Journal of Fuzzy Logic and Modeling in Engineering - Volume 1, Issue 2, 2022

Introduction: In this study, the integrated methods Hesitant Fuzzy Analytic Hierarchy Process (HF-AHP), Fuzzy COmplex Proportional Assessment (F-COPRAS), and Fuzzy Technique for Order Performance to Ideal Solution (F-TOPSIS) were used for job evaluation studies in a food company.

Background: There has been a decline in employee performance in the company. Unfair wages and unequal workload were identified as the reasons for the failure. Therefore, it has been observed that the staff turnover rate in the company is quite high.

Objective: The objective is to determine a fair wage policy that will increase employee satisfaction by stratifying with job evaluation analysis between positions.

Methods: The experts of Human Resources Department determined eight competency evaluation criteria for job evaluation studies in the proposed approach. Based on their judgments on these criteria, the competencies were rated using a linguistic scale and the weighting values were calculated using the HF-AHP method. These values are inputs for the next stage. Employees were ranked using F-COPRAS and F-TOPSIS methods.

Results: This study showed that the integrated method can be an effective alternative solution approach for calculating the weighting values and ranking of competencies in job evaluation studies.

Conclusion: It has been shown that the use of the strata created as a result of this study is a great facilitator in determining employee pay policies.

Background: This work studies the single vehicle routing problem (VRP) with multi-shift and fuzzy uncertainty. In this case, a company perpetually exploits a vehicle to accomplish demand over a scheduling period of several work shifts. In our problem, a crew performs maintenance jobs at different locations. The working team operates in different shifts with a maximum duration but recurrently returns to the depot by the end of the shift to avoid overtime.

Methods: The objective is to minimize the number of shifts and the completion time (makespan). In addition, we analyze the influence of uncertainty in driving and processing times on the overtime avoidance constraint in shift duration. We develop an Artificial Immune Heuristic to determine optimal solutions considering both makespan and overtime avoidance. We implement a Pareto-based framework to evaluate the impact of uncertainty.

Results: We present several numerical case studies to examine the problem. In particular, we analyze different case study scenarios inferred from the environmental changes in travel and processing times observed in the Apulia region (SE Italy) during the COVID-19 lockdown periods that occurred in spring (started on March 9, 2020) and autumn (after November 6, 2020) of the year 2020.

Conclusion: The work program was revised as soon as the Italian COVID-19 restrictions were implemented in the spring and autumn of 2020 due to the changing environment. Our approach allowed for the rapid release of new robust maintenance programs. Results show significant improvements with the presented approach.

Background: Transport models have wide application areas in the real world and play an important role in reducing transportation costs, increasing service quality, etc. These models may have uncertain transportation costs and supply or demand capacities of the product. Hence, it would be effective to model the vagueness of customer demands, economic conditions, and technical or non-technical uncertainties because of uncontrollable factors. Therefore, we focus on developing a mathematical solution approach to the fuzzy transportation problems.

Objective: In this paper, an integrated approach is proposed for the solution of the fuzzy linear transportation problem that has fuzzy cost coefficients in the objective function. Since transportation problem is encountered frequently in the national and international environment, it is considered that proposing a new solution method to this problem will be useful.

Methods: Fuzzy cost coefficients are taken as trapezoidal fuzzy numbers due to their widespread use in the literature. Firstly, the fuzziness is removed by converting the original single objective fuzzy transportation problem into a crisp Multi-Objective Linear Programming Problem (MOLPP). After the classical payoff matrix is constructed, ratio matrices are obtained to scale the objectives. Then, an approach based on game theory is implemented to solve the MOLPP, which is handled as a zero-sum game.

Results: Creating different ratio matrices in the game theory part of the approach can generate compromise solutions for the decision-makers. To demonstrate the effectiveness of the proposed approach, two numerical examples from the literature are solved. While the same solution is obtained in one of the examples, a different compromise solution set is generated, which could be presented to the decision-maker in the other example.

Conclusion: In this paper, we developed a novel game theory-based approach to the fuzzy transportation problem. The proposed approach overcomes the non-linear structure due to the uncertainty in the cost coefficients. The greatest advantage of the proposed approach is that it can generate more than one optimal solution for the decision-maker.

Background: Retail management has evolved into a new business model with the development of online shopping habits. There may be significant differences between onsite service and online service in terms of customer expectations.

Introduction: In this study, companies providing online grocery services in Turkey are evaluated by examining the services they provide from the perspective of customers. Fuzzy Z numbers, which also add the reliability of linguistic assessments to the analysis, are used in order to better describe the uncertainty.

Methods: Fuzzy Z-analytic hierarchy method (FZ-AHP) is used to weight the decision criteria, and fuzzy Z-Grey relational analysis (FZ-GRA) method is used to find the best online market company.

Results: As a result of the analysis, it is revealed that the most important criteria for online grocery shopping are minimum order amount and brand diversity. The results are also compared with ordinary fuzzy methods.

Conclusion: The comparison of the methods used in the study shows that although the ranks of the criteria and alternatives are the same, using fuzzy Z linguistic scale results in a wider interval for the weights and the scores of the alternatives, which could change the ordering, especially in cases where criterion weights or alternative scores are very close to each other.

In this article, we develop new constructed methods with specific conditions. The first method is a generalization of convex combination using n fuzzy implications. The second method is a parameterization of Lukasiewicz implication in an Ordering Property (OP) fuzzy implication form. The innovation in this work is the presentation of three new constructed methods of (OP) polynomial and (OP) rational fuzzy implications. We investigate some families of Ordering Property (OP) and Ordering Property (OP) Rational fuzzy implications. To these methods, we give some coefficient conditions in order to satisfy basic properties like ordering property (OP), identity property (IP) and contrapositive symmetry (CP).

