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Purpose The wider possibility of connectivity offers additional opportunities for customers to experience value propositions. The online world is only one side of the customer experience. The integration of digital technologies, social presence and physical elements increases the complexity of customer journey. This paper aims to map the phygital customer journey by focusing on millennials. Design/methodology/approach The study adopted a qualitative methodology to investigate 50 millennials from Italy. Millennials had to describe, in two phases, a journey they had recently made. First, they used sticky notes with no restrictions on expressing their feelings and structuring their CJ. Second, customers transferred the sticky notes’ contents, consider the information provided and map the journey with additional details using the Uxpressia software. Findings This paper frames the Millennials customer journey as a cycle of four moments: connect, explore, buy and use. Each moment enacts the customer experience as a mixture of emotional, behavioural and social responses. Online and offline interactions blur the boundaries between the physical and digital world (i.e. phygital): millennials move back-and-forth or jump from one action to another according to the evolving path of emotions and interactions. Originality/value The phygital customer journey provides an alternative understanding of customer journey occurring as a fuzzy process or loop. A phygital map develops as a circular path of moments seen as phenomenological microworlds of events, interactions, relationships and emotions.

Process capability indices are numerical tools that quantify how well a process can meet customer requirements, specifications or engineering tolerances. Fuzzy logic is incorporated to deal imprecise, incomplete data along with uncertainty. This paper develops two fuzzy methods for measuring the process capability in simple linear profiles for the circumstances in which lower and upper specification limits are imprecise. To guide practitioners, numerical example is provided.

The present study has been conducted to identify the relationship between Risk Priority Number (RPN) parameters in the Fuzzy Process Failure Mode and Effect Analysis (PFMEA) and Overall Equipment Effectiveness (OEE) in the production process. Initially, the production process map was drawn up according to the IDEF0 standard. The OEE rate was then extracted over a two-month period at one-week intervals as a pre-test. In the next phase, the types of potential failures in the production process were identified and the three parameters of the severity of the failures, probability of occurrence and probability of failure detection for each failure state were extracted in the linguistic variable. Afterward, the Risk Priority Number of each failure was determined by the defuzzification of triangular fuzzy numbers. Furthermore, considering the causes of failures, solutions for the elimination or reduction of the effects of prioritized failures were identified and implemented. The OEE was calculated as a post-test at weekly intervals over the next two months of career time to test the effectiveness of the measures taken, which resulted in a 6.05% increase in OEE indicating the effectiveness of interventions. Finally, in order to study the effect of reducing fuzzy RPN on OEE, the values of the corresponding parameters were extracted weekly over a two-month period and their correlation was tested in the form of 16 hypotheses. The results of the research showed a negative correlation between all the parameters.

Different methods of processing fuzzy information exist. We note, as instance, the Sugeno method (Takagi, and Sugeno (IEEE Trans Syst Man Cyb 15:116–132, 1985)) which allows to simplify the calculations based on an aggregation of the information, in the purpose of obtaining an interpretable solution. This method is often used in real time applications where the problem of computational time arises. Another regularly used one is the Mamdani approach shown in Mamdani and Assilian (Int J Man-Mach Stud 7:1–13, 1975). This one will be developed in this chapter. The Mamdani fuzzy process, also called the Mamdani fuzzy inference system or the fuzzy logic system (FLS), consists of three main steps: fuzzification, IF-THEN rules, and defuzzification.

This study has developed an approach to statistical process control indices for imprecise observations induced from an arbitrary population. For this purpose, most popular non-normal process capability index was extended based on a proposed triangular fuzzy distance between fuzzy numbers. The specific limits and targets are also considered as fuzzy numbers in this method. The order between the proposed fuzzy process capability indices was also investigated. A degree of belonging was proposed to verify the degree of process conditions of the proposed fuzzy process capability indices. The feasibility and effectiveness of the proposed method were also examined using a simulation study.

