Informatica

The extensions of ordinary fuzzy sets are problematic because they require decimal numbers for membership, non-membership and indecision degrees of an element from the experts, which cannot be easily determined. This will be more difficult when three or more digits’ membership degrees have to be assigned. Instead, proportional relations between the degrees of parameters of a fuzzy set extension will make it easier to determine the membership, non-membership, and indecision degrees. The objective of this paper is to present a simple but effective technique for determining these degrees with several decimal digits and to enable the expert to assign more stable values when asked at different time points. Some proportion-based models for the fuzzy sets extensions, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets are proposed, including their arithmetic operations and aggregation operators. Proportional fuzzy sets require only the proportional relations between the parameters of the extensions of fuzzy sets. Their contribution is that these models will ease the use of fuzzy set extensions with the data better representing expert judgments. The imprecise definition of proportions is also incorporated into the given models. The application and comparative analyses result in that proportional fuzzy sets are easily applied to any problem and produce valid outcomes. Furthermore, proportional fuzzy sets clearly showed the role of the degree of indecision in the ranking of alternatives in binomial and trinomial fuzzy sets. In the considered car selection problem, it has been observed that there are minor changes in the ordering of intuitionistic and spherical fuzzy sets.

Picture fuzzy sets (PFSs) utilize the positive, neutral, negative and refusal membership degrees to describe the behaviours of decision-makers in more detail. In this article, we expound the application of extended TODIM based on cumulative prospect theory under picture fuzzy multiple attribute group decision making (MAGDM). In addition, we adopt Information Entropy, which is used to ascertain the weighting vector of attributes to improve the availability of the TODIM method. At last, we exercise the improved TODIM into a numerical case for super market location and testify the effectiveness of this new method by comparing its results with other methods’ results.

From the perspective of multiple attribute decision analysis, the evaluation of decision alternatives should be based on the performance scores determined with respect to more than one attribute. Fuzzy logic concepts can equip the evaluation process with different scales of linguistic terms to let the decision-makers point out their ideas and preferences. A more recent one of fuzzy sets is the picture fuzzy set which covers three separately allocable elements: positive, neutral, and negative membership degrees. The novel and distinctive element included by a picture fuzzy set is the refusal degree which is equal to the difference between 1 and the sum of the other three. In this study, we aim to contribute to the literature of the picture fuzzy sets by (i) proposing two novel entropy measures that can be used in objective attribute weighting and (ii) developing a novel picture fuzzy version of CODAS (COmbinative Distance-based ASsessment) method which is empowered with entropy-based attribute weighting. The applicability of the method is shown in a green supplier selection problem. To clarify the differences of the proposed method, a comparative analysis is provided by considering traditional CODAS, spherical fuzzy CODAS, and spherical fuzzy TOPSIS with different entropy-based scenarios.

As an extension of intuitionistic fuzzy sets, picture fuzzy sets can deal with vague, uncertain, incomplete and inconsistent information. The similarity measure is an important technique to distinguish two objects. In this study, a similarity measure between picture fuzzy sets based on relationship matrix is proposed. The new similarity measure satisfies the axiomatic definition of similarity measure. It can be testified from a numerical experiment that the new similarity measure is more effective. Finally, we apply the proposed similarity measure to multiple-attribute decision making.