Sum Of Memberships Research Articles

Robotic sensor based on score and accuracy values in [formula omitted]-rung complex diophatine neutrosophic normal set with an aggregation operation

The multiple-attribute decision-making (MADM) problem is resolved through the q-rung complex diophantine neutrosophic normal set (q-rung CDNNS). An important way to express uncertain information is using q-rung orthopair fuzzy sets (q-ROFs). Yager introduced q-ROFs as a generalization of intuitionistic fuzzy sets in which the sum of membership and non-membership degrees is one. In addition, they have superiority over intuitionistic fuzzy sets and Pythagorean fuzzy sets. Complex diophantine fuzzy sets are generalizations of neutrosophic and diophantine fuzzy sets, respectively. Several aggregating operations (AOs) are discussed here, as well as their respective interpretations. The paper discusses q-rung CDNN weighted averaging (q-rung CDNNWA), q-rung CDNN weighted geometric (q-rung CDNNWG), q-rung generalized CDNN weighted averaging (q-rung GCDNNWA) and q-rung generalized CDNN weighted geometric (q-rung GCDNNWG). We will review several of these sets with important properties in greater detail using algebraic operations. Additionally, we develop an algorithm for solving MADM problems using these operators. Several real-world examples illustrate how enhanced score values can be applied. Sensor robots are said to rely heavily on computer science and machine tool technology. Four factors are to evaluate when determining a sensor robotics system’s quality: resolution, sensitivity, error, and environment. It is possible to compare expert opinions with the criteria and determine the best alternative. Therefore, the value of q significantly impacts the model’s results. To prove that the models considered are valid and useful, we will compare the current and proposed models. Thus, q has a significant impact on the results of the model.

Rough fermatean fuzzy ideals in semigroups

In multiple criteria decision making (MCDM) problem, the decision maker deal with a situation where the sum of membership and non-membership grade of an attributes does not belongs to [0, 1]. To avoid such a situation, we proposed a new type of fuzzy system known as fermatean fuzzy system. More precisely, we presented the notion of fermatean fuzzy ideal theory and rough fermatean fuzzy sets in semigroups. The idea of lower and upper approximation in fermatean fuzzy sets has been initiated. The study has been further extended to rough fermatean fuzzy left(resp. right, interior) ideals in semigroup. Several results related to this notion are determined.

Küresel Bulanık EDAS ve Bir Uygulama

Several fuzzy set concepts have been developed after the first invention of fuzzy sets in 1960s with the aim of demonstrating the uncertainty and vagueness in human preferences. Spherical fuzzy sets (SFS) as a recent one of these developments support this aim by giving a comprehensive preference domain to decision makers. The distinctive feature of SFS is its rule saying that the squared sum of membership, non-membership, and hesitancy degrees should be within the interval of [0,1] while its each element is independently assigned within the same interval. With this study, EDAS (Evaluation Based on Distance from Average Solution), one of the younger but stronger multiple attribute decision making tools is modified for spherical fuzzy environment. Entropy-based objective attribute weighting is also integrated with this novel version of EDAS to avoid the undesired potential effects of subjective weighting such as longer data collection time. The novel version proposed is applied in an example of a product design selection problem for additive manufacturing.

Extending ARAS with Integration of Objective Attribute Weighting under Spherical Fuzzy Environment

Various fuzzy sets have been developed in the recent years to model the uncertainty in judgments. Spherical fuzzy set (SFS) concept is one of these developments. It can provide an extensive preference domain for decision-makers by allowing them to state their hesitancy more explicitly. The peculiarity of SFS is that the squared sum of membership, nonmembership, and hesitancy degrees should be between 0 and 1 while each is independently defined in [0, 1]. In this study, ARAS as one of the most applied multiple attribute decision-making approaches is extended into a spherical fuzzy environment. Entropy-based and OWA operator-based objective attribute weights are also integrated with the newly proposed spherical fuzzy ARAS for coping with the drawbacks of subjective weighting such as longer data collection time and manipulation risk. The applicability of the proposition is shown in a hypothetical example of a product design problem and its robustness is shown by a comparative analysis.

A novel entropy proposition for spherical fuzzy sets and its application in multiple attribute decision‐making

The inherent vagueness and uncertainty in reaching decisions are effectively coped with fuzzy logic and the concept of spherical fuzzy sets is one of the latest developments in this area. The hesitancy of decision-maker(s) about an attribute can be represented more extensively since the squared sum of membership, nonmembership, and hesitancy degrees should be between 0 and 1 while each degree should be defined in [0, 1]. In this study, we propose a novel entropy measure for spherical fuzzy sets and show its ability to provide the required properties. Then its usage in determining objective attribute weights is shown in an application of SF-WASPAS (Spherical Fuzzy extension of Weighted Aggregated Sum Product Assessment) on an illustrative problem. The robustness of the novel entropy's usage as an objective weighting tool is demonstrated by comparing the ranking solution of the proposed SF-WASPAS with the rankings obtained by SF-TOPSIS, SF-VIKOR, and SF-CODAS.

