Reliability Analysis of Poll Data with Novel Entropy Information Measure in Multicriteria Decision-Making Based upon Picture Fuzzy Environment

,e polling system has a considerable role in the democratic nation. ,e uncertainty of the people’s participation in polling generally affects the electoral-based system. ,erefore, PFS (picture fuzzy set) is the furthermost efficient and useful extension of IFS (intuitionistic fuzzy set) in a fuzzy system capable of precisely handling human perception in the decision-making system.,e PFS structure involves the different degrees, i.e., membership, nonmembership, neutral, and hesitancy which are comprehensively applied to such types of complex practical problems in the real-life scenario. ,is advantage of PFS motivates the author to propose PFSs centred novel entropy measure via this communication, which is comparatively more generalized, reliable, and simplified in place of the existing uncertain measures.,e practicability of the proposed present research work is to deal with realworld problems pertaining to the relative importance of the attributes.,erefore, certainly, the proposed novel entropy developed a different approach to handle the uncertainty more precisely as a part of the existing approaches. ,e validation proof of the proposed entropy measure is proved in an organized manner and practically employed in the perspective of the polling data outcomes about the people’s opinions with the VIKOR-TOPSIS approach.


Introduction
In the modern era, fuzzy sets and their various generalized extensions are predominantly utilized by researchers and decision-makers in the multiple domains of the research field. For the useful life, the different researchers broadly used the concept of fuzzy logic in several applications of modern technology, for instance, washing machine [1], modern cars [2], and traffic signals control system [3]. e author in [4] was the pioneer to present the abstract of fuzzy theory.
Later, various authors presented the modified structure of F ss and their efficient use to explore the vagueness and uncertainty in many problems of multicriteria decisionmaking support systems. Initially, the fuzzy set may be possible to prevail only the knowledge about the membership degree (μ) of the element. It restricts the fuzzy set to the specific domain of M CDM . Further, the author was inspired [5] with the concept of nonmembership function (]) and reshaped the existing structure of F ss and added on one more parameter π: 0 ≤ μ + ] + π ≤ 1 and I FS comes to light. I Fs attracts the great attentions of various researchers, authors, and decision-makers across the globe because of its feature of presenting π. It makes I Fs more reliable and concise towards the challenges in real-life scenario. In this perception, several authors around the globe contributed to the research as per their point of view; for instance, the authors in [6] introduced the idea of homomorphism between the subgroup (cyclic) and I Fs subgroup. Further, the authors in [7] developed complex I Fs approach which relates with group theory and the authors in [8] proposed some important algebraic structures based upon (αβ) complex fuzzy − based subgroup. First time, the author was able to validate various parameters of I Fs in context of human perception and related various components of I Fs as per the public opinion in the voting system, i.e., μ for Support, ] stands for Unsupport, and π implies neither support nor unsupport. As I Fs handles the M C DM problems more precisely and in efficient manner comparatively F ss , however, the researchers analysed that I Fs is not applicable comprehensively in all such fuzzy environment-based situations. For instance, in the voting system, the people who are in the mindset of the dilemma are not undertaken in the framework of I Fs . To encounter such indeterminacy, the authors [9] were motivated with idea of neutral membership degree and incorporated the new component η to the present structure of I Fs : 0 ≤ μ + ] + η + π ≤ 1 which is known as P Fs . erefore, whenever I Fs restricts its scope, P Fs perfectly handles the uncertainty in a better way. Certainly, the parameter η has great importance to capture the logic of the human mind's ambiguity in the behavioural approach towards complex situations. Figure 1 shows the pretty presentation of various parameters from F ss to P Fs . e researchers and decision-makers take advantage of this unique feature of P Fs and used it tremendously in several applications of modern technologies and social issues. e researcher [10] applied the concept of P Fs using the distance measure for the health issues. Nowadays, in various research areas, the researchers are using the framework of P Fs in the hybrid form. Further, the authors [11] successively utilized P Fs -based hybrid distance measure with the concept of rough set theory in selection criteria of the students. In this context, the authors [12] contributed some important correlation coefficients and their application in analysis of clustering and pattern recognition in computing research, and the authors in [13] presented the hybrid form of similarity measures and biparametric distance to handle the uncertainty in medical diagnosis. In the forecasting system, the author [14] significantly implied the P Fs feature and proposed the novel method and created the time series model for forecasting. e decision-makers [15] extended the bidirectional projection method for P Fs and applied to assess the safety features for construction design.
Recently, the researchers have implied the different picture fuzzy uncertain measures with the use of different methods or approaches to cope up the vagueness in M CDM challenges. e authors [16] developed the algorithms based upon interaction aggregation operators defined on P Fs for complex multivariable decision-making models. us, the researcher [17] contributed the concept of cross-entropy in P Fs and its application in M CDM support system. Continuing with the P Fs theory, the authors submitted the entropy weighted picture fuzzy information-based clustering-algorithm for segmentation of images. e important entropy similarity measure was proposed by [18], and their application in the decision-making system was developed. Further, the authors [19] worked upon and submitted the divergence information measure of Jenson Tasalli along with its application in decision problems for P Fs . e concept of R-S norms was broadly used by the authors in [20,21], and the information measure for the picture fuzzy situations was proposed. Moreover, the researchers [22] also proposed the entropy information measure based upon linguistic P Fs with M CDM application. e author [23] proposed the generalized model based upon the concept of maximum entropy negation to explore the information involved in the field of the artificial intelligent decision-making system. Further, the researcher [24] put forwarded the decision-making models to handle the issues like a cost-aware, fault-tolerant, and reliable strategy in complex problems under fuzzy environment. However, the literature findings help us in problem formulation which prevails across the different areas of the research; fuzzy logic and fuzzy sets are considerably applied to capture the ambiguity available in data as well as in practical problems of the real world.

