Concepts in Fuzzy Scaling Theory: order and granularity

This paper continues another our work, which is the first of two parts where the approach to the processing of quantitative expert evaluations in the process of group decision-making under uncertainty is considered. In the second part, represented by this paper, an approach is proposed for the processing of qualitative expert evaluations in the process of group decision-making. The approach is based on the use of triangular fuzzy numbers. In group decision-making the opinions of experts are expressed by linguistic variables like very bad, not very bad, problematic, good, and so on. The technique of conversion of expert quantitative opinions to triangular fuzzy numbers is considered. A simple method of expressing expert opinions by triangular fuzzy numbers is introduced. A new approach to determining the expert degrees of importance is proposed. The proposed methodology is discussed in full detail and its algorithm is described. An illustrative example is given.

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“…." (see [12]). In order to better understand the essence of a linguistic variable, we present one of its formal definitions.…”

Section: Methodology For Fuzzy Aggregation Of Expert Qualitative Opinmentioning

confidence: 96%

“…(see[12]). A classical linguistic variable is a quintuple (X; V ; μ; [0, 1]; ≤), where X is a set (called the 'domain'), V is a set (of 'linguistic values'), ([0, 1], ≤) is the real unit interval with its usual ordering, and μ is mapping μ : V → F (X, [0, 1]) that represents each linguistic value v by a membership function μ v := μ(v) on X.…”

mentioning

confidence: 99%

Application of Fuzzy Sets in Solving Some Management Problem. Part 2

2015

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“…In this spirit, conceptual scale theory [44] may be used to achieve a suitable (Boolean) representation by successive subsumptions.…”

Section: Gradual Properties: Unipolar Vs Bipolar Scale Interpretationmentioning

confidence: 99%

Formal Concept Analysis from the Standpoint of Possibility Theory

Dubois

Prade

2015

Formal Concept Analysis

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15496The contribution was presented at : http://www.matap.uma.es/icfca2015/files/a61b70b0124cd72ef5b1442c0223db4a-0.html Abstract. Formal concept analysis (FCA) and possibility theory (PoTh) have been developed independently. They address different concerns in information processing: while FCA exploits relations linking objects and properties, and has applications in data mining and clustering, PoTh deals with the modeling of (graded) epistemic uncertainty. However, making a formal parallel between FCA and PoTh is fruitful. The four set-functions at work in PoTh have meaningful counterparts in FCA; this leads to consider operators neglected in FCA, and thus new fixed point equations. One of these pairs of equations, paralleling the one defining formal concepts in FCA, defines independent sub-contexts of objects and properties that have nothing in common. The similarity of the structures underlying FCA and PoTh is still more striking, using a cube of opposition (a device extending the traditional square of opposition in logic). Beyond the parallel between FCA and PoTh, this invited contribution, which largely relies on several past publications by the authors, also addresses issues pertaining to the possible meanings, degree of satisfaction vs. degree of certainty, of graded object-property links, which calls for distinct manners of handling the degrees. Other lines of interest for further research are briefly mentioned.

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“…A many valued context may not only have crosses (i.e., yes/no) as entries, but values of attributes pairs. It can be seen as a table of a relational database with the column containing the objects being a primary key [7] .…”

Section: Definition 4 a Fuzzy Formal Context Is A Triplementioning

confidence: 99%

Cooperative Answering of Fuzzy Queries

Hachani

Hassine

Chettaoui

et al. 2009

J. Comput. Sci. Technol.

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The majority of existing information systems deals with crisp data through crisp database systems. Traditional Database Management Systems (DBMS) have not taken into account imprecision so one can say there is some sort of lack of flexibility. The reason is that queries retrieve only elements which precisely match to the given Boolean query. That is, an element belongs to the result if the query is true for this element; otherwise, no answers are returned to the user. The aim of this paper is to present a cooperative approach to handling empty answers of fuzzy conjunctive queries by referring to the Formal Concept Analysis (FCA) theory and fuzzy logic. We present an architecture which combines FCA and databases. The processing of fuzzy queries allows detecting the minimal reasons of empty answers. We also use concept lattice in order to provide the user with the nearest answers in the case of a query failure.

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Concepts in Fuzzy Scaling Theory: order and granularity

Cited by 31 publications

References 5 publications

Application of Fuzzy Sets in Solving Some Management Problem. Part 2

Application of Fuzzy Sets in Solving Some Management Problem. Part 2

Formal Concept Analysis from the Standpoint of Possibility Theory

Cooperative Answering of Fuzzy Queries

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