Affiliations: LGP-ENIT, Université de Toulouse, Tarbes, France | E-mail: [email protected]
Correspondence:
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Corresponding author: LGP-ENIT, Université de Toulouse, Tarbes, France. %****␣idt-13-idt190355_temp.tex␣Line␣25␣**** E-mail: [email protected].
Abstract: Nominal classification (NC) is a subfield of multi-criteria decision making where an object (in a broad sense) characterized by some attributes (with their valuation belonging to an ordered set, numeric in general) must be assigned to one of pre-defined classes or categories; these classes are characterized by some numerical valued features. This is also known as supervised classification as opposed to unsupervised classification in machine learning literature. In many applications such as that of risk analysis, characterization of classes by features may not be precisely defined; they will be rather fuzzily expressed using linguistic appreciation such as high is better, low is more appreciated, medium range is better, etc. leading to what is referred to as fuzzy nominal classification (FNC). On other hand bipolar reasoning is pervasive in classification in the sense that given a couple (feature, class), there will be some values of the feature that lead to automatically assigning (respect. automatically excluding to assign) the considered object into that class leading to what we name bipolar fuzzy nominal classification or BFNC for short; the main purpose of this paper is to develop this BFNC framework with risk analysis as an illustrative application domain. The stepping stones of this framework are two indexes for each couple (class, object) known as classifiability index (that measures the extent to which the considered object can be included into that class) and the rejectability index measuring the extent to which one should avoid including this object into that class. By using two indexes for classification, many classes can be qualified for inclusion of a given object rendering this framework flexible. Analyzing risks for large-scale complex systems requires identifying, assessing, and prioritizing different risk scenarios for their appropriate treatment such as resources allocation for risk mitigation, risk prevention, risk sharing, etc. To this end and given scarcity of resources in general, one must consider first prioritizing, filtering, or scoring risks that return to assigning them to pre-defined classes or categories; that is nominally classifying them. The developed BFNC framework applied to a real world application in the domain of countries’ risk classification shows its practical potentialities.
