International Journal of Fuzzy Computation and Modelling (4 papers in press)

Regular Issues

• Multiobjective Fractional Nonlinear Programming Problems under Pentagonal Intuitionistic Fuzzy environment  
  by Deepanjali Sahoo, Arun Tripathy, Jitendra Kumar Pati 
  Abstract: In this paper, a new linear ranking function is introduced to defuzzify the pentagonal intuitionistic fuzzy numbers. Then an intuitionistic fuzzy multiobjective fractional nonlinear programming problem (IFMOFNLPP) is formulated in which, the cost coefficient of objective functions and constraints and the right hand side constants of the constraints are considered as pentagonal intuitionistic fuzzy numbers. Authors have introduced the process of defuzzification and concept of linearisation to convert the suggested problem (IFMOFNLPP) into intuitionistic fuzzy multi objective nonlinear programming problem (IFMONLPP) and then applied the concept of linear ranking to the resultant (IFMONLPP)which yields crisp multiobjective nonlinear programming problem (CMONLPP). Some theorems are established to validate the method. Then by using Zimmermans technique under suitable nonlinear membership functions,(CMONLPP)is reduced to a standard NLPP which can be easily solved by any NLPP algorithm or software. Numerical example is stated to illustrate the present procedure. A comparative study is done for different nonlinear membership functions.
  Keywords: ranking function; intuitionistic fuzzy multiobjective fractional nonlinear programming problems; efficient solution; nonlinear membership function; Zimmerman’s max-min technique.
  DOI: 10.1504/IJFCM.2023.10051886
   
  
• A fuzzy DEA approach for assessing efficiencies of the public sector banks in India  
  by Dipali Kumbhar, Hemant Umap 
  Abstract: Banks are one of the most significant economic sectors to the financial growth of each country. Certainly, each banks performance must be evaluated to determine the components that contribute to its profit or loss. This paper is an attempt to evaluate the efficiencies of the public sector banks in India using the data envelopment analysis (DEA) technique. Data from the bank, such as the number of staff, branches, deposits, fluctuates over the year, therefore these figures cannot be stated with 100% accuracy. It varies to some extent from its exact value. In this paper to tackle the impreciseness in the data, the classical DEA model is extended to a fuzzy DEA model by applying fuzzy set theory. Here, input and output data are represented by a trapezoidal membership function and defuzzified by using the function principle approach. In this paper 12 public sector banks in India are assessed for the year 20192020. The crisp and sensitivity analysis results are analysed, and benchmarks are established for output variables. This paper emphasises the economic significance of supporting higher efficiency among public sector banks in India from a strategic standpoint.
  Keywords: DEA; data envelopment analysis; bank performance; fuzzy data; trapezoidal membership function; function principle.
  DOI: 10.1504/IJFCM.2023.10057941
   
  
• Estimation of the fractal dimension of the fuzzy-fractional Riemann-Liouville integral of a fuzzy-number-valued function  
  by M. Priya, R. Uthayakumar 
  Abstract: Continuity, boundedness, symmetry, periodicity and bounded variation are considered some of the basic analytical attributes of a function in which these properties of the function can be capable of handling a wide amount of real-life phenomena. Among them the properties, continuity, boundedness and bounded variation get gorgeous attention for examining some special features of a function. This paper analyses some of the characterisitcs for the fuzzy-fractional RiemannLiouville integral (FFRLI) of a fuzzy-number-valued function (FNVF) of a real variable. Applying the exhibited properties it has been appraised that the graph of the fuzzy-fractional Riemann-Liouville integral of a FNVF has the fractal dimension 1. Subsequently, we proved the semigroup property of the FFRLI of a FNVF and using a connection representing the relation of the non-integer order of the FFRLI and its upper box dimension, we brought up an inequality showing the lower and the upper bound of the Hausdorff dimension and upper box dimension when the order of the FFRLI lies above one. Conclusively we exhibited that the graph of the FFRLI of a FNVF contains the fractal dimension nearly 1.
  Keywords: FFRLI; fuzzy-fractional Riemann-Liouville integral; FNVF; fuzzy-number-valued function; box dimension; Hausdorff dimension; semigroup property; fractal dimension.
  DOI: 10.1504/IJFCM.2024.10063375
   
  
• Approximate reasoning and fuzzy linear programming  
  by Arpita Kabiraj, Prasun Kumar Nayak, Swapan Raha 
  Abstract: This research attempts to find a satisfactory solution for a fuzzy linear programming problem (FLPP) without directly transforming it to a crisp one at the structural level so as to provide more flexibility to the decision maker. We propose to find a near optimal satisfactory solution starting with an initial feasible solution from an approximate feasible region and improve it further in an iterative way. It is based on sup min convolution of the constraints and objective function as available in the approximate reasoning methodology. An illustrative example has been considered to show the effectiveness of our proposal. Finally, we compare our result with results of other existing fuzzy as well as intuitionistic fuzzy techniques for solving the same problem and some interesting results are presented. It has also been observed that whatever be the choice of logical operators, we can obtain satisfactory solution for all following our technique and are found to be close to each other.
  Keywords: approximate reasoning; CRI; compositional rule of inference; fuzzy logic; FLPP; fuzzy linear programming problem.
  DOI: 10.1504/IJFCM.2024.10067541