trees and Choquet integral

Modelling an attack tree is basically a matter of associating a logical ÒndÓand a logical ÒrÓ but in most of real world applications related to fraud management the Ònd/orÓlogic is not adequate to effectively represent the relationship between a parent node and its children, most of all when information about attributes is associated to the nodes and the main problem to solve is how to promulgate attribute values up the tree through recursive aggregation operations occurring at the Ònd/orÓnodes. OWA-based aggregations have been introduced to generalize ÒndÓand ÒrÓoperators starting from the observation that in between the extremes Òor allÓ(and) and Òor anyÓ(or), terms (quantifiers) like ÒeveralÓ ÒostÓ ÒewÓ ÒomeÓ etc. can be introduced to represent the different weights associated to the nodes in the aggregation. The aggregation process taking place at an OWA node depends on the ordered position of the child nodes but it doesnÕ take care of the possible interactions between the nodes. In this paper, we propose to overcome this drawback introducing the Choquet integral whose distinguished feature is to be able to take into account the interaction between nodes. At first, the attack tree is valuated recursively through a bottom-up algorithm whose complexity is linear versus the number of nodes and exponential for every node. Then, the algorithm is extended assuming that the attribute values in the leaves are unimodal LR fuzzy numbers and the calculation of Choquet integral is carried out using the alpha-cuts.Fraud detection; attack tree; ordered weighted averaging (OWA) operator; Choquet integral; fuzzy numbers.

New closeness coefficients for fuzzy similarity based fuzzy TOPSIS: an approach combining fuzzy entropy and multidistance

This paper introduces new closeness coefficients for fuzzy similarity based TOPSIS. The new closeness coefficients are based on multidistance or fuzzy entropy, are able to take into consideration the level of similarity between analysed criteria, and can be used to account for the consistency or homogeneity of, for example, performance measuring criteria. The commonly known OWA operator is used in the aggregation process over the fuzzy similarity values. A range of orness values is considered in creating a fuzzy overall ranking for each object, after which the fuzzy rankings are ordered to find a final linear ranking. The presented method is numerically applied to a research and development project selection problem and the effect of using two new closeness coefficients based on multidistance and fuzzy entropy is numerically illustrated

OWA-based fuzzy m-ary adjacency relations in Social Network Analysis

In this paper we propose an approach to Social Network Analysis (SNA) based on fuzzy m-ary adjacency relations. In particular, we show that the dimension of the analysis can naturally be increased and interesting results can be derived. Therefore, fuzzy m-ary adjacency relations can be computed starting from fuzzy binary relations and introducing OWA-based aggregations. The behavioral assumptions derived from the measure and the exam of individual propensity to connect with other suggest that OWA operators can be considered particularly suitable in characterizing such relationships

Stability in Multiobjective Possibilistic Linear Programs

This paper cN tinues the authors'researc h in stability analysis in possibilistic programming in that it extends the results in [7] to possibilistic linear programs with multiple objec4 efunc9N-4 Namely, we show that multiobjec tive possibilistic linear programs withct tinuous fuzzy number ce#c98 ts are well-posed, i.e. smallc hanges in the membershipfuncpN of thec e#c41 ts mayc118 only a small deviation in the possibility distribution of the objec9 e func81N Keywords:Multiob jective possiby'Tk3# linear programs (MPLP), possibky' ytheory, fuzzynumb er,stabw7B y

Stability in GDSS under fuzzy production rules

Fedrizzi and Md h [6] have presented a new Group Decision Support System (GDSS) logic architecture in which linguistic variables and fuzzy production rules have been used for reaching consensus. We show that when all the fuzzy numbers representing the performance levels have continuous membership function, then the consensus degrees (defined by a certain similarity measure) relative to each alternative are stable under small changes of the experts' opinions.

Stability In Possibilistic Linear Programming With Continuous Fuzzy Number Parameters

We prove that possibilistic linear progra#isti problems (introduced by Buckley in [2])a#] well-posed, i.e. sma#. cha#9O of the membership function of the pa#0xO.SR ma yca#93 onlya sma#. devia#RxO in the possibilistic distribution of the objective function

Stability in Multiobjective Possibilistic Linear Programs

This paper continues the authors' research in stability analysis in possibilistic programming in that it extends the results in [7] to possibilistic linear programs with multiple objective functions. Namely, we show that multiobjective possibilistic linear programs with continuous fuzzy number coe#cients are well-posed, i.e. small changes in the membership function of the coe#cients may cause only a small deviation in the possibility distribution of the objective function. Keywords: Multiobjective possibilistic linear programs (MPLP), possibility theory, fuzzy number, stability 1 Introduction Stability and sensitivity analysis becomes more and more attractive also in the area of multiple objective mathematical programming (for excellent surveys see e.g. Gal [10] and Rios Insua [18]). Publications on this topic usually investigate the impact of parameter changes (in the righthand side or/and the objective functions or/and the 'A-matrix' or/and the domination structure) on the solution..