Background: Fuzzy implication functions are one of the main operations in fuzzy logic. They generalize the classical implication, which takes values in the set {0, 1}, to fuzzy logic, where the truth values belong to the unit interval [0, 1]. The study of this class of operations has been extensively developed in the literature in the last 30 years from both theoretical and applicational points of view.

Introduction: In this paper, we develop five new methods for constructing fuzzy implications with specific properties. The paper starts by presenting the first fuzzy implication construction machine that uses n fuzzy implications with specific conditions. Next, we parameterize Lukasiewicz implication and create new families of (OP) polynomial and (OP) rational implications. For each method we investigate which conditions are satisfied and we give some examples.

Methods: The first constructed method uses n fuzzy implications in a linear product representation. The second method is an (OP) polynomial implication a parameterized Lukasiewicz implication. The third method is a rational implication with five parameters. In the fourth method we give a general form in the previous method by changing variables x and y with increasing functions. Finally, the last method is another (OP) rational implication with three parameters.

Results: In each method we present the properties that are satisfied. We generalize the (OP) polynomial and rational by replacing the variables with monotonic functions or add powers on them. Finally, we generalize and we give examples of new produced fuzzy implications.

Conclusion: As a future work, we can create new families of rational implications by changing the polynomials of the numerator and denominator so that they satisfy more properties. Finally, the new methods we presented can contribute in the construction of uninorms and copulas under certain conditions.

Introduction: Tech startups are fast-growing businesses that target the demands of the marketplace by developing innovative products, services, or platforms. Startups ensure socially, economically, or environmentally more effective alternatives by using or by creating appropriate technologies. Many factors have become prominent regarding the success and sustainability of the product or service offered by the startup: investment, experience, and education of the team, the leadership of the management, creativity, innovation, technological breakthroughs, surrounding community, future perspective, target marketing strategy, location and the analysis of the market, etc. But since 80% of startups do not survive after five years, defining the important risk factors is crucial to develop the right strategies for successful startups. In this study, the risk factors have been defined based on the business model, which has an important place in the success of the technology startups, which use technology intensively. Comprehensive risk analysis on identified factors is presented to identify effective managerial strategies for technology startups to not fail.

Methods: Spherical Fuzzy Failure Mode and Impact Analysis (SFFMEA) was used within the framework of a business model canvas for risk analysis for the failure of technology startup projects. Due to the lack of recorded data for analysis, the opinions of field experts were used. While the business model canvas guided the identification of detailed risk factors, FMEA enabled the risk analysis of factors that cause startup projects to fail, and considering parameters related to the probability of the relevant risk factors, their impact on the failure of the project, and the detection level of the risk factor. Spherical Fuzzy, on the other hand, allowed the quantitative inference of FMEA's comprehensive parameter definitions associated with the risk factors through experts. Thus, all risk factors that may cause the failure of tech startups were ranked according to their risk priority numbers (RPNs), with the SFFMEA analysis, which offers a comprehensive risk analysis.

Results: The findings show that the most important causes of the tech startup’s failure are “non-compliance with existing restrictions”, “inappropriate venture capital strategy”, and “lack of clustering support”.

Conclusion: These failure modes can be interpreted according to their frequency of encounter, potential effects, and detectability, and can be considered an important finding in the development of appropriate managerial strategies for the mitigation of the risk factors so the startups can survive in their first five years. Also, with the proposed risk analysis methodology, a comprehensive analysis of any startup project can be performed according to its conditions and characteristics.

Aims: This article deals with a new decision-making process under a neutrosophic fuzzy environment. First of all, we develop various types of neutrosophic set by means of neutrosophic cones. In fact, this set has been developed from the general equation of second degree in the field of classical geometry. Considering the neutrosophic components “true membership”, the “falsity membership” and the “indeterminacy” as the three variables of three-dimensional rectangular axes we develop various types of cones like structures of the traditional neutrosophic set and hence a new defuzzification method.

Background: Fuzzy set has some limitations in its domain [0,1] to describe real-life decision-making problems. The problem of difficulties lies in the variation of lower and upper bound and also the single valued logic (membership function only) systems. In reality, three valued logics (membership function, non-membership function and indeterminacy) have been established in the name of Neutrosophic logic/sets, and two valued logics (membership and non-membership functions) have developed in the name of Intuitionistic fuzzy logic/sets. In three valued logic system, the concepts of negation are now a growing subject of any group decision making problems. However, to draw a clear estimation of a neutrosophic decision has not yet been studied by modern researchers.

Objective: Various kinds of new establishments of the Neutrosophic set have been studied from the algebraic point of view, along with some polynomial structures. We have seen that; no finite geometric structures have been developed yet to qualify the real-world problems.

Methods: We consider the three components of a neutrosophic set as the variables of three-dimensional geometry. Since, the decisions are compact and constructive, we may consider the convex neutrosophic cone for analyzing single/ multiple group decision making problems.

Results: Various definitions are made over the cone- fundamentals using non-standard neutrosophic set in the domain [−1,1] x [−1,1] x [−1,1]. Then, we studied the constructions of several expressions/functions of neutrosophic cones, such as reciprocal cone, and enveloping cone via a novel thinking process. Then using some examples, we have developed a new ranking method along with their geometric structures exclusively.

Conclusion: In this changing world, the nature of decision-making behaviors is also changing rapidly. So, the need of establishing new concepts is an emerging area of research. However, more attention is required in discussing such vital issues in near future. The proposed approach may be applied to the decision-making problems of global issues also.