Research Gap.
e human mindsets seem too inefficient to meet the solution of complex multivariable problems in real-time scenarios. erefore, fuzzy sets are quite proficient and reliable in handling ambiguity and the dilemma approach of human mindsets in complex decision-making issues. P Fs can handle the neutral factors involved in the M CDM problems more efficiently; for instance, in the outcomes of the exit poll in the electoral system, the neutral voters have a vital role. So far, several authors proposed a wide range of diverse information measures and approaches defined on picture fuzzy sets to cope with uncertainty as per their mindsets. However, there is still a scarcity of sophisticated, reliable, and simpler measures defined on P Fs to deal with complicated M CDM problems in a fuzzy environment.
is inspires the authors to work upon the proposed research work. erefore, the proposed research work certainly overcomes the research gap of the different existing approaches and uncertainty measures of P Fs .

Methodology.
e different methodologies are proposed to deal with M CDM problems to select the best alternatives in accordance with the choice of the criteria. e purpose of approaches or techniques is to handle the available data with greater accuracy and to reduce uncertainty. e proposed novel entropy is reliable and more applicable with the complex M CDM problems allied with the relative importance of the criteria. erefore, the practicability of novel entropy is applied to the prediction of the polling data; however, the criteria involved in the present problem have the relative importance of the criteria. erefore, such type of problems handles with the VIKOR approach which provides the compromise solutions. All through the TOPSIS approach was utilized to select the best alternatives irrespective of the relative importance of the different criteria. erefore, the application part of the proposed entropy was validated with both approaches.
Further, the presentation of the proposed work is classified in various parts as shown in Figure 2.

Preliminaries
Definition 1. . e fuzzy set theory generalized the concept of classical sets, which it perceives as an extension of classical sets. e pioneer of the fuzzy set theory was [4] which defined elements of the fuzzy set (F ss ) in terms of the membership function (μ ∇ ) on finite universe of discourse, i.e., Z � Z 1, Z 2, Z 3, . . . . . . Z n, and defined F ss , ∇ as where membership function of F ss is μ ∇ : Z ⟶ [0, 1] and μ ∇ (Z i ) signifies the membership degree μ ∇ (Z i ) of the Z i ∈ Z in F ss . e fuzzy set (F ss ) has only explained μ ∇ (Z i ) and 1 − μ ∇ (Z i ), i.e., nonmembership function and no idea about hesitancy element. e idea of hesitancy element was further introduced by [5] to the existing framework of F ss called the degree of hesitancy.
Definition 2. e fuzzy sets are restricted to employ in certain M CDM problems, which are unable to handle the uncertainty factor precisely. e idea of (I Fs ) intuitionistic fuzzy set was presented by [5] which added on one more important factor, i.e., nonmembership function in the present structure of F ss . Consequently, I Fs Δ defined on Z(universe of discourse) is as follows: stated the membership and nonmembership function of I Fs , and the terms (μ Δ (Z i )) and (] Δ (Z i )) described the degree of membership and nonmembership of the element belongs to I Fs . e author in [5] introduced I Fs which extend the scope of fuzzy set in decision-making environment. In real-life scenario, the I Fs membership, nonmembership, and uncertain degree make the sense of favour, against, and abstain in M CDM problems but are unable to describe refusal degree which restricts its scope of application. erefore, this inconsistency is vanquished in picture fuzzy set (P FS ) to add on one more component "Neutral membership degree" in the present framework of I Fs by [9].
Definition 3. Over the period, the decision-makers analysed that I Fss is not feasible towards certain complex issues. e author in [9] presented the concept of a picture fuzzy set, which is an advanced generalized form of fuzzy sets that are more capable of dealing with complex issues in a fuzzy environment. e picture fuzzy set (P FS ) ∇ ∧ on Z is defined as (3) erefore, the structure of P FS is more generalized and classified form as compared with F ss and I Fs to capture the vagueness in M CDM practical problems.