Process capability indices are used to evaluate the performance of the manufacturing process. When the specification limits and the target value are not precise, the authors cannot use the traditional methods to assess the capability of the process. For the processes with asymmetric tolerance intervals, some fuzzy process capability indices have been introduced such as and . In some cases, these indices may fail to account the process performance. To overcome the problem with them, the authors propose two new fuzzy indices in the case that the specification limits and the target value are fuzzy while the data are crisp. Also, the authors present an application example to demonstrate effectiveness and performance of the proposed indices.

Multi-dimensional Fuzzy differential equations driven by multi-dimen-sional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differential equations. The multi-dimensional fuzzy Taylor expansion is given, based on this expansion, a numerical method which is designed for giving the solution of multi-dimensional fuzzy differential equation via multi-dimensional Euler method will be presented, and its local convergence also will be discussed.

It is shown that an aspect of the process of individuation may be thought of as a fuzzy set. The process of individuation has been interpreted as a two-valued problem in the history of philosophy. In this work, I intend to show that such a process in its psychosocial aspect is better understood in terms of a fuzzy set, characterized by a continuum membership function. According to this perspective, species and their members present different degrees of individuation. Such degrees are measured from the membership function of the psychosocial process of individuation. Thus, a social analysis is suggested by using this approach in human societies., 12 pages, 1 table. V2 with minor changes. Published in The Journal of Mathematical Sociology

Cyanobacteria blooms and toxins released from cyanobacteria, called cyanotoxins, have become a serious environmental issue because of their potential toxicity toward human health. Several conventional and advanced water treatment methods are available for degradation of cyanotoxins from surface water, but a cost-effective and efficient water treatment technique can greatly reduce the processing time and improve the quality of treated water. Selection of an optimum treatment technique for cyanotoxins degradation is a multi-criteria decision-making problem owing to the involvement of several conflicting criteria and constraints. In this paper, an integrated Fuzzy-ELECTRE model was proposed and its potential toward evaluation of different cyanotoxins removal techniques has been explored to select the most suitable technology. In this integrated model, criteria importance weights were determined by Fuzzy process, while the ranking of alternatives was performed using ELECTRE process. The result obtained from the model shows that ‘advanced oxidation by titanium dioxide $${({\rm TiO}_{2})}$$ ’ is the most suitable technology among all considered technology for the removal of cyanotoxins. The developed methodological approach was also used to rank the available treatment techniques within the main group of conventional and advanced oxidation methods (AOMs). The results clearly depict that ozonation and photocatalysis by $${{\rm TiO}_{2}}$$ are the best methods within the group of conventional and AOMs, respectively. The ability of the proposed model for providing complete and clear ranking of all considered alternatives confirms its potential for evaluation of cyanotoxins removal methods.

In this study we analyze an two-dimensional epidemiological model via fuzzy differential equation considering that the solution is an interactive fuzzy process. More particularly, we will consider the case where this process is linearly correlated.

While on the one hand therapists can count on a number of codified and standardized diagnostic procedures, on the other hand it is hard to believe that in their daily work therapists slavishly follow these standardized procedures. In a clinical assessment, the diagnosis seems to be the outcome of a naïve and fuzzy process that is strongly influenced by personal training, by, theoretical models, and by one's masters as well as the experience gained in the field. What happens inside the no man's land of the clinical encounter? Can we identify some landmarks in these "amoeboid" exploratory moves? This paper addresses diagnosis not only as a noun or name ("diagnosis"), but also as a verb ("diagnosing"), arguing that a diagnostic space opens up thanks to an oscillatory state of mind that emerges at the intersection of different ways of looking "through" the symptom.

Liu process is a special fuzzy process which plays an important role in the theory of fuzzy differential equations. This paper proposes the concept of reflected Liu process at the origin. Then some properties of this type of Liu process are deduced.