Spherical fuzzy extension of DEMATEL (SF‐DEMATEL)

In recent years, many versions of fuzzy sets are introduced in the literature. Spherical fuzzy sets (SFSs) concept is one of these latest developments. An SFS is a synthesis of Pythagorean fuzzy set (PFS) and neutrosophic set for providing a larger preference domain for experts and allowing them to express their hesitancy more comprehensively. The distinctive feature of SFSs is that the squared sum of membership, nonmembership, and hesitancy degrees is between 0 and 1 while each degree should be independently defined in [0,1]. The application of SFS on decision-making field may be about describing expert evaluations more informatively and explicitly. In this study, spherical fuzzy version of DEMATEL, one of the most cited multiple criteria decision-making approach, is introduced for considering the hesitancy degrees of experts when they evaluate the potential influences among the criteria. Another contribution made is the fuzzification of all the steps in DEMATEL until the last ones since the existing propositions in literature perform early defuzzification operations. The defuzzification is here applied as close to the end as possible for keeping the whole process fuzzy. The applicability of the proposition is shown in an illustrative example of a building contractor evaluation problem, and its robustness is shown by comparing the results with PFS-based and neutrosophic DEMATEL versions.

A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets

All the extensions of ordinary fuzzy sets with three-dimensional membership functions such as intuitionistic fuzzy sets, second type intuitionistic fuzzy sets (or Pythagorean fuzzy sets) and neutrosophic sets aim at defining the judgments of decision makers/ experts with a more detailed description. As a new extension of intuitionistic fuzzy sets of second type, the emerging spherical fuzzy sets (SFS) have been proposed by Kutlu Gündoğdu and Kahraman (2019b). In spherical fuzzy sets, the sum of membership, non-membership and hesitancy degrees must satisfy the condition0≤μ2+v2+π2≤1 in which these parameters are assigned independently. SFS is an integration of Pythagorean fuzzy sets and neutrosophic sets. In this paper, novel interval-valued spherical fuzzy sets are introduced with their score and accuracy functions; arithmetic and aggregation operations such as interval-valued spherical fuzzy weighted arithmetic mean operator and interval-valued spherical fuzzy geometric mean operator. Later, interval-valued spherical fuzzy sets are employed in developing the extension of TOPSIS under fuzziness. Then, we use the proposed interval-valued spherical fuzzy TOPSIS method in solving a multiple criteria selection problem among 3D printers to verify the developed approach and to demonstrate its practicality and effectiveness. A comparative analysis with single-valued spherical TOPSIS is also performed.

Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making

Recently proposed q-rung orthopair fuzzy set (q-ROFS) is a powerful and effective tool to describe fuzziness, uncertainty and vagueness. The prominent feature of q-ROFS is that the sum and square sum of membership and non-membership degrees are allowed to be greater than one with the sum of qth pow er of the membership degree and qth power of the non-membership degree is less than or equal to one. This characteristic makes q-ROFS more powerful and useful than intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS). The aim of this paper is to develop some aggregation operators for fusing q-rung orthopair fuzzy information. As the Muirhead mean (MM) is considered as a useful aggregation technology which can capture interrelationships among all aggregated arguments, we extend the MM to q-rung orthopair fuzzy environment and propose a family of q-rung orthopair fuzzy Muirhead mean operators. Moreover, we investigate some desirable properties and special cases of the proposed operators. Further, we apply the proposed operators to solve multi-attribute group decision making (MAGDM) problems. Finally, a numerical instance as well as some comparative analysis are provided to demonstrate the validity and superiorities of the proposed method.

Pythagorean Fuzzy Interaction Muirhead Means with Their Application to Multi-Attribute Group Decision-Making

Due to the increased complexity of real decision-making problems, representing attribute values correctly and appropriately is always a challenge. The recently proposed Pythagorean fuzzy set (PFS) is a powerful and useful tool for handling fuzziness and vagueness. The feature of PFS that the square sum of membership and non-membership degrees should be less than or equal to one provides more freedom for decision makers to express their assessments and further results in less information loss. The aim of this paper is to develop some Pythagorean fuzzy aggregation operators to aggregate Pythagorean fuzzy numbers (PFNs). Additionally, we propose a novel approach to multi-attribute group decision-making (MAGDM) based on the proposed operators. Considering the Muirhead mean (MM) can capture the interrelationship among all arguments, and the interaction operational rules for PFNs can make calculation results more reasonable, to take full advantage of both, we extend MM to PFSs and propose a family of Pythagorean fuzzy interaction Muirhead mean operators. Some desirable properties and special cases of the proposed operators are also investigated. Further, we present a novel approach to MAGDM with Pythagorean fuzzy information. Finally, we provide a numerical instance to illustrate the validity of the proposed model. In addition, we perform a comparative analysis to show the superiorities of the proposed method.