Mathematical Problems in Engineering
Definition 4. Let Q and R be P FS defined on Z.
e authors in [25] introduced the following important operations and relations for any Q , R ∈ P Fs (Z) defined as follows: ere are two distance measures, i.e., Hamming distance measure and Euclidean distance between the two P Fs Q and R defined as 3. Fuzzy Entropy Information Measure for P FSS e entropy information measure is the fuzziness degree of F ss . e author [26] introduced the set of postulates based upon probability theory of Shannon for F ss e entropy is a real function θ ∧ : F ss (Z) ⟶ [0, ∞) which satisfies the following axioms: [27]). e entropy is a real function � θ: I Fs (Z) ⟶ [0, ∞) which satisfies the following properties: Moreover, P FSS is the well-known generalized form of I Fs with the four components, i.e., (μ, ], η, π) which hold the condition such that (μ, ], η, π) ∈ [0, 1] and μ + ] + η + π � 0. ese parameters may be presumed as probability measures  that characterized the picture fuzzy set. is indicates that entropy measure must have maximum value if all parameters uniformly have the value one-fourth, i.e., μ Q � η Q � ] Q � π Q � 1/4 and must be zero if all the components vanish except one such as or, Definition 8. e axiomatic definition of entropy measure for P FS proposed in view of the concept of entropy measure of I Fs introduced by [27] is as follows.
e entropy measure is a real function θ: P FS (Z) ⟶ [0, ∞) and agreed with the following axioms: In fact, several authors proposed different uncertain measures on P Fs and utilized them to solve the complex multivariable problems. In this context, the novel entropy measure is proposed to enhance the preciseness and improve the reliability and handle the ambiguity of M CDM problems in a simpler and more logical way.
is would certainly overcome such shortcomings existing in uncertain measures defined on P Fs . In the next part, a novel entropy information measure has been proposed on P FSS , keeping in view these important fundamental concepts.

A Novel Entropy Information
Measure for P FSS Let us assume the finite set of comprehensive probability distribution signified as L n � 〈[ � ″ a 1 , a 2 . . . . . . . . . a n ″ : a i ≥ 0 and n i�1 a i � 1〉; n ≥ 2for any[ ∈ L n . Firstly, Shannon [28] initiated to define the information measure explained which is widely known as Shannon entropy In the passage of time, Zadeh (1965) put forward the concept of fuzzy set which develops the new approach to quantify the uncertainty/fuzziness. Further, in 1968, Zadeh prolonged the concept of Shannon entropy; however, this information was not capable to meet the purpose. e continued efforts of researchers with information measure in 1972 [26] were capable to extend the axioms of Shannon entropy and proposed the new fuzzy information postulates which are accepted widely across the world and set as criteria for fuzzy entropy measure mentioned in Definition 6 is also motivated the authors [26] to propose the fuzzy entropy measure consistent with Shannon entropy presented as is developed the author's insight more into F ss and presented different information measures according to their point of view. e authors [29] contributed exponential entropy measure for I Fs given as follows: Mathematical Problems in Engineering where Δ and Z i ∈ I Fs .
Further, the researchers [30] have explored the idea of entropy measure based on exponential function to P PFS (Pythagorean fuzzy set) given by Over the period, several authors have introduced the different work on entropy information measure. e authors [31] contributed residual entropy information measure in the application of the group decision-making. e geometric aggregation operators were introduced [32] based upon I Fs , respectively, with undefined criteria weights and their application in M CDM . Further, the researcher [33] presented information entropy measure with the generalized form of I Fs and utilized in decision-making problems.
With this information as background, in the next part, new entropy measure is proposed to the picture fuzzy set (P FS ) as the generalized form of I Fs .