Operating system (Os) is the most essential software of the computer system,deprived ofit, the computer system is totally useless. It is the frontier for assessing relevant computer resources . It performance greatly enhances user overall objective across the system. Related literatures have try in different method s and techniques to measure the process matric performanceof the operating system but none has incorporated the use of genetic algorithm and fuzzy logicin their varied techniques which indeed isa novel approach. Extending the work of Michalis,this research focuses on measuring the process matrix performance of an operating system utilizing set of operating system criteria’s while fusing fuzzy logic to handle impreciseness and genetic for process optimization.

In traditional OD survey, too many manpower and material resources are consumed, but the life cycle of the data is shortening and survey cost is increasing. In tackling these questions, the paper put forward the theory of calculating flow of road segments by mobile navigation software, get all the traffic link flow in current city after fuzzy process, finally obtain estimate OD data. Analysis Nanchang main city zone, adopt STOCH algorithm, stochastic user equilibrium assignment and system optimum realize OD matrix estimation. The results of the example show that OD matrix estimation based on mobile navigation data has feasibility, which also large scale reduce the OD investigation cost at the same time improve the effectiveness of the OD data.

In this paper, a new approach to solve the fuzzy linear system of differential equations based on pseudo-inverse is presented. In this work, we discuss the minimal solution of a system of linear fuzzy differential equations such as $$A\dot{x}(t)=B\dot{x}(t)+Cx(t), x(0)=x_0$$ where A, B, and C are three real m × n matrices and the initial condition x 0 is described by a vector made up of n fuzzy numbers. In this paper, we investigated a necessary and sufficient conditions for the existence fuzzy derivative $$\dot{x}(t)$$ of a fuzzy process x(t) and a necessary and sufficient conditions for the minimal solution vector to be a fuzzy vector, given arbitrary input fuzzy vector x 0.

On-line tool wear condition monitoring is a significant area of research in automated machining process. This study concerns the development of an on-line tool wear condition monitoring system based on a fuzzy logic scheme. The feed motor current was measured and used as the input of a fuzzy process. Previously, most studies in this field have assumed the workpiece as rigid. However, in practice, cutting force causes the elastic deflection on workpiece and changes actual cutting depth. Therefore, due to coupling between actual depth of cut and feed motor current, the measured current values vary on cutting length according to workpiece elastic deflection pattern. This oscillation in current signal which is used as the input of monitoring system, can affect output results. Thus, in this study in order to achieve more accurate results, the workpiece clamping condition has been considered and through monitoring software a correction factor has been applied on outputs. Experimental results indicate that the proposed method can be reliable for practical applications of tool monitoring systems.

The index Cpmk is a well-known loss-based process capability index. It can reveal more information about the location of the process mean compared with other classic process capability indices. This index is also more sensitive than other capability indices to any deviations from process mean. When there are some uncertainties in observations, fuzzy logic can be employed to manage these uncertainties. There is some research on different fuzzy process capability indices and this paper is an extension of Tsai and Chen (2006), Chen, Lin, and Chen (2003) for the process capability index Cpmk of fuzzy numbers. In order to find the membership function of process capability index Cpmk, the α-cuts of the fuzzy observation were employed. An example of fuzzy process capability Cpmk calculator was illustrated and compared with other classic fuzzy process capability indices C ~ p , C ~ pl , C ~ pu , C ~ pk and C ~ pm . Results showed that fuzzy C ~ pmk has the advantages of both C ~ pk and C ~ pm . Since the index Cpmk is a more sensitive index compared with other classic indices, the fuzzy process capability index C ~ pmk can be a more sensitive fuzzy index compared with C ~ p , C ~ pl , C ~ pu , C ~ pk and C ~ pm .

This paper presents an actuarial model of life insurance for fuzzy markets based on Liu process. At first, some researches about an actuarial model of life insurance for stochastic market and concepts about fuzzy process have been reviewed. Then, an actuarial model of life insurance for fuzzy process is formulated.

