Interval valued strict preference with Zadeh triples

Developing Fuzzy TOPSIS Method based on Interval-valued Fuzzy Sets

“…Grattan [10] had come to this conclusion that the presentation of a linguistic expression in the form of fuzzy sets is not enough for true decision making all the times. Later, Gorzaczany [11] and Turksen [12] have proposed the interval-valued fuzzy sets that can be used instead. Wang and Li [13] defined interval-valued fuzzy numbers and gave their extended operations.…”

“…This is mainly because human judgment and preference are often ambiguous and cannot be estimated with exact numerical values (Chen [ [58] for the CLINAID system, Gorzaczany [11] in approximate reasoning, Turksen [59] and [60]) in interval-valued logic and in preference modeling [12]. Based upon the definition of the interval-valued fuzzy set in 1986, an interval-valued fuzzy set A defined on (−∞, +∞) is given as: …”

A Survey of Interval‐Valued Fuzzy Sets

“…Approximate reasoning is, formally speaking, as Turksen says [110], the process or processes by which a possible imprecise conclusion is deduced from a collection of imprecise premises. In this section, we present a short review of the inference methods most commonly used in the literature when the imprecise premises and the imprecise conclusions are represented using IVFSs.…”

ارائه‌ی یک مدل ترکیبی از A‌n‌p فازی بازه‌یی، F‌m‌e‌a فازی بازه‌یی و T‌o‌p‌s‌i‌s فازی بازه‌یی برای انتخاب تأمین‌کنندگان تحت شرایط ریسک

“…}U; |HQ=N w |rN=O u}t -=D |xQ}HvR |=ylU}Q |@=} RQ= |= Q@ p=tDL= Q}F -=D T} QD=t C} Q}Ot |= Q@ K}LY OOa |R}Qxt=vQ@ pOt l} |RtQ w |R}Q@D [6] "OvOQm xO=iDU= T} wmQwm [7] "OvOQm x=Q= u}t -=D |xQ}HvR |=yxm@W |L=Q] QO u}t -=D |xQ}HvR lU} Q [8] "OvOQm xO=iDU= u}t -=D |xQ}HvR lU} Q |@=} RQ= |= Q@ FMEA VwQ R= u= Q=mty w xO=iDU= u}t -=D |xQ}HvR lU} Q |@=} RQ= |= Q@ |R=i AHP VwQ R= u= Q=mty w qovt [9] "OvOQm u=oOvvmu}t -=D ?=NDv= |xv}tR QO xOW s=Hv= C=ar=]t "2"2 u=oOvvmu}t -=D ?=NDv= 'OQ}o|t CQwY =yXN=W |QUm} |=v@tQ@ |Q}os}tYD "OQ}o CQwY XN=W |QUm} |=v@t Q@ O}=@ w &CU= |Q}os}tYD`wv l} R}v w |@=} RQ= |= Q@ = Q |}=yQ=}at xOvvmu}t -=D ?=NDv= xv}tR QO xOW s=Hv= C=ar=]t pt=W |rm Q=}at Q=yJ uwUm}O %p=Ft u=wvax@ 'OvDiQo Q_v QO u=oOvvmu}t -=D ?=NDv= |iQat u=oOvvmu}t -=D ?=NDv= |= Q@ |Dv=Q=o |=yCU=}U '|Q}PBp}wLDC}r@=k 'C}i}m 'Ct}k Q=}at xU |wQ u=WC=k}kLD QO u= Q=mty w ww=}r w u= Q=mty w =} R [10] [3] "Ovm ltm Q= Qk Q_v Ot |v=QL@ lU} Q |=yXN=W u}}aD w |Ov@x@DQ QO lU} Q |=yXN=W VwQ 'Ov=xDU@=w Qo}Om} x@ u=oOvvmu}t -=D lU} Q |=yXN=W xm =Hv; R= [1] "OQ}o|tv |Ov@x@DQ w |@=} RQ= |@ wNx@ = Q u=oOvvmu}t -=D |=ylU}Q Ov=wD|tv |DvU FMEA "Ovm|t x@re Xkv u}= Q@ 'ANP VwQ =@ VwQ u}= ? }mQD =@ |O=yvW}B pOt "Ovm QO p}rOx@ xm CU= xQ=}atOvJ |Q}os}tYD |=yl}vmD R= |m} T}UB=D VwQ |oO=U u}vJty '|ivt p;xO}= pL x= Q w C@Ft p;xO}= pL x= Q u=tRsy uDiQo Q_v T}UB=D VwQ [2] [17] 'xOWu=}@h}Q=aD|=v@tQ@ %OwW|t h} QaD u}vJ [14] "OvOwtv xO=iDU= lU} Q pt=wa x@ xHwD =@ |v=yH xOvvmu}t -=D ?=NDv= xrUt '|QDw}Bt=m C=a]k S=Dvwt CmQW l} u=oOvvmu}t -=D ?=NDv= w |@=} RQ= |= Q@ u= Q=mty w x=Q= u=oOvvmu}t -=D lU} Q |=yXN=W uDiQo Q_v QO =@ = Q |R=i ANP VwQ l} lU} Q \}=QW CLD u=oOvvmu}t -=D ?=NDv= w |@=} RQ= x@ u= Q=mty w =} R [15] "OvO=O pOt l} =yu; "OvDN=OQB u=oOvvmu}t -=D |D=}rta lU} Q pt=wa uDiQo Q_v QO =@ |R=i |=yxawtHt pOt w 9 FCM |R=i |DN=vW |=yxWkv R= |@}mQD pt=W ?=NDv= xv}tR QO ww w uJ [16] "OvOQm x=Q= u=oOvvmu}t -=D ?=NDv= xrUt pL |= Q@ u}= QO xm OvO=O x=Q= xOWKqY= FMEA pOt l} lU} Q \}=QW QO u=oOvvmu}t -=D R= nv=R w |r [1] "CU= xOW x@U=Lt AHP VwQ R= xO=iDU= =@ =yQ=}at uRw VwQ xO=iDU= |v=yH u}t -=D |xQ}HvR QO u=oOvvmu}t -=D lU} Q |@=} RQ= QO FMEA VwQ [3] "OvOQm |}xR=@ |R=i C}a]ksOa "3"2 xO=iDU= [18] uUmQ=D w [17] |vWrRQwo \UwD Q=@ u}rw= |= Q@ |R=i |=yxawtHt pOt u}= R= xO=iDU= |= Q@ |r}qO pOvt w l}vQ=m w [19] u= Q=mty w T}rvQwm u}vJty "OW |}=v=wD sOa Q@ |r}qO u}vJty w |v=@ R |=yQ}eDt C}a]ksOa Q@ x@re |= Q@ O=Oa= nv=w [20] "OvOQm x=Q= |v=@ R |=yQ}eDt C}a]ksOa Q@ x@re |= Q@ |rwtat |R=i O=Oa= =yu; x@ \w@Qt |[=} Q C=}rta w OvOQm x=Q= |}xR=@ |R=i O=Oa= |= Q@ = Q |i} Q=aD |r w O=Oa= xawtHt R= xO=iDU= =@ = Q T}UB=D pOt u= Q=mty w |v=}DW; [21] "OvO=O xaUwD = Q O=Oa= xO=iDU= =@ = Q Qwm}w VwQ u= Q=mty w |O}Lw …”