Definition 9.
e real function θ is defined on Q ∈ P FS (Z). e new probability type picture information measure is proposed as follows: e validity of information measure is proved if it satisfied the fundamental postulates of entropy measure listed in Definition 8.

Validation of Proposed Information
Measure. Firstly, the following inequalities for any Q and R ∈ P FS (Z): Q crisper than R listed in axioms P FS3 are proved: 6 Mathematical Problems in Engineering and Proof. (14) and (15) are correct. (16) and (20).
ere are two distance measures, i.e., Hamming and Euclidean distance which are widely used to determine the distance between the two different I Fss . e authors in [34] introduced the concept of distance between the two different I Fss specifically in terms of their parameters (μ, ], π). Subsequently, P FSS is the generalized form of I Fss which have four components, i.e., (μ, ], η, π). erefore, this concept of distance measure is significantly used from I Fss to P FSS .
e proof of the validity of the proposed measure will be established if it agreed with the axioms listed in Definition 8. P FS1 (sharpness). Initially, we assume θ(Q) � 0.
is will hold if following cases are possible: Hence, all the above cases show that θ(Q) � 0. is implies that θ is the crisp set. erefore conversely, assume that θ is the crisp set. is provides us, θ(Q) � 0⇔Q is a crisp set.
is is concluded that θ(Q) holds the property of resolution. P FS4 (symmetry). is property is satisfied directly from the definition, i.e., θ(Q) � θ(Q c ).
is is the complete proof of the theorem.
Proof. Let Z 1 andZ 2 be the two parts of ∈ Z(universal set) such that As accordingly, 8 Mathematical Problems in Engineering erefore, equations (23) and (24) prove that □

The Proposed Picture Fuzzy Entropy Measure with Application in M CDM Process
e M CDM process involves the different techniques to solve the decision and planning problems, which involve multiple criteria.
e objective is to support decision-maker in tackling such problems. To attain the unique optimal solution of such problems, the decision-makers fixed a set of alternatives and criteria. e fuzzy set and its various extended forms were included in M CDM techniques because of the vagueness and ambiguity in the data analysis. erefore, fuzzy sets have a great importance in the decision-making process. e M CDM problems may be symbolized as a matrix say (P FDM ) � m×� n which represents the � m alternatives e statistical tool mentioned in (26)is significantly used if the available data are in the form of numerical quantity. In decision-making analysis, the different degrees of P FS are entirely reliant upon the single opinion or choice of decision-makers apart of any kind of information to render a decision. Such practical problems in P FS decision-making process are solved more effectively with greater accuracy.

