Algorithm for solving group decision-making problems based on the similarity measures under type 2 intuitionistic fuzzy sets environment

Development of hamming and hausdorff distance metrics for cubic intuitionistic fuzzy hypersoft set in cement storage quality control: Development and evaluation

Quality control is paramount in product manufacturing as it ensures consistent production to meet customer expectations, regulatory requirements and maintain a company's reputation and profitability. Distance measures within fuzzy sets serve as powerful tools for quality control, allowing for data comparison and identification of potential defects or outliers within a system. This study aims to develop a hybrid concept by combining a Cubic Intuitionistic Fuzzy Set (CIFS) with Soft Set (SS) and extending it to Cubic Intuitionistic Fuzzy Hypersoft Set (CIFHSS). CIFHSS enables handling multiple distinct attributes at the sub-attribute level within a cubic set environment. The concept includes operations like internal, partial internal, external, complement, direct sum, and product. Additionally, six distance metrics are defined within CIFHSS and applied to establish a quality control management system for industrial applications. The versatility of CIFHSS in quality control management stems from its ability to capture and model uncertainty, vagueness, and imprecision in data. This makes it an effective tool for decision-making, risk analysis, and process optimization across a wide range of industrial applications.

Applications to biogas-plant implementation problem based on type-2 picture fuzzy matrix game under new minkowski type measures

To manage ambiguity and uncertainty information in real life problems, certain intellectuals have initiated numerous modifications of fuzzy sets. But, in certain situations, the decision-makers have been neglected to take a feasible decision. For instance, when an intellectual provides information in the form of a two-dimension or type-1 fuzzy set, then the prevailing theories have been neglected. For this, in this study, we elaborated the new idea of type-2 picture fuzzy sets (T2-PFS) and their algebraic laws have been given. Moreover, by using the T2-PFS, Hamacher aggregation operators are proposed and discussed their important properties. The Minkowski sorts of measures under the T2-PFS are also initiated. In the current study, we aim to utilize the matrix game in a type-2 picture fuzzy environment. By using the proposed operators and measures based on the Hausdorff metric. The elaborated idea has been defined with the biogas-plant implementation dilemma to verify the pertinence and authenticity. Lastly, to discuss the sensitivity analysis and geometrical shown of the initiated works, certain examples are illustrated to determine the supremacy and consistency of the proposed approaches.

Evolved distance measures for circular intuitionistic fuzzy sets and their exploitation in the technique for order preference by similarity to ideal solutions

Circular intuitionistic fuzzy (C-IF) sets are an up-and-coming tool for enforcing indistinct and imprecise information in variable and convoluted decision-making situations. C-IF sets, as opposed to typical intuitionistic fuzzy sets, are better suited for identifying the evaluation data with uncertainty in intricate realistic decision situations. The architecture of the technique for order preference by similarity to ideal solutions (TOPSIS) provides powerful evaluation tools to aid decision-making in intuitionistic fuzzy conditions. To address appraisal issues associated with decision analysis involving extremely convoluted information, this paper propounds a novel C-IF TOPSIS approach in the context of C-IF uncertainty. This research makes three significant contributions. First, based on the three- and four-term operating rules, this research introduces C-IF Minkowski distance measures, which are new generalized representations of distance metrics applicable to C-IF values and C-IF sets. Such general C-IF distance metrics can alleviate the constraints of established C-IF distance measures, provide usage resiliency through parameter settings, and broaden the applicability of metric analysis. Second, unlike existing C-IF TOPSIS methods, this research fully utilizes C-IF information characteristics and extends the core structure of the classic TOPSIS to C-IF contexts. With the newly developed C-IF Minkowski metrics, this study faithfully demonstrates the trade-off evaluation and compromise decision rules in the TOPSIS framework. Third, this research builds on the core strengths of the pioneered C-IF Minkowski distance measures to create innovative C-IF TOPSIS techniques utilizing four different combinations, including displaced and fixed anchoring frameworks, as well as three- and four-term representations. Such a refined C-IF TOPSIS methodology can assist decision-makers in proactively addressing increasingly sophisticated decision-making problems in practical settings. Finally, this research employs two innovative prioritization algorithms to address a site selection issue of large-scale epidemic hospitals to illustrate the superior capabilities of the C-IF TOPSIS methodology over some current related approaches.

A theoretical development of improved cosine similarity measure for interval valued intuitionistic fuzzy sets and its applications

This study mainly focuses on developing a new flexible technique for interval-valued intuitionistic fuzzy cosine similarity measures, which significantly analyzes the strength of the relationship between two objects. Based on the notion of a cosine similarity measure between IVIFSs, the proposed measure is formulated. Then, the measure is demonstrated to satisfy some essential properties, which prepare the ground for applications in different areas. Finally, the study uses the proposed measure to solve real-world decision problems such as pattern recognition, medical diagnosis, and multi-criteria decision-making problems with interval-valued intuitionistic fuzzy information. The numerical examples of the mentioned applications are delivered to validate the effectiveness of the developed approach in solving real-life problems.

