By Patrice Perny, Marc Roubens (auth.), Roman Słowiński (eds.)

ISBN-10: 1461375835

ISBN-13: 9781461375838

ISBN-10: 1461556457

ISBN-13: 9781461556459

*Fuzzy units in choice research, Operations examine and Statistics* contains chapters on fuzzy choice modeling, a number of standards research, rating and sorting tools, team decision-making and fuzzy online game thought. It additionally provides optimization thoughts comparable to fuzzy linear and non-linear programming, functions to graph difficulties and fuzzy combinatorial equipment akin to fuzzy dynamic programming. moreover, the ebook additionally bills for advances in fuzzy information research, fuzzy data, and functions to reliability research. those issues are lined inside 4 elements:

- Decision Making,
- Mathematical Programming,
- Statistics and information research, and
- Reliability, upkeep and substitute.

The scope and content material of the ebook has resulted from a number of interactions among the editor of the quantity, the sequence editors, the sequence advisory board, and specialists in every one bankruptcy region. every one bankruptcy used to be written by means of a widely known researcher at the subject and reviewed through different specialists within the sector. those professional reviewers occasionally grew to become co-authors as a result of quantity in their contribution to the bankruptcy. for this reason, twenty-five authors from twelve international locations and 4 continents have been desirous about the construction of the thirteen chapters, which boosts the overseas personality of the undertaking and offers an concept of the way rigorously the guide has been developed.

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**Additional resources for Fuzzy Sets in Decision Analysis, Operations Research and Statistics**

**Sample text**

The (R-, R+) pair defines an interval valued relation. Moreover, following the idea of equation (54), alternatives could be compared according to the relation: This general construction has been studied by Perny (1994) and some particular results are yet available (many investigations are still to be made on this topic). For example, when B(u, v) E {O, I} for all (u, v) E JR X JR, R is necessarily a crisp preference relation, and R-(a,b) > 0 ¢::> R+(a,b) = 1. In this case, R+(a, b) and R-(a, b) measure the possibility and the necessity of the assertion aRb respectively, and for any G, (J E (0,1), relations R and R{3 are identical up to an automorphism of [0, 1].

E. enumerated values without any structure, such as {cabbage, turnip, horseradish, cucumber} are not suitable. A typical example of non numerical scale is a linguistic scale often used in fuzzy set theory, such as {small, medium, large}, or {unsuitable, acceptable, average, good, excellent}. Numerical scales can be of ordinal or cardinal type. On an ordinal scale, numbers have no other meaning than defining an order relation on the scale, and distances or differences between values cannot be defined.

9 will briefly address this issue. Once values are defined we can aggregate them and obtain a new value defined on the same scale, but this can be done in many different ways according to what is expected from the aggregation operation, what is the nature of the values to be aggregated, and what kind of scale has been used. We elaborate on these three points. Aggregation operators can be roughly divided into three classes, each possessing very distinct behavior or semantic. Conjunctive operators combine values FUZZY AGGREGATION OF NUMERICAL PREFERENCES 33 as if they were related by a logical "and" operator.

### Fuzzy Sets in Decision Analysis, Operations Research and Statistics by Patrice Perny, Marc Roubens (auth.), Roman Słowiński (eds.)

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