The distributed integration of process planning and scheduling (DIPPS) aims to simultaneously arrange the two most important manufacturing stages, process planning and scheduling, in a distributed manufacturing environment. Meanwhile, considering its advantage corresponding to actual situation, the triangle fuzzy number (TFN) is adopted in DIPPS to represent the machine processing and transportation time. In order to solve this problem and obtain the optimal or near-optimal solution, an extended genetic algorithm (EGA) with innovative three-class encoding method, improved crossover, and mutation strategies is proposed. Furthermore, a local enhancement strategy featuring machine replacement and order exchange is also added to strengthen the local search capability on the basic process of genetic algorithm. Through the verification of experiment, EGA achieves satisfactory results all in a very short period of time and demonstrates its powerful performance in dealing with the distributed integration of fuzzy process planning and scheduling (DIFPPS).

As economic trade between Korea and China has been encouraged with the rapid growth of Chinese economy and port competition in Northeast Asia, Korean government is trying to promote development and consolidation of ports to cope with the lack of facilities. Thus, many projects for port development have been propelled including the enactment the 'Private investment promotion law for social overhead capital 1994.' However, there are still some unsettled issues since considerable part of risk is still allocated to the Government when it has to support the private businesses in these port investments whenever unexpected problems arise. Allocation of risk among the participants - in this case especially - is a very subtle issue, however, it was revealed that not many precedent researches were done on the subject. In my previous research, I classified and analyzed 4 principle risks i.e, construction, management, financial and social risk. This research investigates the reasonable allocation of the risks among the participants using the Hierarchial Fuzzy Process. In the result of analysis, responsibility of private party is the most important and it must put the responsibility before Government' roll concerned. Also, this research displayed and proposed the direction of management method on port development in a view of minimizing risk and maximizing initiative of a private party.

The recent paper by Parchami et al. [2] proposes an open problem: Let $\ \hat{\tilde{C\!}}_p = T\left {\frac{{a_u-c_l }} {{6s}},\frac{{b_u-b_l }} {{6s}},\frac{{c_u-a_l }} {{6s}}} \right\$ be a point estimate of fuzzy process capability index $\\tilde{C}_p\$ as definition of Parchami et al. [2], where $\ s = \sqrt {\frac{1}{{n-1}}\sum\limits_{i = 1}^n {\left {x_i-\bar x} \right^2}}\$. Is it true that: $\ \mathop {\lim }\limits_{n \to \infty } \left[ {\hat{\tilde{C\!}}_{p \otimes } \sqrt {\frac{{\chi _{n-1,\alpha /2}^2 }} {{n-1}}},\hat{\tilde{C\!}}_{p \otimes } \sqrt {\frac{{\chi _{n-1,1-\alpha /2}^2 }} {{n-1}}}} \right] = \left\{ {\hat{\tilde{C\!}}_p } \right\}?\$ We modify their open problem and prove that “$\ \mathop {\lim }\limits_{n \to \infty } \left[ {\hat{\tilde{C\!}}_{p \otimes } \sqrt {\frac{{\chi _{n-1,\alpha /2}^2 }} {{n-1}}},\hat{\tilde{C\!}}_{p \otimes } \sqrt {\frac{{\chi _{n-1,1-\alpha /2}^2 }} {{n-1}}} } \right] \cong \left\{ {\hat{\tilde{C\!}}_p } \right\}\$ {for large} n” is true.

A Port Authority system has been regarded as one of the efficient ways of port management. The Korean government is thus now planning to set up such a system into the Busan Port. Busan New Port is located in Kadok Island but divided Busan and Kyongnam administrative district, so complicated in the appropriate selection to Busan New Port Administration. The research method which was used in this study accounted for overlapping between attributes, and introduced the HFP( Hierarchical Fuzzy Process) method that can perform an operation.

Fuzzy process capability indices establish the relationship between the actual performance and the fuzzy specification limits, which are used to determine whether a production process is capable of producing items within fuzzy specification tolerance. In this chapter we test a fuzzy process capability index \( \tilde{C}_{p} \), where instead of precise quality we have two membership functions for specification limits. Also, we develop the operating characteristic (OC) curves for the fuzzy capability index in testing one sided and two sided hypotheses. Numerical examples are given to show the performance of the method.