Picture Fuzzy Sets with Proposed VIKOR Approach.
e author [35] was the pioneer of VIKOR approach to obtain the most desired alternatives based upon the closeness index to the (+) ideal solution and farthest from the (−) ideal solution in decision-making problems. e key salient feature of present approach helps to provide the compromise solution. Initially, the idea of compromise solution was developed by [36] in1973. e following procedural steps are widely used to solve the fuzzy decision-making problems.
Step 1. Formation of picture fuzzy decision matrix (P FDM ) � m×� n . (P FDM ) � m×� n is constructed in such a way that entries of the matrix elements are computed in accordance with different membership degrees of P FS briefed in equation (26).
Step 2. Normalization of (P FDM ) � m×� n . e fabricated matrix (P FDM ) � m×� n is normalized as shown in Table 1.
Step 3. Assessment of criteria weights e choice of selecting the weights of criteria or attributes has a substantial role in the way out of the solution of M CDM problems. e appropriate and justified assessment of criteria weights might lead to the desired result of a suitable alternative. Considering the classified the criteria weights in two categories, i.e., subjective and objective weights [37], the objective weight apprehends the criteria information in a quantified manner; therefore, entropy practice is the best reliable approach to capture and handle such information. Sometimes, in M C DM process, the decision-makers have the criteria weights information in separate manner, i.e., entirely known or unknown and may be partially known according to problem scenario.
As a result, the following approaches are used to compute the criteria weights for both the cases: (a) Methodology for Unknown Criteria Weights. To compute the unspecified criteria-weight, the author [37] proposed the method. where (b) Methodology for Partially Known Criteria Weights. ere are many complexities which are cited by the decision-makers to solve the problems in the decision-making system such as paucity of time, information, and lack of expertise around problem domain.
erefore, the decision-makers are enabled to give their judgment or decision precisely in the form of numeral value. ey often express their opinions of the judgment in intervals to overcome such incongruities. In this framework, to explore the attribute weights from the set of partial information, the decision-makers generally use the method of minimum entropy proposed by [38]. Hence, the alternatives entropy across the distinct criteria CR j is presented as follows: us, the following programming model is frequently used by the decision-makers for the optimum criteria evaluation: β denotes the set of partial known informations to evaluate the weights of different criteria.
Step 4. Determination of the relative ideal solution for P FS .
In M CDM problems, the ideal solution provides the best alternatives which maximize the most benefited attribute or criteria and minimize the least cost criteria. e objective of the VIKOR method is to opt the best alternative nearest to the (+) ideal solution along with farthest away from the (−) ideal solution. Firstly, the picture fuzzy relative (+) ideal solution and (−) ideal solution are constructed to determine the alternatives.
For benefit criteria, where For cost criteria, where Step 5. Evaluation of compromise solution In decision sciences, the VIKOR method is very useful for the compromise solution, when the preference of decision-makers about alternatives is conflicting from the set of criteria information. In the VIKOR method, the compromise solution is obtained with the use of (L ∧ p ) metric which was earlier introduced by [36]. e metric (L ∧ p ) is an aggregate function used as follows: where ALT + and ALT − are described in equations (33) and (35).
w j are the weight of the criteria j th ; j � 1 . . . . . . n.
e parameter p has the distinct values varying between [1, ∞) which imply the different meaning in perspective of group utility and individual regret. As the increased value of p, the individual regret is substantially increased and the group utility or efficacy is decreased Hence, the VIKOR method gives the compromise solution with maximum group efficacy (L ∧ 1,i ) and reduces the individual regret (L ∧ ∞,i ) as follows: Step 6. VIKOR index coefficient.
In addition, the parameters (Θ) and (1 − Θ) represent the group utility weight and individual regret as per the choice of its value by decision-makers as follows: IFΘ � 0.5⇒consenus > 0.5⇒voting by majority < 0.5⇒Veto.

(41)
Step 7. Finally, the ascending order of the determined values of G If the stated condition does not satisfy together, then we look upon a compromise solution proceed as follows.
; m⇒for some maximum and n implies the number of alternatives.

Picture Fuzzy Sets with Proposed TOPSIS Approach.
e concept of TOSIS approach initiates and incorporates in M CDM decision sciences by [39]. Since then, this method is prominently used to many complex practical problems in a fuzzy situation. e selection process of the best attributes in the proposed approach is to focus on the alternatives that one closest to the ideal solution and farthest, respectively, from the (−) ideal solution.
Further, to complete the calculative part of the M CDM problem, we carry forward the first four steps stated above in the first approach.
is step involves the picture fuzzy discriminant measure E + D and E − D for distinct attributes from ALT + and ALT − , respectively, with use of equation (7).
Step 9. e relative closeness coefficient (R cc ) is computed as follows: Step 10. At the end, alternatives ranking have been done according to the ordering the distinct values of R cc . e larger the value is, the most suitable the alternatives are.
us, we have successfully presented the procedural steps to solve the picture fuzzy M CDM problems by employing the proposed picture fuzzy entropy measure with the modified form of VIKOR and TOPSIS and for the sake of understanding the flow chart shown in Figure 3.

