Membership functions representing a number vs. representing a set: Proof of unique reconstruction

Nguyen, Hung T.; Kreinovich, Vladik; Kosheleva, Olga

doi:10.1109/fuzz-ieee.2016.7737749

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…They represent a set of elements that belong more or less necessarily (certainly) to F, itself included in a superset of elements that belong more or less possibly to F, these two fuzzy sets being induced by the fact that the relevant information for concluding to belonging or not is incomplete. Besides, a fuzzy set maybe viewed as a representation of a set with an ill-known location between the core and the support of the fuzzy set, see, e.g., [23].…”

Section: Thick Sets and Other Related Notionsmentioning

confidence: 99%

Thick Sets, Multiple-Valued Mappings, and Possibility Theory

Dubois

Jaulin

Prade

2020

Statistical and Fuzzy Approaches to Data Processing, With Applications to Econometrics and Other Areas

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Carrying uncertain information via a multivalued function can be found in different settings, ranging from the computation of the image of a set by an inverse function to the Dempsterian transfer of a probabilistic space by a multivalued function. We then get upper and lower images. In each case one handles socalled "thick sets' in the sense of Jaulin, i.e., lower and upper bounded ill-known sets. Such ill-known sets can be found under different names in the literature, e.g., "interval sets" after Y. Y. Yao, "twofold fuzzy sets" in the sense of Dubois and Prade, or "interval-valued fuzzy sets", ... Various operations can then be defined on these sets, then understood in a disjunctive manner (epistemic uncertainty), rather than conjunctively. The intended purpose of this note is to propose a unified view of these formalisms in the setting of possibility theory, which should enable us to provide graded extensions to some of the considered calculi.

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Section: Thick Sets and Other Related Notionsmentioning

confidence: 99%

Thick Sets, Multiple-Valued Mappings, and Possibility Theory

Dubois

Jaulin

Prade

2020

Statistical and Fuzzy Approaches to Data Processing, With Applications to Econometrics and Other Areas

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Reproving the basic principles of fuzzy sets for the decisions

Nasution

2021

J. Phys.: Conf. Ser.

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Principles in the logic and the sets form the basis of many societal solutions that are present with physical as well as non-physical phenomena. Non-physical phenomena, for example present language variables that require the presence of the fuzzy logic and the fuzzy sets. Although specific verification of the rules used remains the same, the systematic verification for the fuzzy sets requires a strategy, including when implementing it into a computer program. The final problem has the answer to the change in the operator implemented in the program.

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Membership functions representing a number vs. representing a set: Proof of unique reconstruction

Cited by 2 publications

References 3 publications

Thick Sets, Multiple-Valued Mappings, and Possibility Theory

Thick Sets, Multiple-Valued Mappings, and Possibility Theory

Reproving the basic principles of fuzzy sets for the decisions

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