Transportation Problem for Interval-Valued Trapezoidal Intuitionistic Fuzzy Numbers

Abstract

The aim of the decision-makers in the transportation industry is to maximize profit by minimizing the transportation cost. The transportation structure is the center of economic activity in the business logistics system. However, transportation costs may vary owing to various unpredictable factors. In this study, cost of the transporting unit is considered as an interval-valued trapezoidal intuitionistic fuzzy number to deal with these uncertainties. The transportation problem with interval-valued trapezoidal intuitionistic fuzzy cost is discussed here, and the costs are ordered by score and score expected functions. As a special case, the interval-valued trapezoidal intuitionistic cost is not converted into crisp numbers to solve the transportation problem and derive the initial basic feasible (IBF) solution through interval-valued intuitionistic costs. Furthermore, the optimality of the derived initial basic feasible solution is checked using the modified distribution (MODI) method. The effectiveness and validation of the developed approach were illustrated using numerical examples.

Research on Fuzzy Evaluation of Village Officials Based on Triangular Multiplication Preference Relationship Theory

“…No matter the evaluation method, one thing remains unchanged: using different evaluation methods for the same data must maintain the same order. We applied the fuzzy evaluation method for village officials in this article, compared it with the Dhanasekar, Rani, and Annamalai's [19] and Akram and Ashraf's [18] methods, and obtained consistent conclusions. The specific method data is shown in Figure 4: both methods maintain consistency.…”

“…Akram and Ashraf [18] utilize spherical fuzzy rough numbers to incorporate decision-makers' judgments on the importance of standards and the potential of alternative solutions and propose an AHP-TOPSIS technique based on integral spherical fuzzy rough numbers, which has become an effective method for dealing with uncertainty and subjectivity in group decision-making environments. Dhanasekar, Rani, and Annamalai [19] regard the cost of transportation units as a trapezoidal intuitionistic fuzzy number (TRIFN) in the transportation industry and use fractions and fractional expectation functions to rank the costs effectively, solving the problem of incomplete and uncertain information. Kumar [20,21] proposed that blurring is a process of converting fuzzy sets or numbers into clear values or numbers.…”

Fuzzy model multi-attribute decision-making under information systems

“…In the 1970s, American scholars proposed the hierarchical analysis method [2] , which compares the advantages and disadvantages of each attribute at each level to select a solution. Entropy-TOPSIS method [3][4] is the most widely used multi-attribute decision evaluation method is widely used in industry, agriculture, and other fields. However, the actual decision-making process has many reference elements and much information is fuzzy, i.e.…”

Multi-attribute fuzzy pattern decision making based on information systems

“…A retrospective glance into the 1970s unfurls the inception of the hierarchical analysis method 9 , a pivotal approach that methodically juxtaposes attribute merits and demerits across each tier to judiciously select a solution. Meanwhile, the entropy–TOPSIS method 10 , 11 stands as a preeminent paradigm for multi-attribute decision assessment, enjoying wide-ranging applications across diverse industrial and agricultural spheres. Nonetheless, the actual domain of decision-making is characterized by a plethora of reference points and the enigma of pervasive fuzziness, compelling the expeditious assimilation of fuzzy sets 12 and rough sets 13 within the precincts of decision science.…”