Validation of Proposed Entropy
Measure with Example e application of the PFS is to solve the MCDM problems, where simultaneously several attributes are likely to exist. In such type of environment, the human mindsets are always in dilemma; therefore, P FSS is considerably used. In that point of view, a national welfare society conducted the social survey to get the public opinion for the functioning and implementation of the government policies for the national importance. ey fix the framework of six different criteria, i.e., CR 1 : unemployment CR 2 : foreign relations CR 3 : national education policy CR 4 : financial services CR 5 : strategy for COVID − 19 CR 6 : national policies for social development and empowerment And the national parties are classified into five categories, i.e. , ″ ALT 1 , ALT 2 , ALT 3 , ALT 4 , ALT 5 .
″ e survey was conducted on a sample of 1000 � � N peoples. e results show 450 peoples in support with CR 1 , 320 peoples unsupport with CR 1 , 120 peoples are neutral, and 110 peoples are not participated, i.e., abstain. en, with the use of equation (26), the entries of the P FS matrix can be determined as follows: Further, entries of (P FDM ) 5×6 are computed in the same manner.
VIKOR approach for proposed entropy measure is as follows: (1) e accumulated information as per opinion of peoples constitutes the normalized (P FDM ) 5×6 listed in Table 2. (2) e notion P FDMW used for the calculated values of different criteria with information measure mentioned in (14) is listed in Table 3. (3) Utilizing equation (28), the weights are determined for the defined criteria throughout the alternatives with use of values P F DM W catalogued in Table 4.  Table 5.      Table 7. (7) e indexing shows ALT 1 and ALT 3 located at 2 nd and 1 st position in Table 7.
erefore, we proceed for the compromise solution, i.e., us, ALT 1 , ALT 3 , and ALT 5 hold the CONII condition, and the alternatives ALT 1 , ALT 3 , and ALT 5 are the compromise solution.  Table 8. (9) e value of relative closeness coefficient (R cc ) degree with use of (47) is mentioned in Table 9.
Finally, the indexing of the alternatives in descending order list is shown in Table 10.
From the indexing of the alternatives, it is concluded that ALT 5 is the most desirable alternative.

Comparative Evaluation
To verify the effectiveness and practicability of the proposed information measure with TOSIS and VIKOR approaches, the result prevails in such a way that the TOPSIS method provides the best alternatives ALT 5 whereas VIKOR has a compromise solution, i.e., ALT 1 , ALT 3 , and ALT 5 . us, it is quite natural to think about the most benefited alternative. e authors [40] have briefly explained the relative difference between these two approaches for selection of best alternative. e feasible compromise solution in the VIKOR approach formed a consent of mutual compromises focussed on optimising G ∧ ui and minimising I ∧ Ri ; however, the TOPSIS approach adopts the feasible solution without considering the relative importance of the distances which are nearest and farthest from an ideal solution. In the perspective of the proposed example, if the results are interpreted in the broader sense, then it shows that national party ALT 5 is the choice of the peoples in majority and would be able to form the government. In compromise solution, it reveals that the parties ALT 1 , ALT 3 , and ALT 5 are also the choice of the peoples which leads the alliance situation to establish the      government. ere is also the possibility of an alliance between the parties either two or three to have a majority criterion to form the government.

Concluded Remarks
Till now, several mindsets have developed different approaches or methods of information measure to explore the information in picture fuzzy environment, and still the researchers are working hard to develop such information measures which are more reliable, precise, and informative reasonably with existing measure techniques. e proposed picture novel entropy was validated with the two different approaches. e results reveal that the best alternative is analogous in both approaches and proved that information measure is quite appropriate to solve the complex issues on M CDM system. e trustworthiness and practical applicability of the proposed work proved to improve the voting system and the opinion of the peoples about the parties to the national importance. e proposed model could be used to predict the future outcomes of the polling. e novel research work is significantly suitable to the M CDM complex multivariable problems, relating to the neutral factors or variables.
e role of neutral variables in complex issues affects the result of decision-makers. is advantage of the proposed work facilitates the decision-makers to handle the ambiguity that arises due to neutral variables in complex issues. erefore, it concluded that novel picture information measure is more reliable, sophisticated, and informative as well as simpler, to tackle the uncertainty or vagueness more precisely and effectively in a picture fuzzy environment.

e Advantage and Future Scope of the Current Research.
e present research work could be extensively applied as a model to predict the forthcoming results in the field of data analysis, i.e., healthcare, agriculture, smart cities, and many more approaches in relation to sustainable development. Further, it can be explored to P FSS in terms of divergence measure, intervalued, and many more. e proposed research work could be bridged between the complex evidence theory as well as quantum mechanics theory to envisage the human decision behaviours in decision theory. Moreover, the presented research work model is also utilized in intelligent generalized quality-based approach which is capable enough to fuse the complex multivariable informations. In fact, decision-makers are comfortable to express the human judgments or suggestions in the linguistic form in picture fuzzy environment. erefore, present research works can be utilized in fuzzy linguistic models. Degree of membership function ]:

Abbreviations
Degree of nonmembership function η: Degree of netural-membership function π: Degree of hesitency or refusal G ∧ ui : Group efficacy or group utility I ∧ Ri : Entity regret or individual regret.

Data Availability
e data used to support the findings of the study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this article.