A New Approach to the Rule-Base Evidential Reasoning with Application

Sevastjanov, Pavel; Dymova, Ludmila; Kaczmarek, Krzysztof

doi:10.1007/978-3-319-19324-3_25

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…This is not surprising since the DST acts as a generalizing theory for a number of other well-known theories that model uncertainties. It is known that the probability and possibility theories are in some sense the asymptotic cases of the DST; in [15,22], we have shown that the DST is the useful generalization of the A − IFS, as well as of its intervalvalued extension; in [23], we have proved that the same is true in relation to the hesitant and interval-valued hesitant fuzzy sets; in [24], we have introduced the DST extension of the rule-base evidential reasoning in the intuitionistic fuzzy setting, which was used in [25] for the type 2 diabetes diagnostic; in [26], we have used the DST extension of the A − IFS in the generalization of the TOPSIS method. There is such a strong link between rough set theory and the DST that it is difficult to find a more general theory among them [27].…”

Section: Propositionsmentioning

confidence: 99%

On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Sevastjanov

Dymova

Kaczmarek

2021

Entropy

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In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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Section: Propositionsmentioning

confidence: 99%

On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Sevastjanov

Dymova

Kaczmarek

2021

Entropy

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“…In [61], we presented the DST generalization of the rule-base evidential reasoning in the A − IF S environment. This approach we used in [62] for the type 2 diabetes diagnostic. We used the DST extension of the A − IF S to generalize the T OP SIS method in [7].…”

Section: The Studies Of the Dst Extension Of The A − If S Number Introduction Of A New Mathematical Object Belief-plausibility Numbermentioning

confidence: 99%

The New Definitions of Intuitionistic and Belief-Plausibility Based Local Criteria With Interval and Fuzzy Inputs Applied to the Multiple Criteria Problem of a Raw Material Supplier Selection

2021

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The problems of the A − IF S and A − IV IF S theories are analyzed and to solve them, their Dempster-Shafer theory based redefinition is developed and a new concept called Belief-Plausibility number (BP N ) is introduced. The BP N can be applied beyond semantics of usual fuzzy sets and the A − IF S. Two main sources of uncertainty generating the A − IV IF S are considered: an uncertainty coursed by the membership and non-membership functions multiplicity and an uncertainty of inputs. For the fuzzy inputs, the definition of the fuzzy-valued BP N is proposed. The developed approach to treat interval-valued intuitionistic fuzzy objects and their Belief-Plausibility re-definitions allowed us to introduce a set of useful definitions. It is important that some of the them were not earlier mentioned in the literature. The corresponding new arithmetical operations with such objects are proposed. The practical usefulness of the introduced approach is illustrated by the solution of the real-world Fuzzy-Valued Belief-Plausibility multiple criteria problem of the raw material suppliers selection on the steel rolling plant. The obtained results allowed us to state that the introduced Belief-Plausibility approach can be successfully used in the analysis and applications independently, without the use of the A − IF S concepts. This approach owns visible advantages in comparison with the A − IF S based one.

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A Comparative Study of Two Novel Approaches to the Rule-Base Evidential Reasoning

Dymova¹,

Kaczmarek²,

Sevastjanov³

2017

Artificial Intelligence and Soft Computing

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A New Approach to the Rule-Base Evidential Reasoning with Application

Cited by 4 publications

References 22 publications

On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

The New Definitions of Intuitionistic and Belief-Plausibility Based Local Criteria With Interval and Fuzzy Inputs Applied to the Multiple Criteria Problem of a Raw Material Supplier Selection

A Comparative Study of Two Novel Approaches to the Rule-Base Evidential Reasoning

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