Two-criteria method for comparing real-valued and interval-valued intuitionistic fuzzy values

Dymova, Ludmila; Sevastjanov, Pavel; Tikhonenko, Anna

doi:10.1016/j.knosys.2013.03.003

Cited by 29 publications

(10 citation statements)

References 52 publications

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“…However, IFST does not only contain operations which are compatible on fuzzy sets, but also such operations which cannot be expressed in the framework of the regular fuzzy set theory [34].…”

Section: Basic Definitionsmentioning

confidence: 99%

An approach to exponentiation with interval-valued power

Tikhonenko-Kędziak¹,

Kurkowski²

2016

J. Appl. Math. Comput. Mech.

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Abstract. The main aim of the work is introducing an operation of raising intuitionistic fuzzy values to intuitionistic fuzzy power, which not requiring to conversion of intuitionistic fuzzy values. Introducing an operation of raising intuitionistic fuzzy values to intuitionistic fuzzy power, which does not require conversion of intuitionistic fuzzy values is the main aim of the work. It is known that, in the classical intuitionistic fuzzy sets theory, the use of all aggregation modes is not always possible because of the lack of definition of raising intuitionistic fuzzy values to intuitionistic fuzzy power. Therefore, the specific aim of the work is to present the heuristic method of raising intuitionistic fuzzy values to intuitionistic fuzzy power, and the consideration of its properties.

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Section: Basic Definitionsmentioning

confidence: 99%

An approach to exponentiation with interval-valued power

Tikhonenko-Kędziak¹,

Kurkowski²

2016

J. Appl. Math. Comput. Mech.

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“…Methods developed for interval-valued intuitionistic fuzzy MCDM problems can be classified into three types: (1) the weighted average aggregation operator approaches, which aggregate the information using different degrees of importance to the arguments [2,9,11,13,15]; (2) the score function methods, which incorporate the membership and non-membership degrees to rank the interval-valued intuitionistic fuzzy numbers (IVIFNs) in the decision-making process [8,14,[16][17][18][19]; and (3) the entropy measure methods, which focus on the discrimination among data by measuring uncertain information [12,[20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A New Prospect Projection Multi-Criteria Decision-Making Method for Interval-Valued Intuitionistic Fuzzy Numbers

Gao

Liu

2016

Information

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Abstract:To depict the influence of decision makers' risk psychology on the interval-valued intuitionistic fuzzy multi-criteria decision-making process, this paper proposes a new method based on prospect theory. Considering the risk attitude of the decision maker, we transform interval-valued intuitionistic fuzzy numbers into real numbers via a prospect value function and consequently derive the prospect decision matrices. Regarding the criteria weights that are incompletely known or completely unknown, a new nonlinear optimization model is developed to determine the criteria weights by considering the subjective and objective factors. Furthermore, we calculate the prospect projection of each alternative for the ideal solution and rank all the alternatives according to the prospect projection values. Finally, an example is provided to illustrate the application of the developed approach.

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“…Owing to the advantage of dealing with uncertain information, many methods on IVIFS have been advanced to solve fuzzy MCDM problems (cf. Park et al, 2009;Nayagam et al, 2011;Intepe et al, 2013;Dymova et al, 2013). The above researches, however, generally studied the problems under the expected utility theory framework.…”

Section: Introductionmentioning

confidence: 99%

Interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making method based on Prospect theory

Gao

Liu

2015

Kybernetes

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Purpose -The purpose of this paper is to provide a new approach to solving the interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making (MCDM) problems. Design/methodology/approach -To transform the interval-valued intuitionistic fuzzy number (IVIFN) into a computational numerical value, a new precision score (P-score) function is developed based on the degrees of membership, non-membership and hesitation. The prospect decision-making matrix is derived by applying P-score function and Prospect theory. A new criteria weighting model is put forward based on the least square method, the maximizing deviation method and Prospect theory. Consequently, combined criteria weighting model with the prospect decision-making matrix, the integrated prospect value is derived which presents a measurement scale for ranking the order of alternatives.Findings -As a result, the method of the interval-valued intuitionistic fuzzy stochastic MCDM is suggested. In this method, the new P-score function responses the comprehensive information of the criteria. The prospect decision-making matrix can reflect the risk attitude of the decision maker. The new criteria weighting model can express both the subjective considerations of the decision maker and the objective information meaning.Research limitations/implications -The research results may lack generalizability for other fuzzy decision making because of the chosen research approach for IVIFN decision making. Therefore, researchers are encouraged to test the proposed propositions further. Practical implications -The developed approach can be applied in many decision-making fields such as selection of renewable energy alternatives, assessment of flexible manufacturing system alternatives and human resource alternatives performance evaluation, etc. where the evaluation values are IVIFNs. Originality/value -This paper succeeds in studying the interval-valued intuitionistic fuzzy MCDM based on Prospect theory, which has not been reported in the existing academic literature.

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Two-criteria method for comparing real-valued and interval-valued intuitionistic fuzzy values

Cited by 29 publications

References 52 publications

An approach to exponentiation with interval-valued power

An approach to exponentiation with interval-valued power

A New Prospect Projection Multi-Criteria Decision-Making Method for Interval-Valued Intuitionistic Fuzzy Numbers

Interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making method based on Prospect theory

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