Study on center-of-sets type-reduction of interval type-2 fuzzy logic systems with noniterative algorithms

In recent years, interval type-2 fuzzy logic systems (IT2 FLSs) have become a hot topic for the capability of coping with uncertainties. Compared with the centroid type-reduction (TR), investigating the center-of-sets (COS) TR of IT2 FLSs is more favorable for applying IT2 FLSs. Actually, it is still an open question for comparing Karnik-Mendel (KM) types of algorithms and other types of alternative algorithms for COS TR. This paper gives the block of fuzzy reasoning, COS TR, and defuzzification of IT2 FLSs based on Nagar-Bardini (NB), Nie-Tan (NT) and Begian-Melek-Mendel (BMM) noniterative algorithms. Six simulation experiments are used to show the performances of three types of noniterative algorithms. The proposed noniterative algorithms can obtain much higher computational efficiencies compared with the KM algorithms, which give the potential value for designing T2 FLSs.

Modeling pricing decision problem based on interval type-2 fuzzy theory

In practical decision-making problems, decision makers are often affected by uncertain parameters because the exact distributions of uncertain parameters are usually difficult to determine. In order to deal with this issue, the major contribution in this paper is to propose a new type of type-2 fuzzy variable called level interval type-2 fuzzy variable from the perspective of level-sets, which is a useful tool in modeling distribution uncertainty. With our level interval type-2 fuzzy variable, we give a method for constructing a parametric level interval (PLI) type-2 fuzzy variable from a nominal possibility distribution by introducing the horizontal perturbation parameters. The proposed horizontal perturbation around the nominal distribution is different from the vertical perturbation discussed in the literature. In order to facilitate the modeling in practical decision-making problems, for a level interval type-2 fuzzy variable, we define its selection variable whose distribution can be determined via its level-sets. The numerical characteristics like expected value and second order moments are important indices in practical optimization and decision-making problems. With this consideration, we establish the analytical expressions about the expected values and second order moments of the selection variables of PLI type-2 trapezoidal, normal and log-normal fuzzy variables. Furthermore, in order to derive the analytical expressions about the numerical characteristics of the selection variable for the sums of the common PLI type-2 fuzzy variables, we discuss the arithmetic about the sums of common PLI type-2 fuzzy variables. Finally, we apply the proposed optimization method to a pricing decision problem to demonstrate the efficiency of our new method. The computational results show that even a small perturbation of the nominal possibility distribution can affect the quality of solutions.

Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets

Yager has proposed the decision making under measure-based granular uncertainty, which can make decision with the aid of Choquet integral, measure and representative payoffs. The decision making under measure-based granular uncertainty is an effective tool to deal with uncertain issues. The intuitionistic fuzzy environment is the more real environment. Since the decision making under measure-based granular uncertainty is not based on intuitionistic fuzzy environment, it cannot effectively solve the decision issues in the intuitionistic fuzzy environment. Then, when the issues of decision making are under intuitionistic fuzzy environment, what is the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets is still an open issue. To deal with this kind of issues, this paper proposes the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. The decision making under measure-based granular uncertainty with intuitionistic fuzzy sets can effectively solve the decision making issues in the intuitionistic fuzzy environment, in other words, it can extend the decision making under measure-based granular uncertainty to the intuitionistic fuzzy environment. Numerical examples are applied to verify the validity of the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. The experimental results demonstrate that the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets can represent the objects successfully and make decision effectively. In addition, a practical application of applied intelligence is used to compare the performance between the proposed model and the decision making under measure-based granular uncertainty. The experimental results show that the proposed model can solve some decision problems that the decision making under measure-based granular uncertainty cannot solve.

Solving fuzzy multi-objective shortest path problem based on data envelopment analysis approach

The shortest path problem (SPP) is a special network structured linear programming problem that appears in a wide range of applications. Classical SPPs consider only one objective in the networks while some or all of the multiple, conflicting and incommensurate objectives such as optimization of cost, profit, time, distance, risk, and quality of service may arise together in real-world applications. These types of SPPs are known as the multi-objective shortest path problem (MOSPP) and can be solved with the existing various approaches. This paper develops a Data Envelopment Analysis (DEA)-based approach to solve the MOSPP with fuzzy parameters (FMOSPP) to account for real situations where input–output data include uncertainty of triangular membership form. This approach to make a connection between the MOSPP and DEA is more flexible to deal with real practical applications. To this end, each arc in a FMOSPP is considered as a decision-making unit with multiple fuzzy inputs and outputs. Then two fuzzy efficiency scores are obtained corresponding to each arc. These fuzzy efficiency scores are combined to define a unique fuzzy relative efficiency. Hence, the FMOSPP is converted into a single objective Fuzzy Shortest Path Problem (FSPP) that can be solved using existing FSPP algorithms.

Modified Vogel’s approximation method for transportation problem under uncertain environment

The fuzzy transportation problem is a very popular, well-known optimization problem in the area of fuzzy set and system. In most of the cases, researchers use type 1 fuzzy set as the cost of the transportation problem. Type 1 fuzzy number is unable to handle the uncertainty due to the description of human perception. Interval type 2 fuzzy set is an extended version of type 1 fuzzy set which can handle this ambiguity. In this paper, the interval type 2 fuzzy set is used in a fuzzy transportation problem to represent the transportation cost, demand, and supply. We define this transportation problem as interval type 2 fuzzy transportation problems. The utility of this type of fuzzy set as costs in transportation problem and its application in different real-world scenarios are described in this paper. Here, we have modified the classical Vogel’s approximation method for solved this fuzzy transportation problem. To the best of our information, there exists no algorithm based on Vogel’s approximation method in the literature for fuzzy transportation problem with interval type 2 fuzzy set as transportation cost, demand, and supply. We have used two Numerical examples to describe the efficiency of the proposed algorithm.