Pythagorean Membership Grade Aggregation Operators: Application in Financial Knowledge

This paper presents the Pythagorean membership grade induced ordered weighted moving average (PMGIOWMA) operator with some particular cases and theorems. The main advantage of this new operator is that can include the knowledge, expectation, and aptitude of the decision maker into the Pythagorean membership function by using a weighting vector and induced variables. An application in financial knowledge based on a survey conducted in 13 provinces in Boyacá, Colombia, is presented.

Interval Valued T-Spherical Fuzzy Information Aggregation Based on Dombi t-Norm and Dombi t-Conorm for Multi-Attribute Decision Making Problems

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives.

A novel approach to optimize the production cost of railway coaches of India using situational-based composite triangular and trapezoidal fuzzy LPP models

This article offers a comparative study of maximizing and modelling production costs by means of composite triangular fuzzy and trapezoidal FLPP. It also outlines five different scenarios of instability and has developed realistic models to minimize production costs. Herein, the first attempt is made to examine the credibility of optimized cost via two different composite FLP models, and the results were compared with its extension, i.e., the trapezoidal FLP model. To validate the models with real-time phenomena, the Production cost data of Rail Coach Factory (RCF) Kapurthala has been taken. The lower, static, and upper bounds have been computed for each situation, and then systems of optimized FLP are constructed. The credibility of each model of composite-triangular and trapezoidal FLP concerning all situations has been obtained, and using this membership grade, the minimum and the greatest minimum costs have been illustrated. The performance of each composite-triangular FLP model was compared to trapezoidal FLP models, and the intense effects of trapezoidal on composite fuzzy LPP models are investigated.

Cubic M-polar Fuzzy Hybrid Aggregation Operators with Dombi’s T-norm and T-conorm with Application

A cubic m-polar fuzzy set (CmPFS) is a new hybrid extension of cubic set (CS) and m-polar fuzzy set (mPFS). A CS comprises two parts; one part consists of a fuzzy interval (may sometimes be a fuzzy number) acting as membership grade (MG), and the second part consists of a fuzzy number acting as non-membership grade (NMG). An mPFS assigns m number of MGs against each alternative in the universe of discourse. A CmPFS deals with single as well as multi-polar information in the cubic environment. In this article, we explore some new aspects and consequences of the CmPFS. We define score and accuracy functions to find the priorities of alternatives/objects in multi-criteria decision-making (MCDM). For this objective, some new operations, like addition, scalar/usual multiplication, and power, are defined under Dombi’s t-norm and t-conorm. We develop several new aggregation operators (AOs) using cubic m-polar fuzzy Dombi’s t-norm and t-conorm. We present certain properties of suggested operators like monotonicity, commutativity, idempotency, and boundedness. Additionally, to discuss the application of these AOs, we present an advanced superiority and inferiority ranking (SIR) technique to deal with the problem of conversion from a linear economy to a circular economy. Moreover, a comparison analysis of proposed methodology with some other existing methods is also given.

Power Aggregation Operators and VIKOR Methods for Complex q-Rung Orthopair Fuzzy Sets and Their Applications

The aim of this paper is to present the novel concept of Complex q-rung orthopair fuzzy set (Cq-ROFS) which is a useful tool to cope with unresolved and complicated information. It is characterized by a complex-valued membership grade and a complex-valued non-membership grade, the distinction of which is that the sum of q-powers of the real parts (imaginary parts) of the membership and non-membership grades is less than or equal to one. To explore the study, we present some basic operational laws, score and accuracy functions and investigate their properties. Further, to aggregate the given information of Cq-ROFS, we present several weighted averaging and geometric power aggregation operators named as complex q-rung orthopair fuzzy (Cq-ROF) power averaging operator, Cq-ROF power geometric operator, Cq-ROF power weighted averaging operator, Cq-ROF power weighted geometric operator, Cq-ROF hybrid averaging operator and Cq-ROF power hybrid geometric operator. Properties and special cases of the proposed approaches are discussed in detail. Moreover, the VIKOR (“VIseKriterijumska Optimizacija I Kompromisno Resenje”) method for Cq-ROFSs is introduced and its aspects discussed. Furthermore, the above mentioned approaches apply to multi-attribute decision-making problems and VIKOR methods, in which experts state their preferences in the Cq-ROF environment to demonstrate the feasibility, reliability and effectiveness of the proposed approaches. Finally, the proposed approach is compared with existing methods through numerical examples.

Multi-Criteria Decision-Making Approach Based on Moderator Intuitionistic Fuzzy Hybrid Aggregation Operators

It has been seen in literature that the notion of intuitionistic fuzzy sets (IFSs) is very powerful tool to deal with real life problems under the environment of uncertainty. This notion of IFSs favours the intermingling of the uncertainty index in membership functions. The uncertainty index is basically generated from a lot of parameters such as lack of awareness, historical information, situation, short of standard terminologies, etc. Hence, the uncertainty index appended finding the membership grade under IFSs needs additional enhancement. Then, the concept of a moderator intuitionistic fuzzy set (MIFS) is defined by adding a parameter in the IFSs environment to make the uncertain behaviour more accurate. In this chapter, some new moderator intuitionistic fuzzy hybrid aggregation operators are presented on the basis of averaging and geometric point of views to aggregate moderator intuitionistic fuzzy information. Then, a multi-criteria decision-making (MCDM) approach is provided and successfully implemented to real-life problems of candidate selection.

A parts supplier selection framework of mechanical manufacturing enterprise based on D-S evidence theory

Parts supplier selection (PSS) is an important part of supply chain management of manufacturing enterprise. In the PSS process, the values of evaluation indicators are often uncertain and incomplete and the importance degrees of evaluation indicators are often instable. To solve this problem, a PSS framework of manufacturing enterprise based on D-S evidence theory is proposed. The indicator system for PSS is established, and the indicators are divided into three categories: quantitative, comprehensive qualitative and direct qualitative. The initial indicator values are processed by membership grade method to obtain the tendency degree. A two-order weighted D-S evidence theory model is constructed to evaluate the screened candidate suppliers. A manufacturing enterprise application case is given finally to illustrate the correctness and feasibility of the proposed framework.

Fuzzy Logic Based Approach for Power System Fault Section Analysis

In this chapter, a fuzzy expert system is developed to assist the operators in fault detection. It requires much less memory to store the database (power system topology and the post fault status of circuit breakers and protective relays). The fuzzy expert system identifies two basic network section sets, Shealthy for the healthy sub network and Sisland for the fault islands, using the post fault status of circuit breakers and relays. It then calculates membership function for each possible fault section. The objective of this calculation is to determine the likelihood of each candidate fault section as the actual fault section. Moreover membership functions provide a convenient means of ranking among possible (or candidate) fault sections, and are the most important factors in decision making. During decision making, the most possible fault section is determined by maximum selection method. In this method most possible fault section is the one which is having highest membership grade. MATLAB code for the proposed scheme is developed and the results obtained in four cases for a power- system network.